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 : n006.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 14:43:24 EDT 2019 0.13/0.34 % CPUTime : 1.01/1.24 %----Proving TF0_NAR, FOF, or CNF 1.01/1.25 ------- cvc4-fof casc 27 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 180... 1.01/1.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 21.01/21.20 % SZS status Theorem for theBenchmark 21.01/21.20 % SZS output start Proof for theBenchmark 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) K_2)))) )) ) 21.01/21.20 ( skv_1 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2))) (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) K_2)))) ))) ) 21.01/21.20 ( skv_2 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((M1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (not (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_3 _let_4 v) _let_2)) (hAPP nat int (hAPP int _let_3 _let_4 w) _let_2)) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) M1)))))))) ) 21.01/21.20 ( skv_3 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((X_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_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 bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) X_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong s1) X_1) _let_2))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) Y_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong s1) Y_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) Y_1) _let_2))) (= (ti int X_1) (ti int Y_1))) )) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) X_1))))))) ) 21.01/21.20 ( skv_4 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((S_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_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 bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong s1) S_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) S_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) S_1))))))) ) 21.01/21.20 ( skv_5 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (times_times int))) (let ((_let_5 (fun nat int))) (let ((_let_6 (power_power int))) (not (= (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_5 _let_6 X_1) _let_3)) (hAPP nat int (hAPP int _let_5 _let_6 Y_1) _let_3))))))))))) ) 21.01/21.20 ( skv_6 skv_7 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) )) ) 21.01/21.20 ( skv_8 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ) 21.01/21.20 ( skv_9 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((X_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (= _let_0 (hAPP real real cos X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (= _let_0 (hAPP real real cos Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) Y_1))) (= X_1 Y_1)) )) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) X_1))))))) ) 21.01/21.20 ( skv_10 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) K_2)))) ))) ) 21.01/21.20 ( skv_11 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ) 21.01/21.20 ( skv_12 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((S_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) W_1))) _let_2))) (not (= (ti int W_1) (hAPP int int (hAPP int _let_0 (minus_minus int) y) (hAPP int int (hAPP int _let_0 _let_1 S_1) _let_2)))))))) ) 21.01/21.20 ( skv_13 skv_14 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2)))) ) 21.01/21.20 ( skv_15 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((S1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (fun int bool))) (let ((_let_3 (number_number_of int))) (not (hBOOL (hAPP int bool (hAPP int _let_2 (hAPP int (fun int _let_2) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) S1) (hAPP int nat (number_number_of nat) _let_1))) (hAPP int int _let_3 min)) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_3 (hAPP int int bit0 _let_1))) m)) (one_one int))))))))) ) 21.01/21.20 ( skv_16 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (not (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) )) ) 21.01/21.20 ( skv_17 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) K_2))) ))) ) 21.01/21.20 ( skv_18 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((R_1 $$unsorted) (V_3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) V_3))) _let_2))) (not (= (hAPP int int (hAPP int _let_0 (minus_minus int) x) (hAPP int int (hAPP int _let_0 _let_1 R_1) _let_2)) (ti int V_3))))))) ) 21.01/21.20 ( skv_19 skv_20 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((T_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (times_times int))) (not (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) _let_3))) _let_2) (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_3))) m)) _let_2)) T_4)))))))) ) 21.01/21.20 ( skv_21 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((P_1 $$unsorted)) (hBOOL P_1) ) 21.01/21.20 ( skv_22 ) 21.01/21.20 ) 21.01/21.20 (skolem (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (not (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_3 _let_4 X_1) _let_2)) (hAPP nat int (hAPP int _let_3 _let_4 Y_1) _let_2))))))))) ) 21.01/21.20 ( skv_23 skv_24 ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (= M (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) M)) N))) ) 21.01/21.20 ( (one_one nat), (one_one nat) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) Ma)) (hAPP int real (number_number_of real) Na))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Ma) (hAPP int int (number_number_of int) Na)))) ) 21.01/21.20 ( min, pls ) 21.01/21.20 ( (zero_zero int), pls ) 21.01/21.20 ( (zero_zero int), (hAPP int int bit1 pls) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((T_1 $$unsorted)) (comple44059174attice (filter T_1)) ) 21.01/21.20 ( nat ) 21.01/21.20 ( real ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real cos Xa)) (hAPP real real sin Xa)))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (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_0 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) Xa) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_3) _let_3))))))) ) 21.01/21.20 ( pi ) 21.01/21.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.20 ( (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)))) ) 21.01/21.20 ( (zero_zero real) ) 21.01/21.20 ( (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))))) ) 21.01/21.20 ( (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) ) 21.01/21.20 ( (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))))) ) 21.01/21.20 ( (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)))) ) 21.01/21.20 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.20 ( skv_10 ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min)) (hAPP real real cos X))) ) 21.01/21.20 ( pi ) 21.01/21.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.20 ( (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)))) ) 21.01/21.20 ( (zero_zero real) ) 21.01/21.20 ( (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))))) ) 21.01/21.20 ( (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) ) 21.01/21.20 ( (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))))) ) 21.01/21.20 ( (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)))) ) 21.01/21.20 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.20 ( skv_10 ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 Ya)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 Xa)))) (= (or (and (not _let_1) (not _let_2)) (and _let_2 _let_1)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Xa) Ya))))))) ) 21.01/21.20 ( (one_one nat), (one_one nat) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Xa $$unsorted) (A_3 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) Xa)) A_3)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) Xa) (hAPP int real (real_1 int) A_3)))) ) 21.01/21.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min))) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))))) ) 21.01/21.20 ( pls ) 21.01/21.20 ( (hAPP int int bit1 pls) ) 21.01/21.20 ( min ) 21.01/21.20 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.20 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((K $$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)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))))) ) 21.01/21.20 ( pls ) 21.01/21.20 ( (hAPP int int bit1 pls) ) 21.01/21.20 ( min ) 21.01/21.20 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.20 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat suc N)))) ) 21.01/21.20 ( (zero_zero nat) ) 21.01/21.20 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.20 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt Xa)) (hAPP real real sqrt Ya))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) Ya))))) ) 21.01/21.20 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.20 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) (hAPP nat nat suc Na))))) ) 21.01/21.20 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((M $$unsorted)) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) M)) ) 21.01/21.20 ( (hAPP int nat nat_1 t) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun real bool))) (= (or (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Xa) Ya)) (= Xa Ya)) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) Xa) Ya)))) ) 21.01/21.20 ( pi, (zero_zero real) ) 21.01/21.20 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.01/21.20 ( (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))) ) 21.01/21.20 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.20 ( (zero_zero real), pi ) 21.01/21.20 ( (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)))) ) 21.01/21.20 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.20 ( (zero_zero real), skv_2 ) 21.01/21.20 ( (zero_zero real), skv_9 ) 21.01/21.20 ( (zero_zero real), skv_10 ) 21.01/21.20 ( (zero_zero real), skv_11 ) 21.01/21.20 ( (zero_zero real), skv_12 ) 21.01/21.20 ( (zero_zero real), skv_15 ) 21.01/21.20 ( (zero_zero real), skv_18 ) 21.01/21.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.01/21.20 ( (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) ) 21.01/21.20 ( (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 ) 21.01/21.20 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.20 ) 21.01/21.20 (instantiation (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_0 (ti T A))) (= _let_0 (ti T _let_0))) ) 21.01/21.20 ( int, pls ) 21.01/21.20 ( int, min ) 21.01/21.20 ( int, s ) 21.01/21.20 ( int, s1 ) 21.01/21.20 ( int, m ) 21.01/21.20 ( int, t ) 21.01/21.20 ( int, v ) 21.01/21.20 ( int, w ) 21.01/21.20 ( int, y ) 21.01/21.20 ( int, sa ) 21.01/21.20 ( int, x ) 21.01/21.20 ( int, r ) 21.01/21.20 ( int, m1 ) 21.01/21.20 ( (fun int int), bit1 ) 21.01/21.20 ( (fun int int), bit0 ) 21.01/21.20 ( (fun int int), succ ) 21.01/21.20 ( (fun int int), pred ) 21.01/21.20 ( (fun int int), (fact_fact int) ) 21.01/21.20 ( (fun int int), zfact ) 21.01/21.20 ( nat, n ) 21.01/21.20 ( nat, tn ) 21.01/21.20 ( bool, fTrue ) 21.01/21.20 ( bool, fFalse ) 21.01/21.20 ( real, pi ) 21.01/21.20 ( (fun nat real), (real_1 nat) ) 21.01/21.20 ( (fun nat real), cos_coeff ) 21.01/21.20 ( (fun nat real), sin_coeff ) 21.01/21.20 ( (fun real real), sin ) 21.01/21.20 ( (fun real real), cos ) 21.01/21.20 ( (fun real real), sqrt ) 21.01/21.20 ( (fun real real), tan ) 21.01/21.20 ( (fun real real), ln ) 21.01/21.20 ( (fun real real), arctan ) 21.01/21.20 ( (fun real real), arcsin ) 21.01/21.20 ( (fun real real), arccos ) 21.01/21.20 ( (fun nat nat), suc ) 21.01/21.20 ( (fun nat nat), (fact_fact nat) ) 21.01/21.20 ( (fun nat nat), nat_size ) 21.01/21.20 ( (fun nat nat), (size_size nat) ) 21.01/21.20 ( (fun nat nat), fact ) 21.01/21.20 ( (filter nat), sequentially ) 21.01/21.20 ( (fun int (fun int rat)), fract ) 21.01/21.20 ( complex, ii ) 21.01/21.20 ( (fun int bool), zOdd ) 21.01/21.20 ( (fun int bool), zprime ) 21.01/21.20 ( (fun int bool), zEven ) 21.01/21.20 ( (fun int bool), nat_neg ) 21.01/21.20 ( (fun int bool), nat_is_nat ) 21.01/21.20 ( (fun int bool), (even_odd_even int) ) 21.01/21.20 ( (fun int bool), twoSqu1091635170sum2sq ) 21.01/21.20 ( (fun int (fun int int)), legacy_zgcd ) 21.01/21.20 ( (fun int (fun int int)), (gcd_gcd int) ) 21.01/21.20 ( (fun int (fun int int)), inv ) 21.01/21.20 ( (fun int (fun int int)), multInv ) 21.01/21.20 ( (fun int (fun int int)), legendre ) 21.01/21.20 ( (fun int (fun int int)), standardRes ) 21.01/21.20 ( (fun int (fun int int)), nat_tsub ) 21.01/21.20 ( (fun int (fun int int)), z3div ) 21.01/21.20 ( (fun int (fun int int)), z3mod ) 21.01/21.20 ( (fun int (fun int int)), int_lcm ) 21.01/21.20 ( (fun int (fun int int)), int_gcd ) 21.01/21.20 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.01/21.20 ( (fun bool bool), fNot ) 21.01/21.20 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.01/21.20 ( (fun bool (fun bool bool)), fconj ) 21.01/21.20 ( (fun bool (fun bool bool)), fdisj ) 21.01/21.20 ( (fun bool (fun bool bool)), fimplies ) 21.01/21.20 ( (fun int (fun int bool)), quadRes ) 21.01/21.20 ( (fun int (fun int bool)), d22set ) 21.01/21.20 ( (fun int (fun int bool)), norRRset ) 21.01/21.20 ( (fun int (fun int bool)), sRStar ) 21.01/21.20 ( (fun int (fun int bool)), sr ) 21.01/21.20 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.01/21.20 ( (fun nat bool), (even_odd_even nat) ) 21.01/21.20 ( (fun nat bool), prime ) 21.01/21.20 ( (fun real complex), cis ) 21.01/21.20 ( (fun nat (fun nat bool)), coprime ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.01/21.20 ( (fun (product_prod int int) bool), frac_1 ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.01/21.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.01/21.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.01/21.20 ( (fun (fun int bool) bool), nat_nat_set ) 21.01/21.20 ( (fun nat (fun real real)), root ) 21.01/21.20 ( (fun real (fun real real)), log ) 21.01/21.20 ( (fun real (fun real real)), powr ) 21.01/21.20 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.01/21.20 ( (fun complex complex), cnj ) 21.01/21.20 ( (fun complex complex), expi ) 21.01/21.20 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.01/21.20 ( (fun nat (fun nat nat)), nat_gcd ) 21.01/21.20 ( (fun nat (fun nat nat)), nat_lcm ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.01/21.20 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.01/21.20 ( (fun int (fun (fun int bool) bool)), resSet ) 21.01/21.20 ( (fun int nat), nat_1 ) 21.01/21.20 ( (fun int nat), phi ) 21.01/21.20 ( (fun complex real), re ) 21.01/21.20 ( (fun complex real), im ) 21.01/21.20 ( (fun complex real), arg ) 21.01/21.20 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.01/21.20 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.01/21.20 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.01/21.20 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.01/21.20 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.01/21.20 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.01/21.20 ( (fun (product_prod nat nat) bool), pred_nat ) 21.01/21.20 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.01/21.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.01/21.21 ( (fun (fun int bool) int), (the int) ) 21.01/21.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.01/21.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.01/21.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.01/21.21 ( (fun real (fun real complex)), rcis ) 21.01/21.21 ( (fun real (fun real complex)), complex_1 ) 21.01/21.21 ( (fun int (fun int (fun int bool))), zcong ) 21.01/21.21 ( (fun int (fun int (fun int bool))), wset ) 21.01/21.21 ( (fun int (fun int (fun int bool))), noXRRset ) 21.01/21.21 ( (fun int (fun int (fun int bool))), bnorRset ) 21.01/21.21 ( (fun int (fun int (fun int bool))), zcongm ) 21.01/21.21 ( (fun real nat), natceiling ) 21.01/21.21 ( (fun real nat), natfloor ) 21.01/21.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.01/21.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.01/21.21 ( (fun int real), (real_1 int) ) 21.01/21.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.01/21.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.01/21.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.01/21.21 ( (fun complex nat), (size_size complex) ) 21.01/21.21 ( (fun complex nat), complex_size ) 21.01/21.21 ( (fun (fun nat rat) bool), vanishes ) 21.01/21.21 ( (fun (product_prod int int) rat), frct ) 21.01/21.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.01/21.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.01/21.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.01/21.21 ( (fun rat real), ratreal ) 21.01/21.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.01/21.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.01/21.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.01/21.21 ( (fun rat (product_prod int int)), quotient_of ) 21.01/21.21 ( (fun int (fun nat nat)), nat_aux ) 21.01/21.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.01/21.21 ( (fun int (list int)), quickc666637781d_zero ) 21.01/21.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.01/21.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.01/21.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.01/21.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.01/21.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.01/21.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.01/21.21 ( (fun code_code_numeral int), code_int_of ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$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 Xa)) (hAPP real real sin Xa)))) (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)) Xa) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) _let_2)))))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (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 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (hBOOL (hAPP _let_0 bool (hAPP (fun X_a X_b) (fun _let_0 bool) (nat_tr1645093318rphism X_a X_b) F) A_2))) ) 21.01/21.21 ( int, nat, nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.21 ( nat, int, (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X $$unsorted)) (not (= (zero_zero real) (hAPP real real cos (hAPP real real arctan X)))) ) 21.01/21.21 ( (one_one real) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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))))) ) 21.01/21.21 ( (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)))))))))) ) 21.01/21.21 ) 21.01/21.21 (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))))) ) 21.01/21.21 ( pls, pls ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Na) 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 int real _let_0 Na)) (one_one real))) (hAPP int real _let_0 Ma))))) ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, min ) 21.01/21.21 ( min, (zero_zero int) ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (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))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Wa) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Wa) (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int)))))) ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, pls ) 21.01/21.21 ( min, min ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (zero_zero int), s ) 21.01/21.21 ( (zero_zero 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) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), skv_4 ) 21.01/21.21 ( (zero_zero int), skv_5 ) 21.01/21.21 ( 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) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 21.01/21.21 ( 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) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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) ) 21.01/21.21 ( skv_5, (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) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Z_1 $$unsorted)) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (semiring_1_of_nat int) Z_1))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( n ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$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) Na)) (ring_1_Ints real)))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((M $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) M))) ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$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) Xa))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Xa))))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( skv_2 ) 21.01/21.21 ( skv_9 ) 21.01/21.21 ( skv_12 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP int real (real_1 int) Na))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Na))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ( s ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( skv_4 ) 21.01/21.21 ( skv_5 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) min))) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP nat int (semiring_1_of_nat int) Na))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( n ) 21.01/21.21 ( tn ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$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)))) ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, pls ) 21.01/21.21 ( min, min ) 21.01/21.21 ( min, (zero_zero int) ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (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))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)))) (= (or (hBOOL (hAPP nat bool _let_0 Na)) (hBOOL (hAPP nat bool _let_0 Ma))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) Na))))) ) 21.01/21.21 ( (one_one nat), (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X))) (one_one real)))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (one_one real) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (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))))) ) 21.01/21.21 ( (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)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((A_3 $$unsorted) (Xa $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) A_3)) Xa)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_3) (hAPP real int (archimedean_ceiling real) Xa)))) ) 21.01/21.21 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (zero_zero int), pi ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (zero_zero int), skv_2 ) 21.01/21.21 ( (zero_zero int), skv_9 ) 21.01/21.21 ( (zero_zero int), skv_12 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int (hAPP int (fun int int) (plus_plus int) Wa) (one_one int))) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Wa) Z)))) ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, min ) 21.01/21.21 ( min, (zero_zero int) ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (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))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( 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))) ) 21.01/21.21 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc Ma)) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) Na)))) ) 21.01/21.21 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero nat), n ) 21.01/21.21 ( (zero_zero nat), tn ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) min)) (hAPP real real sin X))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$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)) pi))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((D_3 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D_3) (hAPP int int (abs_abs int) D_3))) ) 21.01/21.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( v ) 21.01/21.21 ( w ) 21.01/21.21 ( skv_14 ) 21.01/21.21 ( skv_20 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$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) min)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))))) ) 21.01/21.21 ( (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))))))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Na) (hAPP nat nat suc _let_0))) (= _let_0 Na))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real re X)) (hAPP complex real (norm_norm complex) X))) ) 21.01/21.21 ( (zero_zero complex) ) 21.01/21.21 ( ii ) 21.01/21.21 ( (one_one complex) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (list X_a))) (let ((_let_1 (size_size _let_0))) (= _let_1 (ti (fun _let_0 nat) _let_1)))) ) 21.01/21.21 ( int ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) Xa))) (= (not (hBOOL (hAPP _let_0 bool _let_1 zEven))) (hBOOL (hAPP _let_0 bool _let_1 zOdd))))) ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) pls))) (= (hBOOL (hAPP int bool _let_0 K)) (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$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))))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K)) (hAPP int int bit1 L))))) ) 21.01/21.21 ( pls, min ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, pls ) 21.01/21.21 ( min, min ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (zero_zero int), s ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), skv_4 ) 21.01/21.21 ( (zero_zero int), skv_5 ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ) 21.01/21.21 (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)))) ) 21.01/21.21 ( (hAPP nat int (hAPP 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)))) ) 21.01/21.21 ( (hAPP nat int (hAPP 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) ) 21.01/21.21 ( s1, s ) 21.01/21.21 ( s1, skv_4 ) 21.01/21.21 ( s1, skv_5 ) 21.01/21.21 ( (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) ) 21.01/21.21 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 21.01/21.21 ) 21.01/21.21 (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))))) ) 21.01/21.21 ( pls, min ) 21.01/21.21 ( pls, (zero_zero int) ) 21.01/21.21 ( (one_one int), (zero_zero int) ) 21.01/21.21 ( (one_one int), t ) 21.01/21.21 ( min, pls ) 21.01/21.21 ( min, min ) 21.01/21.21 ( min, (zero_zero int) ) 21.01/21.21 ( (zero_zero int), pls ) 21.01/21.21 ( (zero_zero int), (one_one int) ) 21.01/21.21 ( (zero_zero int), min ) 21.01/21.21 ( (zero_zero int), s ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero int), skv_4 ) 21.01/21.21 ( (zero_zero int), skv_5 ) 21.01/21.21 ( s, (zero_zero int) ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.01/21.21 ( t, (one_one int) ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( skv_4, (zero_zero int) ) 21.01/21.21 ( skv_5, (zero_zero int) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (not (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) J_2)) I_1))) ) 21.01/21.21 ( (one_one nat), (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) N))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted) (A_3 $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP real int (archim2085082626_floor real) Xa)) A_3)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Xa) (hAPP int real (real_1 int) A_3)))) ) 21.01/21.21 ( pi, (zero_zero int) ) 21.01/21.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 21.01/21.21 ( (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) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (fun real bool))) (let ((_let_5 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_4 (hAPP _let_1 (fun real _let_4) (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_0 real) (power_power real)) sin)) (hAPP int nat (number_number_of nat) _let_3))) Xa) (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) _let_3)) (hAPP real real cos Xa))) (hAPP real real sin Xa)))))))))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (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 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (hAPP nat real (real_1 nat) (hAPP real nat natceiling X)))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (one_one real) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (deriv real) arctan) Xa) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_0 (plus_plus real) (one_one real)) (hAPP nat real (hAPP real (fun nat real) (power_power real) Xa) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) min) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) pls))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (= N (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat suc N)) (one_one nat))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.21 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) Na)) (zero_zero real))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Na) (zero_zero int)))) ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Z_1 $$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) Z_1))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( n ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Na)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP int real (real_1 int) Na)))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) cos_coeff)) (hAPP real _let_0 (power_power real) Xa))) (hAPP real real cos Xa)))))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) min) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (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 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_4 (fun real bool))) (let ((_let_5 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_4 (hAPP _let_1 (fun real _let_4) (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_0 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) _let_3))) Xa) (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) _let_3)) (hAPP real real cos Xa))) (hAPP real real sin Xa))))))))))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (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 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (the _let_0))) (= _let_1 (ti (fun (fun _let_0 bool) _let_0) _let_1)))) ) 21.01/21.21 ( int, int ) 21.01/21.21 ( int, (product_prod int int) ) 21.01/21.21 ( nat, nat ) 21.01/21.21 ( real, real ) 21.01/21.21 ( (product_prod int int), (product_prod int int) ) 21.01/21.21 ( quickcheck_code_int, quickcheck_code_int ) 21.01/21.21 ( code_code_numeral, code_code_numeral ) 21.01/21.21 ( (product_prod nat nat), (product_prod nat nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat nat))) (let ((_let_4 (hAPP nat _let_3 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (let ((_let_5 (fun nat _let_2))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (fun real _let_2))) (let ((_let_9 (fun _let_0 _let_5))) (let ((_let_10 (combb real _let_2 nat))) (let ((_let_11 (fun _let_3 _let_0))) (let ((_let_12 (combb nat real nat))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 (hAPP _let_8 _let_9 _let_10 (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 (hAPP _let_8 _let_9 _let_10 (inverse_divide real)) (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)))) (hAPP _let_3 _let_0 (hAPP _let_0 _let_11 _let_12 (real_1 nat)) (hAPP _let_3 _let_3 (hAPP _let_3 (fun _let_3 _let_3) (combb nat nat nat) (fact_fact nat)) _let_4))))) (hAPP _let_3 _let_0 (hAPP _let_0 _let_11 _let_12 (hAPP real _let_0 _let_1 Xa)) _let_4))) (hAPP real real cos Xa)))))))))))))))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) min) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (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 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N))))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$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))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (= N (hAPP nat nat (size_size nat) N)) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) K) pls)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int bit1 K)) pls)))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ( s ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( t ) 21.01/21.21 ( m1 ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (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)))))) ) 21.01/21.21 ( (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))))))) ) 21.01/21.21 ( skv_4 ) 21.01/21.21 ( skv_5 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real (real_1 nat) N))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Z))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (zero_zero int) ) 21.01/21.21 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.21 ( t ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0)))))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (one_one real) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) Xa)) (hBOOL (hAPP nat bool (even_odd_even nat) Xa))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (complex_rec X_a))) (= _let_0 (ti (fun (fun real (fun real X_a)) (fun complex X_a)) _let_0))) ) 21.01/21.21 ( nat ) 21.01/21.21 ( bool ) 21.01/21.21 ( real ) 21.01/21.21 ( complex ) 21.01/21.21 ( (fun nat (product_prod real real)) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) pls) K)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) pls) (hAPP int int bit1 K))))) ) 21.01/21.21 ( pls ) 21.01/21.21 ( (hAPP int int bit1 pls) ) 21.01/21.21 ( (one_one int) ) 21.01/21.21 ( min ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.21 ( s ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.21 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.21 ( skv_4 ) 21.01/21.21 ( skv_5 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) Na))) (= (hBOOL (hAPP nat bool _let_0 Na)) (hBOOL (hAPP nat bool _let_0 Ma))))) ) 21.01/21.21 ( (one_one nat), (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((R_3 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_3) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_3))) (one_one real)))) ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (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)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) W) W)) ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( skv_10 ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$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) _let_1)) N)))) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((N $$unsorted)) (not (= N (hAPP nat nat suc N))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.21 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) Ma) Na)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_0 Ma)) (hAPP nat int _let_0 Na))))) ) 21.01/21.21 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.21 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (zero_zero nat), (one_one nat) ) 21.01/21.21 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) Xa) (hAPP nat nat suc (hAPP nat nat suc _let_0)))) (hBOOL (hAPP nat bool (even_odd_even nat) Xa)))) ) 21.01/21.21 ( (zero_zero nat) ) 21.01/21.21 ( (one_one nat) ) 21.01/21.21 ) 21.01/21.21 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) sin) Xa) (hAPP real real cos Xa)))) ) 21.01/21.21 ( pi ) 21.01/21.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.21 ( (zero_zero real) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.01/21.22 ( skv_10 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_3) (zero_zero int)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) A_3)))) ) 21.01/21.22 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((R_3 $$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_3) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_3)))) ) 21.01/21.22 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Xa) Ya)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 Xa)) (hAPP int real _let_0 Ya))))) ) 21.01/21.22 ( (one_one int), t ) 21.01/21.22 ( min, min ) 21.01/21.22 ( min, (zero_zero int) ) 21.01/21.22 ( (zero_zero int), pls ) 21.01/21.22 ( (zero_zero int), (one_one int) ) 21.01/21.22 ( (zero_zero int), min ) 21.01/21.22 ( (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))) ) 21.01/21.22 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (combi X_a))) (= _let_0 (ti (fun X_a X_a) _let_0))) ) 21.01/21.22 ( int ) 21.01/21.22 ( (fun int int) ) 21.01/21.22 ( nat ) 21.01/21.22 ( bool ) 21.01/21.22 ( real ) 21.01/21.22 ( (fun nat real) ) 21.01/21.22 ( (fun real real) ) 21.01/21.22 ( complex ) 21.01/21.22 ( (fun int bool) ) 21.01/21.22 ( (product_prod int int) ) 21.01/21.22 ( (fun (product_prod int int) int) ) 21.01/21.22 ( (fun int (fun int bool)) ) 21.01/21.22 ( (fun nat bool) ) 21.01/21.22 ( (fun (product_prod int int) bool) ) 21.01/21.22 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.01/21.22 ( (fun real bool) ) 21.01/21.22 ( code_code_numeral ) 21.01/21.22 ( (fun int (fun int (fun int bool))) ) 21.01/21.22 ( (fun int real) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Xa)) (not (hBOOL (hAPP int bool nat_neg Xa)))) ) 21.01/21.22 ( pls ) 21.01/21.22 ( (one_one int) ) 21.01/21.22 ( min ) 21.01/21.22 ( (zero_zero int) ) 21.01/21.22 ( s ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (hAPP int int (number_number_of int) min) ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( skv_4 ) 21.01/21.22 ( skv_5 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (ord_less nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) I) K)) J)) (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_2 I) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) J) K))))))) ) 21.01/21.22 ( (zero_zero nat), (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat fact N))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) Na)))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ( n ) 21.01/21.22 ( tn ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$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)))) (zero_zero int))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.22 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.22 ) 21.01/21.22 (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))) ) 21.01/21.22 ( int, int ) 21.01/21.22 ( int, nat ) 21.01/21.22 ( int, bool ) 21.01/21.22 ( int, (fun int bool) ) 21.01/21.22 ( int, (product_prod int int) ) 21.01/21.22 ( (fun int int), int ) 21.01/21.22 ( nat, nat ) 21.01/21.22 ( nat, bool ) 21.01/21.22 ( nat, (product_prod nat nat) ) 21.01/21.22 ( bool, bool ) 21.01/21.22 ( real, int ) 21.01/21.22 ( real, bool ) 21.01/21.22 ( real, real ) 21.01/21.22 ( real, (filter nat) ) 21.01/21.22 ( real, (filter real) ) 21.01/21.22 ( (fun nat real), nat ) 21.01/21.22 ( (fun int bool), int ) 21.01/21.22 ( (product_prod int int), int ) 21.01/21.22 ( (product_prod int int), bool ) 21.01/21.22 ( (product_prod int int), (product_prod int int) ) 21.01/21.22 ( (fun (product_prod int int) int), (product_prod int int) ) 21.01/21.22 ( (fun int (fun int bool)), int ) 21.01/21.22 ( (fun nat bool), nat ) 21.01/21.22 ( (fun (product_prod int int) bool), (product_prod int int) ) 21.01/21.22 ( (fun real bool), real ) 21.01/21.22 ( quickcheck_code_int, quickcheck_code_int ) 21.01/21.22 ( code_code_numeral, code_code_numeral ) 21.01/21.22 ( (product_prod nat nat), (product_prod nat nat) ) 21.01/21.22 ( (fun int real), int ) 21.01/21.22 ( (fun real (fun int bool)), real ) 21.01/21.22 ( (fun int (fun nat bool)), int ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real _let_0 Na)) (hAPP nat real _let_0 Ma))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Na) Ma)))) ) 21.01/21.22 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (zero_zero nat), n ) 21.01/21.22 ( (zero_zero nat), tn ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N)) M)) ) 21.01/21.22 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (= (hBOOL (hAPP _let_0 bool (finite_finite_1 int) (hAPP _let_1 _let_0 (hAPP (fun nat int) (fun _let_1 _let_0) (image nat int) (semiring_1_of_nat int)) A_2))) (hBOOL (hAPP _let_1 bool (finite_finite_1 nat) A_2))))) ) 21.01/21.22 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X $$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)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_2)))))) ) 21.01/21.22 ( pi ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.22 ( skv_10 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted) (Ya $$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 Xa)) (hAPP nat int _let_0 Ya))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Xa) Ya)))) ) 21.01/21.22 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.22 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (zero_zero nat), (one_one nat) ) 21.01/21.22 ( (zero_zero nat), n ) 21.01/21.22 ( (zero_zero nat), tn ) 21.01/21.22 ) 21.01/21.22 (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)))))) ) 21.01/21.22 ( pls, min ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) M))) (= _let_0 (hAPP int int (abs_abs int) _let_0))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( n ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((B_1_1 $$unsorted)) (= (hBOOL (ti bool B_1_1)) (hBOOL B_1_1)) ) 21.01/21.22 ( fTrue ) 21.01/21.22 ( fFalse ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((W $$unsorted)) (not (= ii (hAPP int complex (number_number_of complex) W))) ) 21.01/21.22 ( min ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted) (Ya $$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) Xa) Ya))) (or (hBOOL (hAPP int bool _let_0 Xa)) (hBOOL (hAPP int bool _let_0 Ya))))) ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 21.01/21.22 ( (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 (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( (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))), t ) 21.01/21.22 ( (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))), m1 ) 21.01/21.22 ( (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 (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.01/21.22 ( (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))), skv_21 ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 21.01/21.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.01/21.22 ( y, v ) 21.01/21.22 ( y, w ) 21.01/21.22 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( sa, v ) 21.01/21.22 ( sa, w ) 21.01/21.22 ( x, v ) 21.01/21.22 ( x, w ) 21.01/21.22 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.01/21.22 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( r, v ) 21.01/21.22 ( r, w ) 21.01/21.22 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 21.01/21.22 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 21.01/21.22 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 21.01/21.22 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.01/21.22 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$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_3) B_2))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_3) B_2) Ma)))) ) 21.01/21.22 ( (hAPP nat int (hAPP 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))) ) 21.01/21.22 ( (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (filter complex))) (let ((_let_1 (fun _let_0 bool))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun complex real) (fun real _let_1) (tendsto complex real) re) (hAPP complex real re A_3)) (hAPP complex _let_0 (at complex) A_3))))) ) 21.01/21.22 ( (zero_zero complex) ) 21.01/21.22 ( ii ) 21.01/21.22 ( (one_one complex) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$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))) pi))))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (collect X_a))) (= _let_1 (ti (fun _let_0 _let_0) _let_1)))) ) 21.01/21.22 ( int ) 21.01/21.22 ( nat ) 21.01/21.22 ( bool ) 21.01/21.22 ( real ) 21.01/21.22 ( (filter nat) ) 21.01/21.22 ( (fun int bool) ) 21.01/21.22 ( (product_prod int int) ) 21.01/21.22 ( (fun nat bool) ) 21.01/21.22 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.01/21.22 ( (product_prod real real) ) 21.01/21.22 ( (filter real) ) 21.01/21.22 ( (product_prod nat nat) ) 21.01/21.22 ( (fun nat rat) ) 21.01/21.22 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat (fact_fact nat) N))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (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)))))) ) 21.01/21.22 ( pls, pls ) 21.01/21.22 ( pls, (hAPP int int bit1 pls) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((K_4 $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) K_4)) (zero_zero int)))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( n ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat nat))) (let ((_let_4 (fun nat _let_2))) (let ((_let_5 (fun _let_0 _let_0))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (fun real _let_2))) (let ((_let_8 (fun _let_0 _let_4))) (let ((_let_9 (combb real _let_2 nat))) (let ((_let_10 (fun _let_3 _let_0))) (let ((_let_11 (combb nat real nat))) (let ((_let_12 (fun nat _let_3))) (let ((_let_13 (hAPP nat _let_3 (hAPP _let_12 _let_12 (combc nat nat nat) (hAPP _let_3 _let_12 (hAPP _let_12 (fun _let_3 _let_12) (combb nat _let_3 nat) (plus_plus nat)) (hAPP nat _let_3 (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_0 (fun real bool) (sums real) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 (hAPP _let_7 _let_8 _let_9 (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 (hAPP _let_7 _let_8 _let_9 (inverse_divide real)) (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)))) (hAPP _let_3 _let_0 (hAPP _let_0 _let_10 _let_11 (real_1 nat)) (hAPP _let_3 _let_3 (hAPP _let_3 (fun _let_3 _let_3) (combb nat nat nat) (fact_fact nat)) _let_13))))) (hAPP _let_3 _let_0 (hAPP _let_0 _let_10 _let_11 (hAPP real _let_0 _let_1 Xa)) _let_13))) (hAPP real real sin Xa))))))))))))))))) ) 21.01/21.22 ( (hAPP int real (number_number_of real) min) ) 21.01/21.22 ( pi ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X $$unsorted)) (= X (hAPP int quickcheck_code_int quickcheck_of_int (hAPP quickcheck_code_int int quickcheck_int_of X))) ) 21.01/21.22 ( (zero_zero quickcheck_code_int) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (= (zero_zero nat) (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N)))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( n ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (measure X_a))) (= _let_0 (ti (fun (fun X_a nat) (fun (product_prod X_a X_a) bool)) _let_0))) ) 21.01/21.22 ( int ) 21.01/21.22 ( nat ) 21.01/21.22 ( real ) 21.01/21.22 ( complex ) 21.01/21.22 ( (product_prod int int) ) 21.01/21.22 ( quickcheck_code_int ) 21.01/21.22 ( code_code_numeral ) 21.01/21.22 ( (product_prod nat nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun real bool))) (= (and (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) Xa) Ya)) (not (= Xa Ya))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Xa) Ya)))) ) 21.01/21.22 ( pi, (zero_zero real) ) 21.01/21.22 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.01/21.22 ( (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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (zero_zero real), pi ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (zero_zero real), skv_2 ) 21.01/21.22 ( (zero_zero real), skv_9 ) 21.01/21.22 ( (zero_zero real), skv_10 ) 21.01/21.22 ( (zero_zero real), skv_11 ) 21.01/21.22 ( (zero_zero real), skv_12 ) 21.01/21.22 ( (zero_zero real), skv_15 ) 21.01/21.22 ( (zero_zero real), skv_18 ) 21.01/21.22 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.01/21.22 ( (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) ) 21.01/21.22 ( (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 ) 21.01/21.22 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 Wa)) (hAPP int nat nat_1 Z))) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Wa) Z)))))) ) 21.01/21.22 ( (one_one int), t ) 21.01/21.22 ( min, min ) 21.01/21.22 ( min, (zero_zero int) ) 21.01/21.22 ( (zero_zero int), pls ) 21.01/21.22 ( (zero_zero int), (one_one int) ) 21.01/21.22 ( (zero_zero int), min ) 21.01/21.22 ( (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))) ) 21.01/21.22 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (zero_zero nat)) (hAPP real nat natceiling X))) ) 21.01/21.22 ( (one_one real) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP int bool nat_neg (hAPP nat int (semiring_1_of_nat int) N)))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( n ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) Na)) Ma)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (number_number_of real) Na)) (hAPP int real (real_1 int) Ma)))) ) 21.01/21.22 ( pls, pls ) 21.01/21.22 ( pls, (one_one int) ) 21.01/21.22 ( pls, min ) 21.01/21.22 ( pls, s ) 21.01/21.22 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( pls, skv_4 ) 21.01/21.22 ( pls, skv_5 ) 21.01/21.22 ( (hAPP int int bit1 pls), t ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (= (hBOOL (hAPP real bool _let_0 Ya)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Ya))))) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one real) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((T_1 $$unsorted)) (preorder (filter T_1)) ) 21.01/21.22 ( nat ) 21.01/21.22 ( real ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((D_3 $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (abs_abs int) D_3)) D_3)) ) 21.01/21.22 ( v ) 21.01/21.22 ( w ) 21.01/21.22 ( skv_14 ) 21.01/21.22 ( skv_20 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat suc N))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.22 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Wa $$unsorted)) (let ((_let_0 (number_number_of int))) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit1 Wa)))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 Wa))))) ) 21.01/21.22 ( pls ) 21.01/21.22 ( (hAPP int int bit1 pls) ) 21.01/21.22 ( min ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.22 ( (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)))))) ) 21.01/21.22 ( (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))))))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0)))))) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one real) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) Xa))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) Xa) (hAPP nat nat suc _let_0))))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (product_apsnd X_c X_b X_a))) (= _let_0 (ti (fun (fun X_c X_b) (fun (product_prod X_a X_c) (product_prod X_a X_b))) _let_0))) ) 21.01/21.22 ( int, int, int ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (= (one_one nat) (hAPP nat nat (hAPP nat (fun nat nat) (gcd_gcd nat) (hAPP nat nat suc N)) N)) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.22 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 21.01/21.22 ( pls ) 21.01/21.22 ( (hAPP int int bit1 pls) ) 21.01/21.22 ( min ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit0 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 21.01/21.22 ( pls ) 21.01/21.22 ( (hAPP int int bit1 pls) ) 21.01/21.22 ( min ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.22 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted) (Ya $$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 (uminus_uminus real) Xa)) Ya)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real (hAPP real (fun real real) (plus_plus real) Xa) Ya)))))) ) 21.01/21.22 ( (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)))), (zero_zero real) ) 21.01/21.22 ( (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), pi ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((V $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP int complex (number_number_of complex) V))) ) 21.01/21.22 ( min ) 21.01/21.22 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) Na)) (and (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) Na)) (not (= Ma Na))))) ) 21.01/21.22 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (zero_zero nat), n ) 21.01/21.22 ( (zero_zero nat), tn ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat (fact_fact nat) N))) ) 21.01/21.22 ( (zero_zero nat) ) 21.01/21.22 ( (one_one nat) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (uminus_uminus real) (hAPP real real sin Xa))) (hAPP real real cos Xa)))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (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_0 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) Xa) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_3) _let_3))))))) ) 21.01/21.22 ( pi ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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) ) 21.01/21.22 ( (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))))) ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.22 ( skv_10 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less quickcheck_code_int) Na) Ma)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP quickcheck_code_int int quickcheck_int_of Na)) (hAPP quickcheck_code_int int quickcheck_int_of Ma)))) ) 21.01/21.22 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Z $$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)))) ) 21.01/21.22 ( pls ) 21.01/21.22 ( (one_one int) ) 21.01/21.22 ( min ) 21.01/21.22 ( (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))) ) 21.01/21.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( t ) 21.01/21.22 ) 21.01/21.22 (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 K1) K2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K1)) (hAPP int int bit1 K2)))))) ) 21.01/21.22 ( min, min ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((A_3 $$unsorted) (Xa $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_3)) Xa)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_3) (hAPP real int (archim2085082626_floor real) Xa)))) ) 21.01/21.22 ( (zero_zero int), pi ) 21.01/21.22 ( (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)))) ) 21.01/21.22 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.22 ( (zero_zero int), skv_10 ) 21.01/21.22 ( (zero_zero int), skv_11 ) 21.01/21.22 ( (zero_zero int), skv_15 ) 21.01/21.22 ( (zero_zero int), skv_18 ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (= (hBOOL (hAPP real bool _let_0 Ya)) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Ya))))) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( (one_one real) ) 21.01/21.22 ( (zero_zero real) ) 21.01/21.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ) 21.01/21.22 (instantiation (forall ((X_a $$unsorted) (P $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP X_a bool P X))) (hBOOL (hAPP (fun X_a bool) bool (fEx X_a) P))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 21.01/21.22 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( 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) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) min), min ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 21.01/21.22 ( int, nat_neg, (one_one int) ) 21.01/21.22 ( int, nat_neg, (zero_zero int) ) 21.01/21.22 ( int, nat_neg, (hAPP int int (number_number_of int) min) ) 21.01/21.22 ( int, nat_is_nat, (one_one int) ) 21.01/21.22 ( int, nat_is_nat, (zero_zero int) ) 21.01/21.22 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.22 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 21.01/21.22 ( int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 21.01/21.22 ( int, (even_odd_even int), (one_one int) ) 21.01/21.22 ( int, (even_odd_even int), (zero_zero int) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) pls), min ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 21.01/21.22 ( 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))) ) 21.01/21.22 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 21.01/21.22 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.22 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( 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) (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)) ) 21.01/21.23 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ( int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( nat, (even_odd_even nat), (zero_zero nat) ) 21.01/21.23 ( nat, (even_odd_even nat), (one_one nat) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.01/21.23 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.01/21.23 ( nat, prime, (zero_zero nat) ) 21.01/21.23 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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) ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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) ) 21.01/21.23 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 21.01/21.23 ( 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 ) 21.01/21.23 ( 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 ) 21.01/21.23 ( 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) ) 21.01/21.23 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 21.01/21.23 ( (filter nat), (trivial_limit nat), sequentially ) 21.01/21.23 ( (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)) ) 21.01/21.23 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 21.01/21.23 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.01/21.23 ( (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) ) 21.01/21.23 ( (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))))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((K $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (dvd_dvd nat) K))) (= (hBOOL (hAPP nat bool _let_0 Na)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Na) K))))) ) 21.01/21.23 ( (one_one nat), (one_one nat) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP nat nat suc N)) N))) ) 21.01/21.23 ( (zero_zero nat) ) 21.01/21.23 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.23 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((R_3 $$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_3) (one_one real))) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_3)))) ) 21.01/21.23 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP complex real im X))) (hAPP complex real (norm_norm complex) X))) ) 21.01/21.23 ( (zero_zero complex) ) 21.01/21.23 ( ii ) 21.01/21.23 ( (one_one complex) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (semiring_1_of_nat int))) (= (and (= _let_0 Na) (= _let_0 Ma)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int _let_1 Na)) (hAPP int int (uminus_uminus int) (hAPP nat int _let_1 Ma))))))) ) 21.01/21.23 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.23 ( (zero_zero nat), (one_one nat) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (image X_b X_a))) (= _let_0 (ti (fun (fun X_b X_a) (fun (fun X_b bool) (fun X_a bool))) _let_0))) ) 21.01/21.23 ( int, int ) 21.01/21.23 ( nat, nat ) 21.01/21.23 ( real, real ) 21.01/21.23 ( (product_prod int int), (product_prod int int) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((J_2 $$unsorted) (I_1 $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) J_2) I_1)) I_1))) ) 21.01/21.23 ( (one_one nat), (one_one nat) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((M $$unsorted)) (= M (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) (zero_zero nat))) ) 21.01/21.23 ( (hAPP int nat nat_1 t) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Ya)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 Xa)))) (= (or (and (not _let_1) (not _let_2)) (and _let_1 _let_2)) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) Xa) Ya))))))) ) 21.01/21.23 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.01/21.23 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.23 ( (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)))), (one_one int) ) 21.01/21.23 ( (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) ) 21.01/21.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.01/21.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.01/21.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.01/21.23 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.01/21.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real cos X)) (one_one real))) ) 21.01/21.23 ( pi ) 21.01/21.23 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (zero_zero real) ) 21.01/21.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.23 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.01/21.23 ( skv_10 ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) min))) (= (hBOOL (hAPP int bool _let_0 (hAPP int int bit1 K))) (hBOOL (hAPP int bool _let_0 K)))) ) 21.01/21.23 ( pls ) 21.01/21.23 ( (hAPP int int bit1 pls) ) 21.01/21.23 ( min ) 21.01/21.23 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.23 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.23 ( (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)))))) ) 21.01/21.23 ( (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))))))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Wa) Z)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Wa) (hAPP int int (hAPP int (fun int int) (minus_minus int) Z) (one_one int)))))) ) 21.01/21.23 ( (one_one int), t ) 21.01/21.23 ( min, min ) 21.01/21.23 ( min, (zero_zero int) ) 21.01/21.23 ( (zero_zero int), pls ) 21.01/21.23 ( (zero_zero int), (one_one int) ) 21.01/21.23 ( (zero_zero int), min ) 21.01/21.23 ( (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))) ) 21.01/21.23 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) Ya)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt Xa)) (hAPP real real sqrt Ya)))))) ) 21.01/21.23 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) min)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min))))) ) 21.01/21.23 ( pls ) 21.01/21.23 ( (hAPP int int bit1 pls) ) 21.01/21.23 ( min ) 21.01/21.23 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.23 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.23 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Z_1 $$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))) ) 21.01/21.23 ( (zero_zero complex) ) 21.01/21.23 ( ii ) 21.01/21.23 ( (one_one complex) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) Xa)) (hBOOL (hAPP int bool (even_odd_even int) (hAPP nat int (semiring_1_of_nat int) Xa)))) ) 21.01/21.23 ( (zero_zero nat) ) 21.01/21.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (one_one nat) ) 21.01/21.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.23 ( n ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((X_a $$unsorted) (Xa $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (hBOOL (hAPP X_a bool A_2 Xa)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) Xa) A_2)))) ) 21.01/21.23 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 21.01/21.23 ( int, pls, (hAPP int (fun int bool) (ord_less int) pls) ) 21.01/21.23 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min) ) 21.01/21.23 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 21.01/21.23 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.23 ( int, (one_one int), zEven ) 21.01/21.23 ( int, (one_one int), nat_neg ) 21.01/21.23 ( int, (one_one int), nat_is_nat ) 21.01/21.23 ( int, (one_one int), (even_odd_even int) ) 21.01/21.23 ( int, min, (hAPP int (fun int bool) (ord_less int) min) ) 21.01/21.23 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 21.01/21.23 ( int, min, (hAPP int (fun int bool) (ord_less int) pls) ) 21.01/21.23 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) min) ) 21.01/21.23 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) min) ) 21.01/21.23 ( int, (zero_zero int), nat_neg ) 21.01/21.23 ( int, (zero_zero int), nat_is_nat ) 21.01/21.23 ( int, (zero_zero int), (even_odd_even int) ) 21.01/21.23 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5)) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5) ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))) ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 21.01/21.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 21.01/21.23 ( int, (hAPP int int (number_number_of int) min), (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)))) ) 21.01/21.23 ( int, (hAPP int int (number_number_of int) min), nat_neg ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))) ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) m1) ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))) ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))) ) 21.01/21.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))) ) 21.01/21.23 ( int, t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 21.01/21.23 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 21.01/21.23 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))), twoSqu1091635170sum2sq ) 21.01/21.23 ( int, (hAPP 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)), (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)))) ) 21.01/21.23 ( 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 ) 21.01/21.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))), twoSqu1091635170sum2sq ) 21.01/21.23 ( int, skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.23 ( int, skv_5, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.23 ( nat, (zero_zero nat), (even_odd_even nat) ) 21.01/21.23 ( nat, (zero_zero nat), prime ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 21.01/21.23 ( nat, (one_one nat), (even_odd_even nat) ) 21.01/21.23 ( nat, (hAPP nat nat suc (zero_zero nat)), prime ) 21.01/21.23 ( nat, n, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 21.01/21.23 ( nat, tn, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 21.01/21.23 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 21.01/21.23 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( 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)))) ) 21.01/21.23 ( 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))) ) 21.01/21.23 ( 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))))) ) 21.01/21.23 ( 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))))) ) 21.01/21.23 ( 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_10) ) 21.01/21.23 ( 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 real (fun real bool) (ord_less real) (zero_zero real)) ) 21.01/21.23 ( 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 real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( real, (one_one real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))) ) 21.01/21.23 ( 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)))))) ) 21.01/21.23 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi) ) 21.01/21.23 ( 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))))) ) 21.01/21.23 ( 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))))) ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( 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)) ) 21.01/21.23 ( 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) ) 21.01/21.23 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 21.01/21.23 ( real, skv_9, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 21.01/21.23 ( real, skv_10, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( real, skv_11, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( real, skv_12, (hAPP real (fun real bool) (ord_less real) (zero_zero real)) ) 21.01/21.23 ( real, skv_15, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( real, skv_18, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 21.01/21.23 ( (filter nat), sequentially, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))) ) 21.01/21.23 ( (filter nat), sequentially, (trivial_limit nat) ) 21.01/21.23 ( (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) ) 21.01/21.23 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)) ) 21.01/21.23 ( (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)) ) 21.01/21.23 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (finite_finite_1 nat) ) 21.01/21.23 ( (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))))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real _let_0 Xa)) (hAPP int real _let_0 Ya))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Xa) Ya)))) ) 21.01/21.23 ( (one_one int), t ) 21.01/21.23 ( min, pls ) 21.01/21.23 ( min, min ) 21.01/21.23 ( (zero_zero int), pls ) 21.01/21.23 ( (zero_zero int), (one_one int) ) 21.01/21.23 ( (zero_zero int), min ) 21.01/21.23 ( (zero_zero int), s ) 21.01/21.23 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (zero_zero int), skv_4 ) 21.01/21.23 ( (zero_zero int), skv_5 ) 21.01/21.23 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N))) (zero_zero int))) ) 21.01/21.23 ( (zero_zero nat) ) 21.01/21.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (one_one nat) ) 21.01/21.23 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.23 ( n ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 N))) (hAPP nat int _let_0 M)))) ) 21.01/21.23 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.23 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (zero_zero nat), (one_one nat) ) 21.01/21.23 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (one_one nat), (zero_zero nat) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Z_1 $$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 Z_1) W)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 W) Z_1))))) ) 21.01/21.23 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( pi, (zero_zero real) ) 21.01/21.23 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.01/21.23 ( (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)))) ) 21.01/21.23 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.01/21.23 ( (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 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( (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 pls)))), (zero_zero real) ) 21.01/21.23 ( (zero_zero real), pi ) 21.01/21.23 ( (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)))) ) 21.01/21.23 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.23 ( (zero_zero real), skv_10 ) 21.01/21.23 ( (zero_zero real), skv_11 ) 21.01/21.23 ( (zero_zero real), skv_15 ) 21.01/21.23 ( (zero_zero real), skv_18 ) 21.01/21.23 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.01/21.23 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.01/21.23 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.23 ( skv_10, (zero_zero real) ) 21.01/21.23 ( skv_11, (zero_zero real) ) 21.01/21.23 ( skv_15, (zero_zero real) ) 21.01/21.23 ( skv_18, (zero_zero real) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (inverse_divide 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_0 _let_1 Xa) (hAPP int nat (number_number_of nat) _let_4)))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combb real real nat) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 _let_3 _let_6) _let_5))) (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_2 _let_3 (one_one real)) _let_5)))) _let_6))))))))) ) 21.01/21.23 ( (hAPP int real (number_number_of real) min) ) 21.01/21.23 ( (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)))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (nat_case X_a))) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)))) ) 21.01/21.23 ( rat ) 21.01/21.23 ( int ) 21.01/21.23 ( (fun int int) ) 21.01/21.23 ( nat ) 21.01/21.23 ( bool ) 21.01/21.23 ( real ) 21.01/21.23 ( (fun real real) ) 21.01/21.23 ( (fun nat nat) ) 21.01/21.23 ( complex ) 21.01/21.23 ( (product_prod int int) ) 21.01/21.23 ( (fun bool bool) ) 21.01/21.23 ( (fun nat bool) ) 21.01/21.23 ( (fun nat (fun nat bool)) ) 21.01/21.23 ( (fun nat (product_prod int int)) ) 21.01/21.23 ( (product_prod real real) ) 21.01/21.23 ( (product_prod nat nat) ) 21.01/21.23 ( (fun (product_prod nat nat) bool) ) 21.01/21.23 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.01/21.23 ( (fun nat (product_prod nat nat)) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 K)) (hAPP int int bit0 L)))))) ) 21.01/21.23 ( pls, pls ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((N $$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))))) ) 21.01/21.23 ( (zero_zero nat) ) 21.01/21.23 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.23 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP nat nat (fact_fact nat) N))) ) 21.01/21.23 ( (zero_zero nat) ) 21.01/21.23 ( (one_one nat) ) 21.01/21.23 ) 21.01/21.23 (instantiation (forall ((K $$unsorted) (Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K))) (= (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) Na) (hAPP int int (hAPP int _let_0 (times_times int) K) Ma)))) (hBOOL (hAPP int bool _let_1 Na))))) ) 21.01/21.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.01/21.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3 ) 21.01/21.23 ( y, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w ) 21.01/21.23 ( sa, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w ) 21.01/21.24 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w ) 21.01/21.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (= (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Ma) Na)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) Ma) Na))) ) 21.01/21.24 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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 A_3) B_2) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B_2) A_3) Ma))))) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( (hAPP nat int (hAPP 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))) ) 21.01/21.24 ( (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ( (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))) ) 21.01/21.24 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP 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))) ) 21.01/21.24 ( (hAPP int int (number_number_of int) min), (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))) ) 21.01/21.24 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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))) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( skv_5, 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))) ) 21.01/21.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (even_odd_even int))) (let ((_let_1 (hBOOL (hAPP int bool _let_0 Xa)))) (let ((_let_2 (hBOOL (hAPP int bool _let_0 Ya)))) (= (or (and _let_1 _let_2) (and (not _let_2) (not _let_1))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya))))))) ) 21.01/21.24 ( (hAPP nat int (hAPP 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) ) 21.01/21.24 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.24 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.24 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.24 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.24 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.01/21.24 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun (fun nat nat) _let_0))) (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_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_2 _let_3 (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_3 (combb real real nat) (inverse_inverse real)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _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_0 (hAPP _let_0 _let_4 _let_5 (hAPP real _let_0 (power_power real) Xa)) _let_6))))))))))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) min) ) 21.01/21.24 ( (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)))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (= M (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) M)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int _let_0 N)) (hAPP int int (uminus_uminus int) (hAPP nat int _let_0 M)))))) ) 21.01/21.24 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.24 ( (zero_zero nat), (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$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)) pi))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N))) ) 21.01/21.24 ( (one_one nat), (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int bit0 K)) min)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) min)))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (zero_zero int) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP nat int (semiring_1_of_nat int) Ma)) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) (hAPP int nat nat_1 Z)))) ) 21.01/21.24 ( (zero_zero nat), pls ) 21.01/21.24 ( (zero_zero nat), (one_one int) ) 21.01/21.24 ( (zero_zero nat), min ) 21.01/21.24 ( (zero_zero nat), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ( (zero_zero nat), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (zero_zero nat), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.24 ( (one_one nat), t ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((L $$unsorted)) (= (= pls (ti int L)) (= pls (hAPP int int bit0 L))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( s ) 21.01/21.24 ( s1 ) 21.01/21.24 ( m ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( t ) 21.01/21.24 ( v ) 21.01/21.24 ( w ) 21.01/21.24 ( y ) 21.01/21.24 ( sa ) 21.01/21.24 ( x ) 21.01/21.24 ( r ) 21.01/21.24 ( m1 ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ( skv_14 ) 21.01/21.24 ( skv_20 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N)))))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.24 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (one_one real)) Xa)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (one_one nat)) (hAPP real nat natfloor Xa)))) ) 21.01/21.24 ( (one_one real) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ) 21.01/21.24 (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 bit1 K1)) (hAPP int int bit1 K2)))))) ) 21.01/21.24 ( min, min ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$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 Xa))) (hAPP real real cos Xa)))) (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)) Xa) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) _let_2)))))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP real 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))))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.24 ( (hAPP real real (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))))) ) 21.01/21.24 ( (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)))) ) 21.01/21.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.24 ( skv_10 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Na $$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) Na)) (field_char_0_Rats real)))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Ma) (hAPP int int (number_number_of int) Na))) (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) Na)))) ) 21.01/21.24 ( min, pls ) 21.01/21.24 ( (zero_zero int), pls ) 21.01/21.24 ( (zero_zero int), (hAPP int int bit1 pls) ) 21.01/21.24 ( (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (= (= _let_0 (hAPP real real sqrt Xa)) (= _let_0 Xa))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (one_one real) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP nat nat fact N))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) Xa))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Xa))))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( skv_10 ) 21.01/21.24 ( skv_11 ) 21.01/21.24 ( skv_15 ) 21.01/21.24 ( skv_18 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$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) Xa)) (ring_1_Ints real)))) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( (zero_zero int) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Va $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) Va)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP int nat (number_number_of nat) Va)))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((R_3 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_3) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real (real_1 int) (hAPP real int (archim2085082626_floor real) R_3))) (one_one real)))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (one_one real) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.24 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 K)) (hAPP int int bit0 L)))))) ) 21.01/21.24 ( min, pls ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero real) (hAPP complex real im (hAPP real complex (of_real complex) Z_1))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) min) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_3 (hAPP _let_1 (fun real _let_3) (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_0 real) (power_power real)) cos)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) Xa) (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))) (hAPP real real cos Xa))) (hAPP real real sin Xa))))))))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP real 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))))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.24 ( (hAPP real real (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))))) ) 21.01/21.24 ( (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)))) ) 21.01/21.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.24 ( skv_10 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (= N (hAPP int nat nat_1 (hAPP nat int (semiring_1_of_nat int) N))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ( n ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (deriv real) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb real _let_0 real) _let_1) cos)) cos)) Xa) (hAPP real real (uminus_uminus real) (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 real real cos Xa))) (hAPP real real sin Xa))))))))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP real 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))))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.24 ( (hAPP real real (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))))) ) 21.01/21.24 ( (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)))) ) 21.01/21.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.24 ( skv_10 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (zero_zero nat) (hAPP complex nat complex_size (hAPP real complex (hAPP real (fun real complex) complex_1 Real1_1) Real2_1))) ) 21.01/21.24 ( (one_one real), (zero_zero real) ) 21.01/21.24 ( (zero_zero real), (one_one real) ) 21.01/21.24 ( (zero_zero real), (zero_zero real) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((T_1 $$unsorted)) (order (filter T_1)) ) 21.01/21.24 ( nat ) 21.01/21.24 ( real ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) X) (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( min ) 21.01/21.24 ( (zero_zero int) ) 21.01/21.24 ( s ) 21.01/21.24 ( s1 ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.24 ( v ) 21.01/21.24 ( w ) 21.01/21.24 ( y ) 21.01/21.24 ( (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)))) (hAPP int int (abs_abs int) w)) ) 21.01/21.24 ( x ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.01/21.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.01/21.24 ( (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)))) (hAPP int int (abs_abs int) v)) ) 21.01/21.24 ( skv_6 ) 21.01/21.24 ( skv_7 ) 21.01/21.24 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.01/21.24 ( skv_16 ) 21.01/21.24 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.01/21.24 ( skv_23 ) 21.01/21.24 ( skv_24 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (zero_zero nat) (hAPP complex nat (size_size complex) (hAPP real complex (hAPP real (fun real complex) complex_1 Real1_1) Real2_1))) ) 21.01/21.24 ( (one_one real), (zero_zero real) ) 21.01/21.24 ( (zero_zero real), (one_one real) ) 21.01/21.24 ( (zero_zero real), (zero_zero real) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((L_4 $$unsorted)) (not (= pls (hAPP int int bit1 L_4))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.24 ( (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)))))) ) 21.01/21.24 ( (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))))))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc N))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.24 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) Z)) (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)))) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( (zero_zero int) ) 21.01/21.24 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( t ) 21.01/21.24 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted) (M $$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)))) (hAPP nat int _let_0 M)))) ) 21.01/21.24 ( (zero_zero nat), (zero_zero nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (fun real bool))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun real _let_0))) (let ((_let_8 (combc real nat real))) (let ((_let_9 (hAPP _let_7 (fun _let_1 _let_7) (combb real _let_0 real) (power_power real)))) (let ((_let_10 (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_1))) (hAPP real real sin X_1)))) (hBOOL (hAPP real bool (hAPP real _let_4 (hAPP _let_1 (fun real _let_4) (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_1) (hAPP real real (hAPP real _let_1 (minus_minus real) _let_10) _let_10)))))))))))))) ) 21.01/21.24 ( pi ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP real 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))))) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.24 ( (hAPP real real (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))))) ) 21.01/21.24 ( (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)))) ) 21.01/21.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.24 ( skv_10 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((K_4 $$unsorted)) (not (= min (hAPP int int bit0 K_4))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (number_number_of real) Na)) (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) Na)) Ma))) ) 21.01/21.24 ( pls, pls ) 21.01/21.24 ( pls, (one_one int) ) 21.01/21.24 ( pls, min ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.24 ( (hAPP int int bit1 pls), t ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Na) 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 Na)) (one_one real))) (hAPP nat real _let_0 Ma))))) ) 21.01/21.24 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (zero_zero nat), n ) 21.01/21.24 ( (zero_zero nat), tn ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero real))) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N) _let_0))) ) 21.01/21.24 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) coprime (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat))) N)) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (ord_less int))) (let ((_let_4 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) Z)) Z)) _let_4)) (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 Z) _let_4)))))))) ) 21.01/21.24 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.01/21.24 ( (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (= (= _let_0 Xa) (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) Xa) Xa)))))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ( (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))))) ) 21.01/21.24 ) 21.01/21.24 (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))) ) 21.01/21.24 ( int, int, int ) 21.01/21.24 ( int, int, (fun int int) ) 21.01/21.24 ( int, int, bool ) 21.01/21.24 ( int, int, (fun int bool) ) 21.01/21.24 ( int, (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 21.01/21.24 ( int, (fun int int), (fun int (fun int bool)) ) 21.01/21.24 ( int, bool, (fun int int) ) 21.01/21.24 ( int, bool, bool ) 21.01/21.24 ( int, bool, (fun int bool) ) 21.01/21.24 ( int, bool, (fun bool bool) ) 21.01/21.24 ( int, real, bool ) 21.01/21.24 ( int, real, real ) 21.01/21.24 ( int, real, (fun real real) ) 21.01/21.24 ( int, real, (fun int real) ) 21.01/21.24 ( int, (fun nat real), (fun nat bool) ) 21.01/21.24 ( int, (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 21.01/21.24 ( int, (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 21.01/21.24 ( int, (fun int bool), bool ) 21.01/21.24 ( int, (fun int bool), (fun int bool) ) 21.01/21.24 ( int, (fun int bool), (fun int (fun bool bool)) ) 21.01/21.24 ( int, (fun int bool), (fun (fun int int) (fun int bool)) ) 21.01/21.24 ( int, (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 21.01/21.24 ( int, (fun int (fun int bool)), (fun int (fun int bool)) ) 21.01/21.24 ( int, (fun nat bool), bool ) 21.01/21.24 ( int, (fun nat bool), (fun nat (fun bool bool)) ) 21.01/21.24 ( int, (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 21.01/21.24 ( int, (fun int real), (fun int bool) ) 21.01/21.24 ( nat, nat, real ) 21.01/21.24 ( nat, nat, (fun nat nat) ) 21.01/21.24 ( nat, nat, (fun nat bool) ) 21.01/21.24 ( nat, bool, bool ) 21.01/21.24 ( nat, bool, (fun bool bool) ) 21.01/21.24 ( nat, real, bool ) 21.01/21.24 ( nat, real, real ) 21.01/21.24 ( nat, real, (fun real real) ) 21.01/21.24 ( real, bool, bool ) 21.01/21.24 ( real, bool, (fun bool bool) ) 21.01/21.24 ( real, real, real ) 21.01/21.24 ( real, real, (fun real real) ) 21.01/21.24 ( real, real, (fun real bool) ) 21.01/21.24 ( real, (fun int bool), bool ) 21.01/21.24 ( real, (fun int (fun int bool)), (fun int bool) ) 21.01/21.24 ( real, (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 21.01/21.24 ( real, (fun real bool), (fun (fun nat real) (fun nat bool)) ) 21.01/21.24 ( real, (fun real bool), (fun (fun int real) (fun int bool)) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( real, (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 21.01/21.24 ( real, (fun int (fun nat bool)), (fun int bool) ) 21.01/21.24 ( real, (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 21.01/21.24 ( 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))) ) 21.01/21.24 ( real, (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 21.01/21.24 ( real, (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 21.01/21.24 ( real, (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 21.01/21.24 ( (product_prod int int), int, int ) 21.01/21.24 ( (product_prod int int), int, (fun int int) ) 21.01/21.24 ( (product_prod int int), int, bool ) 21.01/21.24 ( (product_prod int int), int, (fun int bool) ) 21.01/21.24 ( (product_prod int int), int, (fun (product_prod int int) int) ) 21.01/21.24 ( (product_prod int int), (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 21.01/21.24 ( (product_prod int int), bool, bool ) 21.01/21.24 ( (product_prod int int), bool, (fun bool bool) ) 21.01/21.24 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 21.01/21.24 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 21.01/21.24 ( (product_prod int int), (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 21.01/21.24 ( (product_prod int int), (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 21.01/21.24 ( (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))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((N $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N)) (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))) ) 21.01/21.24 ( (zero_zero nat) ) 21.01/21.24 ( (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real (real_1 int) Na)) (zero_zero real))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Na) (zero_zero int)))) ) 21.01/21.24 ( (one_one int) ) 21.01/21.24 ( min ) 21.01/21.24 ( (zero_zero int) ) 21.01/21.24 ( s ) 21.01/21.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.24 ( t ) 21.01/21.24 ( m1 ) 21.01/21.24 ( skv_4 ) 21.01/21.24 ( skv_5 ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((K $$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)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) min))))) ) 21.01/21.24 ( pls ) 21.01/21.24 ( (hAPP int int bit1 pls) ) 21.01/21.24 ( min ) 21.01/21.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.24 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (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))) ) 21.01/21.24 ( int, int ) 21.01/21.24 ( int, (product_prod int int) ) 21.01/21.24 ( nat, nat ) 21.01/21.24 ( real, real ) 21.01/21.24 ( (product_prod int int), (product_prod int int) ) 21.01/21.24 ( quickcheck_code_int, quickcheck_code_int ) 21.01/21.24 ( code_code_numeral, code_code_numeral ) 21.01/21.24 ( (product_prod nat nat), (product_prod nat nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Ya))) (hBOOL (hAPP real bool _let_0 Ya)))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.24 ( (one_one real) ) 21.01/21.24 ( (zero_zero real) ) 21.01/21.24 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((X_b $$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))) ) 21.01/21.24 ( int, int, int ) 21.01/21.24 ( int, int, (product_prod int int) ) 21.01/21.24 ( int, (fun int int), int ) 21.01/21.24 ( int, (fun int int), (product_prod int int) ) 21.01/21.24 ( int, bool, int ) 21.01/21.24 ( int, bool, (product_prod int int) ) 21.01/21.24 ( int, (fun int bool), int ) 21.01/21.24 ( int, (fun int bool), (product_prod int int) ) 21.01/21.24 ( int, (fun (product_prod int int) int), (product_prod int int) ) 21.01/21.24 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)), int ) 21.01/21.24 ( (fun int int), (fun int (fun int bool)), int ) 21.01/21.24 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 21.01/21.24 ( nat, real, nat ) 21.01/21.24 ( nat, (fun nat nat), nat ) 21.01/21.24 ( nat, (fun nat bool), nat ) 21.01/21.24 ( bool, (fun int int), int ) 21.01/21.24 ( bool, bool, int ) 21.01/21.24 ( bool, bool, nat ) 21.01/21.24 ( bool, bool, real ) 21.01/21.24 ( bool, bool, (product_prod int int) ) 21.01/21.24 ( bool, (fun int bool), int ) 21.01/21.24 ( bool, (fun bool bool), int ) 21.01/21.24 ( bool, (fun bool bool), nat ) 21.01/21.24 ( bool, (fun bool bool), real ) 21.01/21.24 ( bool, (fun bool bool), (product_prod int int) ) 21.01/21.24 ( real, bool, int ) 21.01/21.24 ( real, bool, nat ) 21.01/21.24 ( real, real, int ) 21.01/21.24 ( real, real, nat ) 21.01/21.24 ( real, real, real ) 21.01/21.24 ( real, (fun real real), int ) 21.01/21.24 ( real, (fun real real), nat ) 21.01/21.24 ( real, (fun real real), real ) 21.01/21.24 ( real, (fun real bool), real ) 21.01/21.24 ( real, (fun int real), int ) 21.01/21.24 ( (fun nat real), (fun nat bool), int ) 21.01/21.24 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 21.01/21.24 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)), int ) 21.01/21.24 ( (fun int bool), bool, int ) 21.01/21.24 ( (fun int bool), bool, real ) 21.01/21.24 ( (fun int bool), (fun int bool), int ) 21.01/21.24 ( (fun int bool), (fun int (fun bool bool)), int ) 21.01/21.24 ( (fun int bool), (fun (fun int int) (fun int bool)), int ) 21.01/21.24 ( (fun (product_prod int int) int), (fun (product_prod int int) bool), (product_prod int int) ) 21.01/21.24 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (product_prod int int) ) 21.01/21.24 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)), (product_prod int int) ) 21.01/21.24 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), int ) 21.01/21.24 ( (fun int (fun int bool)), (fun int bool), real ) 21.01/21.24 ( (fun int (fun int bool)), (fun int (fun int bool)), int ) 21.01/21.24 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))), real ) 21.01/21.24 ( (fun nat bool), bool, int ) 21.01/21.24 ( (fun nat bool), (fun nat (fun bool bool)), int ) 21.01/21.24 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool), (product_prod int int) ) 21.01/21.24 ( (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) ) 21.01/21.24 ( (fun real bool), (fun (fun nat real) (fun nat bool)), real ) 21.01/21.24 ( (fun real bool), (fun (fun int real) (fun int bool)), real ) 21.01/21.24 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 21.01/21.24 ( (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 ) 21.01/21.24 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 21.01/21.24 ( (fun int real), (fun int bool), int ) 21.01/21.24 ( (fun int (fun nat bool)), (fun int bool), real ) 21.01/21.24 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))), real ) 21.01/21.24 ( (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 ) 21.01/21.24 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), real ) 21.01/21.24 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))), real ) 21.01/21.24 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))), real ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((M $$unsorted) (N $$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)) N))) ) 21.01/21.24 ( (one_one nat), (one_one nat) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) cos_coeff)) (hAPP real _let_0 (power_power real) Xa))))))) ) 21.01/21.24 ( (hAPP int real (number_number_of real) min) ) 21.01/21.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.24 ) 21.01/21.24 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_fst X_a X_b))) (= _let_0 (ti (fun (product_prod X_a X_b) X_a) _let_0))) ) 21.01/21.24 ( int, int ) 21.01/21.24 ( int, (product_prod int int) ) 21.01/21.24 ( nat, nat ) 21.01/21.24 ( real, real ) 21.01/21.25 ( (product_prod int int), (product_prod int int) ) 21.01/21.25 ( quickcheck_code_int, quickcheck_code_int ) 21.01/21.25 ( code_code_numeral, code_code_numeral ) 21.01/21.25 ( (product_prod nat nat), (product_prod nat nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((A_3 $$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_3)) (hAPP complex _let_0 (at complex) A_3))))) ) 21.01/21.25 ( (zero_zero complex) ) 21.01/21.25 ( ii ) 21.01/21.25 ( (one_one complex) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (one_one int))) (= (= _let_0 (hAPP int int (abs_abs int) Xa)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Xa) _let_0)))) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( v ) 21.01/21.25 ( w ) 21.01/21.25 ( skv_14 ) 21.01/21.25 ( skv_20 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (even_odd_even int))) (= (hBOOL (hAPP int bool _let_0 Xa)) (hBOOL (hAPP int bool _let_0 (hAPP int int (uminus_uminus int) Xa))))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( min ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) Ma)))))) ) 21.01/21.25 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Va $$unsorted)) (= (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) (hAPP int int pred Va)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) Va))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) M))) ) 21.01/21.25 ( (one_one nat), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((N $$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) _let_1)) N)))) ) 21.01/21.25 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( y ) 21.01/21.25 ( x ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.01/21.25 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.01/21.25 ( (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))) m1))) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (product_Pair int int))) (= (hAPP int _let_1 (hAPP int _let_2 _let_3 _let_0) (one_one int)) (hAPP _let_1 _let_1 normalize (hAPP int _let_1 (hAPP int _let_2 _let_3 P_5) _let_0))))))) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ( s ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((N $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP nat real (real_1 nat) N)) (zero_zero real)))) ) 21.01/21.25 ( (zero_zero nat) ) 21.01/21.25 ( (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fequal X_a))) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0))) ) 21.01/21.25 ( int ) 21.01/21.25 ( nat ) 21.01/21.25 ( bool ) 21.01/21.25 ( real ) 21.01/21.25 ( (filter nat) ) 21.01/21.25 ( (fun int bool) ) 21.01/21.25 ( (product_prod int int) ) 21.01/21.25 ( (fun nat bool) ) 21.01/21.25 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.01/21.25 ( (product_prod real real) ) 21.01/21.25 ( (filter real) ) 21.01/21.25 ( (product_prod nat nat) ) 21.01/21.25 ( (fun nat rat) ) 21.01/21.25 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (number_number_of int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 K)) (hAPP int int _let_2 L))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L)))))) ) 21.01/21.25 ( pls, pls ) 21.01/21.25 ( pls, (hAPP int int bit1 pls) ) 21.01/21.25 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc Xa))) (not (hBOOL (hAPP nat bool _let_0 Xa))))) ) 21.01/21.25 ( (zero_zero nat) ) 21.01/21.25 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.25 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (hBOOL (hAPP nat bool _let_0 Ya)))) (let ((_let_2 (hBOOL (hAPP nat bool _let_0 Xa)))) (= (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Xa) Ya)) (and (not _let_1) (not _let_2)) (and _let_2 _let_1)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Xa) Ya))))))) ) 21.01/21.25 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero nat), n ) 21.01/21.25 ( (zero_zero nat), tn ) 21.01/21.25 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted) (Ya $$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 Xa) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya)) zEven)))))) ) 21.01/21.25 ( (hAPP nat int (hAPP 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) ) 21.01/21.25 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.25 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.25 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.25 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.25 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.01/21.25 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) sin_coeff)) (hAPP real _let_0 (power_power real) Xa))) (hAPP real real sin Xa)))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) min) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Wa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit0 Wa)) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Wa) _let_2)))))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt Xa)) _let_0)))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Ra $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (combb real real nat))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 (fun real _let_3) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 _let_5 (hAPP real _let_1 (times_times real) Ra)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 _let_5 (hAPP real _let_1 (plus_plus real) (one_one real))) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 _let_5 (uminus_uminus real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 _let_5 (inverse_inverse real)) (hAPP _let_2 _let_0 (hAPP _let_0 (fun _let_2 _let_0) (combb nat real nat) (real_1 nat)) suc)))))) Ra) sequentially)))))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (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))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (exp real) Xa)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (zero_zero real)))))) ) 21.01/21.25 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real sin X)) (one_one real))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (power_1 X_a))) (= _let_0 (ti (fun X_a (fun (fun X_a (fun X_a X_a)) (fun X_a (fun nat X_a)))) _let_0))) ) 21.01/21.25 ( rat ) 21.01/21.25 ( int ) 21.01/21.25 ( (fun int int) ) 21.01/21.25 ( nat ) 21.01/21.25 ( bool ) 21.01/21.25 ( real ) 21.01/21.25 ( (fun nat real) ) 21.01/21.25 ( (fun real real) ) 21.01/21.25 ( (fun nat nat) ) 21.01/21.25 ( complex ) 21.01/21.25 ( (fun int bool) ) 21.01/21.25 ( (product_prod int int) ) 21.01/21.25 ( (fun (product_prod int int) int) ) 21.01/21.25 ( (fun bool bool) ) 21.01/21.25 ( (fun int (fun int bool)) ) 21.01/21.25 ( (fun nat bool) ) 21.01/21.25 ( (fun nat (fun nat bool)) ) 21.01/21.25 ( (fun (product_prod int int) bool) ) 21.01/21.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.01/21.25 ( (fun real bool) ) 21.01/21.25 ( code_code_numeral ) 21.01/21.25 ( (fun nat (product_prod int int)) ) 21.01/21.25 ( (product_prod real real) ) 21.01/21.25 ( (product_prod nat nat) ) 21.01/21.25 ( (fun (product_prod nat nat) bool) ) 21.01/21.25 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.01/21.25 ( (fun nat (product_prod nat nat)) ) 21.01/21.25 ( (fun int (fun int (fun int bool))) ) 21.01/21.25 ( (fun int real) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Z_5 $$unsorted)) (= (hBOOL (hAPP int bool nat_neg Z_5)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Z_5) (zero_zero int)))) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( min ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ( s ) 21.01/21.25 ( (hAPP int int (number_number_of int) min) ) 21.01/21.25 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( t ) 21.01/21.25 ( m1 ) 21.01/21.25 ( skv_4 ) 21.01/21.25 ( skv_5 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Wa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int bit1 Wa)) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Wa) _let_2)))))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((I_1 $$unsorted) (M $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) M)))) ) 21.01/21.25 ( (one_one nat), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$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) (one_one real))) (hAPP nat real (real_1 nat) (hAPP real nat natfloor X)))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (deriv real) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb real _let_0 real) _let_1) sin)) sin)) Xa) (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 real real cos Xa))) (hAPP real real sin Xa)))))))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ( skv_10 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (finite_finite_1 X_a))) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0))) ) 21.01/21.25 ( int ) 21.01/21.25 ( nat ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Wa $$unsorted)) (let ((_let_0 (number_number_of int))) (= (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 (hAPP int int bit0 Wa)))) (hBOOL (hAPP int bool nat_neg (hAPP int int _let_0 Wa))))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((A_3 $$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_3)) (hAPP complex _let_0 (at complex) A_3))))) ) 21.01/21.25 ( (zero_zero complex) ) 21.01/21.25 ( ii ) 21.01/21.25 ( (one_one complex) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (one_one real) (hAPP real real cos (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat real (real_1 nat) N))) pi))))) ) 21.01/21.25 ( (zero_zero nat) ) 21.01/21.25 ( (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((K $$unsorted)) (= (hBOOL (hAPP rat bool (iszero rat) (hAPP int rat (number_number_of rat) K))) (hBOOL (hAPP int bool (iszero int) (hAPP int int (number_number_of int) K)))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (trivial_limit X_a))) (= _let_0 (ti (fun (filter X_a) bool) _let_0))) ) 21.01/21.25 ( nat ) 21.01/21.25 ( real ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt Ya))) (hBOOL (hAPP real bool _let_0 Ya)))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) K) L)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int pred K)) L)))) ) 21.01/21.25 ( pls, min ) 21.01/21.25 ( pls, (zero_zero int) ) 21.01/21.25 ( (one_one int), t ) 21.01/21.25 ( min, pls ) 21.01/21.25 ( min, min ) 21.01/21.25 ( (zero_zero int), pls ) 21.01/21.25 ( (zero_zero int), (one_one int) ) 21.01/21.25 ( (zero_zero int), min ) 21.01/21.25 ( (zero_zero int), s ) 21.01/21.25 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero int), skv_4 ) 21.01/21.25 ( (zero_zero int), skv_5 ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (not (= Ma Na)) (or (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Na) Ma)))))) ) 21.01/21.25 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero nat), n ) 21.01/21.25 ( (zero_zero nat), tn ) 21.01/21.25 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.01/21.25 ( n, (zero_zero nat) ) 21.01/21.25 ( tn, (zero_zero nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_0 (product_prod_rec X_b X_c X_a))) (= _let_0 (ti (fun (fun X_b (fun X_c X_a)) (fun (product_prod X_b X_c) X_a)) _let_0))) ) 21.01/21.25 ( int, int, rat ) 21.01/21.25 ( int, int, int ) 21.01/21.25 ( int, int, (fun int int) ) 21.01/21.25 ( int, int, bool ) 21.01/21.25 ( int, int, (fun int bool) ) 21.01/21.25 ( int, int, (product_prod int int) ) 21.01/21.25 ( int, int, (fun (product_prod int int) int) ) 21.01/21.25 ( int, int, (fun bool bool) ) 21.01/21.25 ( int, int, (fun (product_prod int int) bool) ) 21.01/21.25 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 21.01/21.25 ( int, int, (fun (product_prod int int) (fun int bool)) ) 21.01/21.25 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 21.01/21.25 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 21.01/21.25 ( nat, nat, bool ) 21.01/21.25 ( nat, nat, (fun (product_prod nat nat) bool) ) 21.01/21.25 ( real, real, bool ) 21.01/21.25 ( (product_prod int int), (product_prod int int), bool ) 21.01/21.25 ( (product_prod nat nat), (product_prod nat nat), bool ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$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) Xa)) (one_one real))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (zero_zero real)))))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (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))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Xa)) (hBOOL (hAPP int bool nat_is_nat Xa))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( min ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ( s ) 21.01/21.25 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ( skv_4 ) 21.01/21.25 ( skv_5 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (zero_zero nat)) (hAPP real nat natfloor X))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_0))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (deriv real) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb real _let_0 real) _let_1) cos)) cos)) Xa) (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 min))) (hAPP real real cos Xa))) (hAPP real real sin Xa)))))))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ( skv_10 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_0 _let_0))) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_0 _let_3 (hAPP (fun real _let_1) (fun _let_0 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP _let_2 _let_0 (hAPP _let_0 (fun _let_2 _let_0) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP real _let_0 (power_power real) Xa))))))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) min) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (= (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) Na))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Na) (hAPP nat nat suc Ma)))))) ) 21.01/21.25 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero nat), n ) 21.01/21.25 ( (zero_zero nat), tn ) 21.01/21.25 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (= (hBOOL (hAPP quickcheck_code_int bool (hAPP quickcheck_code_int (fun quickcheck_code_int bool) (ord_less_eq quickcheck_code_int) Na) Ma)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP quickcheck_code_int int quickcheck_int_of Na)) (hAPP quickcheck_code_int int quickcheck_int_of Ma)))) ) 21.01/21.25 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun int bool))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong M) (zero_zero int)) M))) ) 21.01/21.25 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( s1 ) 21.01/21.25 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((K_4 $$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)))) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (hAPP real real cos X))) (let ((_let_3 (hAPP real real sin X))) (= (one_one real) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 _let_2) _let_2)) (hAPP real real (hAPP real _let_0 _let_1 _let_3) _let_3))))))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.01/21.25 ( skv_10 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sqrt Xa)) _let_0)))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted) (Xa $$unsorted) (Ya $$unsorted) (F $$unsorted)) (let ((_let_0 (product_prod X_a X_a))) (let ((_let_1 (fun _let_0 bool))) (= (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) Xa) Ya)) (hAPP (fun X_a nat) _let_1 (measure X_a) F))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP X_a nat F Xa)) (hAPP X_a nat F Ya)))))) ) 21.01/21.25 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)), (number_number_of nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((K $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) min) K)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) min) (hAPP int int bit0 K))))) ) 21.01/21.25 ( pls ) 21.01/21.25 ( (hAPP int int bit1 pls) ) 21.01/21.25 ( min ) 21.01/21.25 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.25 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling Xa)) (one_one nat))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) Xa) (one_one real)))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (one_one real) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( skv_10 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= X (hAPP complex real re (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y))) ) 21.01/21.25 ( (one_one real), (zero_zero real) ) 21.01/21.25 ( (zero_zero real), (one_one real) ) 21.01/21.25 ( (zero_zero real), (zero_zero real) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (= (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) Xa) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hBOOL (hAPP int bool (even_odd_even int) Xa))) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$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) Xa) (hAPP real real (uminus_uminus real) (hAPP real real sin Xa))))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (let ((_let_3 (hAPP real _let_1 _let_2 _let_0))) (= (and (or (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Ya) _let_0)) (hBOOL (hAPP real bool _let_3 Xa))) (or (hBOOL (hAPP real bool _let_3 Ya)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0)))) (hBOOL (hAPP real bool _let_3 (hAPP real real (hAPP real (fun real real) (inverse_divide real) Xa) Ya)))))))) ) 21.01/21.25 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (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))))))))) ) 21.01/21.25 ( (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))) ) 21.01/21.25 ( (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))) ) 21.01/21.25 ( (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))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N)) (hAPP nat nat suc M))) ) 21.01/21.25 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (= (zero_zero nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) M)))) ) 21.01/21.25 ( (one_one nat), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) sin_coeff)) (hAPP real _let_0 (power_power real) Xa))))))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) min) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((W $$unsorted)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) W) W)) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( min ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) w)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) v)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP int bool (even_odd_even int) Xa)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) Xa))) ) 21.01/21.25 ( (one_one int) ) 21.01/21.25 ( (zero_zero int) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (product_Pair X_a X_b))) (= _let_0 (ti (fun X_a (fun X_b (product_prod X_a X_b))) _let_0))) ) 21.01/21.25 ( int, int ) 21.01/21.25 ( int, (product_prod int int) ) 21.01/21.25 ( nat, nat ) 21.01/21.25 ( real, real ) 21.01/21.25 ( (product_prod int int), (product_prod int int) ) 21.01/21.25 ( quickcheck_code_int, quickcheck_code_int ) 21.01/21.25 ( code_code_numeral, code_code_numeral ) 21.01/21.25 ( (product_prod nat nat), (product_prod nat nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) Ya)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (minus_minus real) Xa) Ya)) (zero_zero real)))))) ) 21.01/21.25 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (member X_a))) (= _let_0 (ti (fun X_a (fun (fun X_a bool) bool)) _let_0))) ) 21.01/21.25 ( int ) 21.01/21.25 ( nat ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 int))) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP int real _let_0 Na)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 Ma)) (one_one real)))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Na) Ma)))) ) 21.01/21.25 ( (one_one int), t ) 21.01/21.25 ( min, pls ) 21.01/21.25 ( min, min ) 21.01/21.25 ( (zero_zero int), pls ) 21.01/21.25 ( (zero_zero int), (one_one int) ) 21.01/21.25 ( (zero_zero int), min ) 21.01/21.25 ( (zero_zero int), s ) 21.01/21.25 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (zero_zero int), skv_4 ) 21.01/21.25 ( (zero_zero int), skv_5 ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((R_3 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) R_3) (hAPP int real (real_1 int) (hAPP real int (archimedean_ceiling real) R_3)))) ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( skv_10 ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((T_1 $$unsorted)) (ord (filter T_1)) ) 21.01/21.25 ( nat ) 21.01/21.25 ( real ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP nat int (semiring_1_of_nat int) Na)) (zero_zero int))) (= (zero_zero nat) Na)) ) 21.01/21.25 ( (zero_zero nat) ) 21.01/21.25 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (one_one nat) ) 21.01/21.25 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.25 ( n ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$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))) (one_one real))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real 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))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (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))))) ) 21.01/21.25 ( (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)))) ) 21.01/21.25 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.25 ) 21.01/21.25 (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)))) ) 21.01/21.25 ( (one_one nat), (one_one nat) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP complex real re X))) (hAPP complex real (norm_norm complex) X))) ) 21.01/21.25 ( (zero_zero complex) ) 21.01/21.25 ( ii ) 21.01/21.25 ( (one_one complex) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((Ma $$unsorted) (X_1 $$unsorted) (Xa_1 $$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_1) Xa_1) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcongm Ma) X_1) Xa_1))))) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.25 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 21.01/21.25 ) 21.01/21.25 (instantiation (forall ((X $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) (hAPP real real cos X))) (one_one real))) ) 21.01/21.25 ( pi ) 21.01/21.25 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.25 ( (zero_zero real) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.25 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.01/21.26 ( skv_10 ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) Na)) (not (= _let_0 Na)))) ) 21.01/21.26 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( n ) 21.01/21.26 ( tn ) 21.01/21.26 ) 21.01/21.26 (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)))) ) 21.01/21.26 ( int, int ) 21.01/21.26 ( nat, nat ) 21.01/21.26 ) 21.01/21.26 (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 (hAPP int (fun int int) (minus_minus int) K) L)) (zero_zero int))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) L))))) ) 21.01/21.26 ( (hAPP nat int (hAPP 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) ) 21.01/21.26 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.01/21.26 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.01/21.26 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.26 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.01/21.26 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.26 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((Nat_4 $$unsorted)) (not (= (zero_zero nat) (hAPP nat nat suc Nat_4))) ) 21.01/21.26 ( (zero_zero nat) ) 21.01/21.26 ( (hAPP nat nat suc (zero_zero nat)) ) 21.01/21.26 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X $$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)) (hAPP real real sin X))) ) 21.01/21.26 ( pi ) 21.01/21.26 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( (zero_zero real) ) 21.01/21.26 ( (hAPP real 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))))) ) 21.01/21.26 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.26 ( (hAPP real real (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))))) ) 21.01/21.26 ( (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)))) ) 21.01/21.26 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (zero_zero int)) Z_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 X) (hAPP int int (hAPP int _let_0 (times_times int) Y) Z_1)))) (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int _let_0 (div_div int) X) Z_1)) Y)))))) ) 21.01/21.26 ( min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit0 (hAPP int int succ K_4)) (hAPP int int succ (hAPP int int bit1 K_4))) ) 21.01/21.26 ( pls ) 21.01/21.26 ( (hAPP int int bit1 pls) ) 21.01/21.26 ( min ) 21.01/21.26 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.26 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.26 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.01/21.26 ( (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)))))) ) 21.01/21.26 ( (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))))))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (= X (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N) X)) N))) ) 21.01/21.26 ( (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))) ) 21.01/21.26 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( (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))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101566 $$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_101566))) (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_101566))) ) 21.01/21.26 ( rat, (zero_zero rat) ) 21.01/21.26 ( int, pls ) 21.01/21.26 ( int, (one_one int) ) 21.01/21.26 ( int, min ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.26 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.26 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( nat, n ) 21.01/21.26 ( nat, tn ) 21.01/21.26 ( real, pi ) 21.01/21.26 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( real, (zero_zero real) ) 21.01/21.26 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( real, skv_2 ) 21.01/21.26 ( real, skv_9 ) 21.01/21.26 ( real, skv_12 ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101590 $$unsorted) (BOUND_VARIABLE_101591 $$unsorted) (BOUND_VARIABLE_101592 $$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_101592))) (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_101590) BOUND_VARIABLE_101592)) BOUND_VARIABLE_101591))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101590) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_101591) BOUND_VARIABLE_101592))))))) ) 21.01/21.26 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w) ) 21.01/21.26 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v) ) 21.01/21.26 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14) ) 21.01/21.26 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.26 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fact_fact nat))) (let ((_let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)))) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_1) (hAPP nat nat _let_0 N)) (hAPP nat nat _let_0 _let_1)))) ) 21.01/21.26 ( (one_one nat) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_1 _let_0) Na))) (= (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) (hAPP int (fun int bool) (ord_less int) _let_0))) (hAPP int (fun int bool) (hAPP _let_4 _let_4 (combc int int bool) _let_1) Na)))) (hAPP int nat nat_1 Na)))))))) ) 21.01/21.26 ( pls ) 21.01/21.26 ( (one_one int) ) 21.01/21.26 ( min ) 21.01/21.26 ( (zero_zero int) ) 21.01/21.26 ( s ) 21.01/21.26 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( t ) 21.01/21.26 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.26 ( skv_4 ) 21.01/21.26 ( skv_5 ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101653 $$unsorted) (BOUND_VARIABLE_101654 $$unsorted) (BOUND_VARIABLE_101655 $$unsorted)) (let ((_let_0 (plus_plus X_a))) (let ((_let_1 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_101653))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) _let_0 BOUND_VARIABLE_101654) BOUND_VARIABLE_101655)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_101654)) (hAPP X_a X_a _let_1 BOUND_VARIABLE_101655)))))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.26 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.01/21.26 ( int, sa, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.26 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, r, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.26 ( int, skv_13, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.26 ( int, skv_19, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101678 $$unsorted) (BOUND_VARIABLE_101679 $$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 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_101679)))) (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_101678) BOUND_VARIABLE_101679)) _let_2)) (and (or (and (= _let_2 (ti X_a BOUND_VARIABLE_101678)) _let_3) (and (not _let_3) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101678) _let_2)))) (not (= (zero_zero nat) BOUND_VARIABLE_101679))))))))) ) 21.01/21.26 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101738 $$unsorted) (BOUND_VARIABLE_101739 $$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_101739))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_101738))) (or (not (division_ring X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_101739)) (= _let_0 (ti X_a BOUND_VARIABLE_101738)) (= (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_101739) BOUND_VARIABLE_101738))) _let_6) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) _let_6)))))))))) ) 21.01/21.26 ( 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)))) ) 21.01/21.26 ( 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) ) 21.01/21.26 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.01/21.26 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.01/21.26 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.01/21.26 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.01/21.26 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.01/21.26 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.01/21.26 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.26 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( nat, (one_one nat), (one_one nat) ) 21.01/21.26 ) 21.01/21.26 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101805 $$unsorted) (BOUND_VARIABLE_101806 $$unsorted) (BOUND_VARIABLE_101807 $$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_101806)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101806) _let_2)))) (let ((_let_7 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) BOUND_VARIABLE_101807) BOUND_VARIABLE_101806))) (or (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_3 _let_7) BOUND_VARIABLE_101805))) (or _let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_2) BOUND_VARIABLE_101807))))) (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_101805) _let_7)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_101805) BOUND_VARIABLE_101806)) BOUND_VARIABLE_101807)))))))))))) ) 21.01/21.26 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.26 ( int, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( 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))) ) 21.01/21.27 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((X $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP real int (archimedean_ceiling real) X)) A_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (hAPP int real (real_1 int) A_1)))) ) 21.01/21.27 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((A_3 $$unsorted) (Xa $$unsorted)) (let ((_let_0 (uminus_uminus int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (let ((_let_4 (hAPP int nat nat_1 Xa))) (or (not (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) Xa) zOdd))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) Xa))) (= (hAPP nat int (hAPP int _let_2 _let_3 (hAPP int int _let_0 A_3)) _let_4) (hAPP int int _let_0 (hAPP nat int (hAPP int _let_2 _let_3 A_3) _let_4))))))))) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_101937 $$unsorted) (BOUND_VARIABLE_101938 $$unsorted) (BOUND_VARIABLE_101939 $$unsorted) (BOUND_VARIABLE_101940 $$unsorted) (BOUND_VARIABLE_101941 $$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_101941))) (or (not (semiri456707255roduct X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_101941)) (not (= (ti X_a BOUND_VARIABLE_101940) (ti X_a BOUND_VARIABLE_101939))) (= (ti X_a BOUND_VARIABLE_101938) (ti X_a BOUND_VARIABLE_101937)) (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101940) (hAPP X_a X_a _let_2 BOUND_VARIABLE_101938)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_101939) (hAPP X_a X_a _let_2 BOUND_VARIABLE_101937)))))))) ) 21.01/21.27 ( int, pls, pls, pls, pls, pls ) 21.01/21.27 ( int, pls, w, w, w, w ) 21.01/21.27 ( int, min, min, min, min, min ) 21.01/21.27 ( int, min, s, s, s, s ) 21.01/21.27 ( int, s, min, min, min, min ) 21.01/21.27 ( int, s1, s1, s1, s1, s1 ) 21.01/21.27 ( int, s1, v, v, v, v ) 21.01/21.27 ( int, m, r, r, r, r ) 21.01/21.27 ( int, t, t, t, t, t ) 21.01/21.27 ( int, t, y, y, y, y ) 21.01/21.27 ( int, v, s1, s1, s1, s1 ) 21.01/21.27 ( int, w, pls, pls, pls, pls ) 21.01/21.27 ( int, y, t, t, t, t ) 21.01/21.27 ( int, sa, m1, m1, m1, m1 ) 21.01/21.27 ( int, x, x, x, x, x ) 21.01/21.27 ( int, x, skv_14, skv_14, skv_14, skv_14 ) 21.01/21.27 ( int, r, m, m, m, m ) 21.01/21.27 ( int, r, r, r, r, r ) 21.01/21.27 ( int, m1, sa, sa, sa, sa ) 21.01/21.27 ( int, m1, m1, m1, m1, m1 ) 21.01/21.27 ( int, skv_14, x, x, x, x ) 21.01/21.27 ( int, skv_20, skv_20, skv_20, skv_20, skv_20 ) 21.01/21.27 ( (fun int int), bit1, (fact_fact int), (fact_fact int), (fact_fact int), (fact_fact int) ) 21.01/21.27 ( (fun int int), bit0, pred, pred, pred, pred ) 21.01/21.27 ( (fun int int), succ, succ, succ, succ, succ ) 21.01/21.27 ( (fun int int), succ, zfact, zfact, zfact, zfact ) 21.01/21.27 ( (fun int int), pred, bit0, bit0, bit0, bit0 ) 21.01/21.27 ( (fun int int), pred, pred, pred, pred, pred ) 21.01/21.27 ( (fun int int), (fact_fact int), bit1, bit1, bit1, bit1 ) 21.01/21.27 ( (fun int int), (fact_fact int), (fact_fact int), (fact_fact int), (fact_fact int), (fact_fact int) ) 21.01/21.27 ( (fun int int), zfact, succ, succ, succ, succ ) 21.01/21.27 ( nat, n, n, n, n, n ) 21.01/21.27 ( nat, n, tn, tn, tn, tn ) 21.01/21.27 ( nat, tn, n, n, n, n ) 21.01/21.27 ( bool, fTrue, fTrue, fTrue, fTrue, fTrue ) 21.01/21.27 ( bool, fTrue, fFalse, fFalse, fFalse, fFalse ) 21.01/21.27 ( bool, fFalse, fTrue, fTrue, fTrue, fTrue ) 21.01/21.27 ( real, pi, pi, pi, pi, pi ) 21.01/21.27 ( (fun nat real), (real_1 nat), (real_1 nat), (real_1 nat), (real_1 nat), (real_1 nat) ) 21.01/21.27 ( (fun nat real), cos_coeff, sin_coeff, sin_coeff, sin_coeff, sin_coeff ) 21.01/21.27 ( (fun nat real), sin_coeff, cos_coeff, cos_coeff, cos_coeff, cos_coeff ) 21.01/21.27 ( (fun nat real), sin_coeff, sin_coeff, sin_coeff, sin_coeff, sin_coeff ) 21.01/21.27 ( (fun real real), sin, sin, sin, sin, sin ) 21.01/21.27 ( (fun real real), sin, ln, ln, ln, ln ) 21.01/21.27 ( (fun real real), cos, cos, cos, cos, cos ) 21.01/21.27 ( (fun real real), cos, arccos, arccos, arccos, arccos ) 21.01/21.27 ( (fun real real), sqrt, arcsin, arcsin, arcsin, arcsin ) 21.01/21.27 ( (fun real real), tan, arctan, arctan, arctan, arctan ) 21.01/21.27 ( (fun real real), ln, sin, sin, sin, sin ) 21.01/21.27 ( (fun real real), arctan, tan, tan, tan, tan ) 21.01/21.27 ( (fun real real), arctan, arctan, arctan, arctan, arctan ) 21.01/21.27 ( (fun real real), arcsin, sqrt, sqrt, sqrt, sqrt ) 21.01/21.27 ( (fun real real), arcsin, arcsin, arcsin, arcsin, arcsin ) 21.01/21.27 ( (fun real real), arccos, cos, cos, cos, cos ) 21.01/21.27 ( (fun nat nat), suc, suc, suc, suc, suc ) 21.01/21.27 ( (fun nat nat), suc, fact, fact, fact, fact ) 21.01/21.27 ( (fun nat nat), (fact_fact nat), (fact_fact nat), (fact_fact nat), (fact_fact nat), (fact_fact nat) ) 21.01/21.27 ( (fun nat nat), nat_size, nat_size, nat_size, nat_size, nat_size ) 21.01/21.27 ( (fun nat nat), nat_size, (size_size nat), (size_size nat), (size_size nat), (size_size nat) ) 21.01/21.27 ( (fun nat nat), (size_size nat), nat_size, nat_size, nat_size, nat_size ) 21.01/21.27 ( (fun nat nat), fact, suc, suc, suc, suc ) 21.01/21.27 ( (filter nat), sequentially, sequentially, sequentially, sequentially, sequentially ) 21.01/21.27 ( (fun int (fun int rat)), fract, fract, fract, fract, fract ) 21.01/21.27 ( complex, ii, ii, ii, ii, ii ) 21.01/21.27 ( (fun int bool), zOdd, zOdd, zOdd, zOdd, zOdd ) 21.01/21.27 ( (fun int bool), zOdd, zprime, zprime, zprime, zprime ) 21.01/21.27 ( (fun int bool), zprime, zOdd, zOdd, zOdd, zOdd ) 21.01/21.27 ( (fun int bool), zEven, nat_neg, nat_neg, nat_neg, nat_neg ) 21.01/21.27 ( (fun int bool), nat_neg, zEven, zEven, zEven, zEven ) 21.01/21.27 ( (fun int bool), nat_neg, nat_neg, nat_neg, nat_neg, nat_neg ) 21.01/21.27 ( (fun int bool), nat_is_nat, nat_is_nat, nat_is_nat, nat_is_nat, nat_is_nat ) 21.01/21.27 ( (fun int bool), nat_is_nat, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 21.01/21.27 ( (fun int bool), (even_odd_even int), (even_odd_even int), (even_odd_even int), (even_odd_even int), (even_odd_even int) ) 21.01/21.27 ( (fun int bool), twoSqu1091635170sum2sq, nat_is_nat, nat_is_nat, nat_is_nat, nat_is_nat ) 21.01/21.27 ( (fun int (fun int int)), legacy_zgcd, z3div, z3div, z3div, z3div ) 21.01/21.27 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int), (gcd_gcd int), (gcd_gcd int), (gcd_gcd int) ) 21.01/21.27 ( (fun int (fun int int)), (gcd_gcd int), multInv, multInv, multInv, multInv ) 21.01/21.27 ( (fun int (fun int int)), inv, int_gcd, int_gcd, int_gcd, int_gcd ) 21.01/21.27 ( (fun int (fun int int)), multInv, (gcd_gcd 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21.01/21.27 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size, code_c271388182l_size, code_c271388182l_size, code_c271388182l_size ) 21.01/21.27 ( (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 ) 21.01/21.27 ( (fun code_code_numeral int), code_int_of, code_int_of, code_int_of, code_int_of, code_int_of ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((N $$unsorted)) (= (zero_zero real) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (times_times real) pi) (hAPP nat real (real_1 nat) N)))) ) 21.01/21.27 ( (zero_zero nat) ) 21.01/21.27 ( (one_one nat) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((Xa $$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 Xa))) ) 21.01/21.27 ( pls, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 21.01/21.27 ( pls, (hAPP int (fun int bool) (ord_less int) pls) ) 21.01/21.27 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min) ) 21.01/21.27 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 21.01/21.27 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.27 ( (one_one int), nat_neg ) 21.01/21.27 ( (one_one int), nat_is_nat ) 21.01/21.27 ( (one_one int), (even_odd_even int) ) 21.01/21.27 ( min, (hAPP int (fun int bool) (ord_less int) min) ) 21.01/21.27 ( min, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 21.01/21.27 ( min, (hAPP int (fun int bool) (ord_less int) pls) ) 21.01/21.27 ( min, (hAPP int (fun int bool) (ord_less_eq int) min) ) 21.01/21.27 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min) ) 21.01/21.27 ( (zero_zero int), nat_neg ) 21.01/21.27 ( (zero_zero int), nat_is_nat ) 21.01/21.27 ( (zero_zero int), (even_odd_even int) ) 21.01/21.27 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5)) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5) ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))) ) 21.01/21.27 ( (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)) ) 21.01/21.27 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 21.01/21.27 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 21.01/21.27 ( (hAPP int int (number_number_of int) min), (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)))) ) 21.01/21.27 ( (hAPP int int (number_number_of int) min), nat_neg ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) m1) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))) ) 21.01/21.27 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))) ) 21.01/21.27 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 21.01/21.27 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 21.01/21.27 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 21.01/21.27 ( (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)) ) 21.01/21.27 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))), twoSqu1091635170sum2sq ) 21.01/21.27 ( (hAPP 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)), (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)))) ) 21.01/21.27 ( (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 ) 21.01/21.27 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))), twoSqu1091635170sum2sq ) 21.01/21.27 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.27 ( skv_5, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((N $$unsorted)) (= (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) N)) (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP nat real (real_1 nat) N)))) ) 21.01/21.27 ( (zero_zero nat) ) 21.01/21.27 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( (one_one nat) ) 21.01/21.27 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.27 ( n ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102220 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) BOUND_VARIABLE_102220) (one_one X_a)) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_102220))) ) 21.01/21.27 ( complex, (hAPP int real (number_number_of real) min) ) 21.01/21.27 ( complex, pi ) 21.01/21.27 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (not (hBOOL (hAPP nat bool prime P_5))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (zero_zero nat)) X))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 X) P_5))) (hBOOL (hAPP nat bool (hAPP nat _let_0 coprime X) P_5))))) ) 21.01/21.27 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.27 ( (zero_zero nat), n ) 21.01/21.27 ( (zero_zero nat), tn ) 21.01/21.27 ) 21.01/21.27 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102385 $$unsorted) (BOUND_VARIABLE_102386 $$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_102386) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_102385) _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_102386) BOUND_VARIABLE_102385)) _let_3))))))) ) 21.01/21.27 ( 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)))) ) 21.01/21.27 ( 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) ) 21.01/21.27 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.01/21.27 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.01/21.27 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.27 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.27 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.01/21.27 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.01/21.27 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.27 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.01/21.27 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.01/21.27 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.01/21.27 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.01/21.27 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.01/21.27 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( nat, (one_one nat), (one_one nat) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102416 $$unsorted) (BOUND_VARIABLE_102417 $$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_102417) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_102416) _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_102417) BOUND_VARIABLE_102416)) _let_3))))))) ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.01/21.28 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 21.01/21.28 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 21.01/21.28 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.01/21.28 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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 F A_3) B_2))) (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_3) B_2)))))) ) 21.01/21.28 ( int, int, (ord_less int), (one_one int), t ) 21.01/21.28 ( int, int, (ord_less int), min, min ) 21.01/21.28 ( int, int, (ord_less int), min, (zero_zero int) ) 21.01/21.28 ( int, int, (ord_less int), (zero_zero int), pls ) 21.01/21.28 ( int, int, (ord_less int), (zero_zero int), (one_one int) ) 21.01/21.28 ( int, int, (ord_less int), (zero_zero int), min ) 21.01/21.28 ( int, int, (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))) ) 21.01/21.28 ( int, int, (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( int, int, (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( int, int, (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( int, int, (ord_less_eq int), (one_one int), t ) 21.01/21.28 ( int, int, (ord_less_eq int), min, pls ) 21.01/21.28 ( int, int, (ord_less_eq int), min, min ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), pls ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), min ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), s ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), skv_4 ) 21.01/21.28 ( int, int, (ord_less_eq int), (zero_zero int), skv_5 ) 21.01/21.28 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( 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) ) 21.01/21.28 ( 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) (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)) ) 21.01/21.28 ( int, int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.01/21.28 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( nat, nat, (ord_less nat), (zero_zero nat), n ) 21.01/21.28 ( nat, nat, (ord_less nat), (zero_zero nat), tn ) 21.01/21.28 ( real, real, (ord_less real), pi, (zero_zero real) ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( real, real, (ord_less real), (zero_zero real), pi ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 21.01/21.28 ( real, real, (ord_less real), (zero_zero real), skv_9 ) 21.01/21.28 ( real, real, (ord_less real), (zero_zero real), skv_12 ) 21.01/21.28 ( 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) ) 21.01/21.28 ( 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) ) 21.01/21.28 ( 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 ) 21.01/21.28 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( real, real, (ord_less_eq real), (zero_zero real), skv_10 ) 21.01/21.28 ( real, real, (ord_less_eq real), (zero_zero real), skv_11 ) 21.01/21.28 ( real, real, (ord_less_eq real), (zero_zero real), skv_15 ) 21.01/21.28 ( real, real, (ord_less_eq real), (zero_zero real), skv_18 ) 21.01/21.28 ( 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) ) 21.01/21.28 ( real, real, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( real, (fun nat real), (sums real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))), (one_one real) ) 21.01/21.28 ( (filter nat), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 21.01/21.28 ( (fun int bool), int, (member int), (one_one int), zEven ) 21.01/21.28 ( (fun int bool), (fun int nat), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 21.01/21.28 ( (fun nat bool), (fun nat int), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 21.01/21.28 ( (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))))) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun real bool))) (let ((_let_5 (fun nat _let_2))) (let ((_let_6 (fun _let_0 _let_0))) (let ((_let_7 (combs nat real real))) (let ((_let_8 (hAPP (fun real _let_2) (fun _let_0 _let_5) (combb real _let_2 nat) (times_times real)))) (let ((_let_9 (fun real _let_0))) (let ((_let_10 (fun (fun nat nat) _let_0))) (let ((_let_11 (combb nat real nat))) (let ((_let_12 (suminf real))) (let ((_let_13 (fun _let_9 _let_9))) (let ((_let_14 (combb _let_0 _let_0 real))) (let ((_let_15 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)))))) (let ((_let_16 (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_17 (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_16)) (one_one nat)))) (let ((_let_18 (fun real _let_10))) (or (not (hBOOL (hAPP real bool (hAPP real _let_4 (ord_less real) (hAPP real real (abs_abs real) Xa)) _let_3))) (hBOOL (hAPP real bool (hAPP real _let_4 (hAPP _let_2 (fun real _let_4) (deriv real) (hAPP _let_9 _let_2 (hAPP (fun _let_0 real) (fun _let_9 _let_2) (combb _let_0 real real) _let_12) (hAPP _let_9 _let_9 (hAPP _let_6 _let_13 _let_14 _let_15) (hAPP _let_9 _let_9 (hAPP _let_6 _let_13 _let_14 (hAPP _let_5 _let_6 _let_7 (hAPP _let_0 _let_5 _let_8 (hAPP _let_0 _let_0 (hAPP _let_2 _let_6 (combb real real nat) (hAPP real _let_2 (inverse_divide real) _let_3)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_10 _let_11 (real_1 nat)) _let_17))))) (hAPP (fun nat nat) _let_9 (hAPP _let_18 (fun (fun nat nat) _let_9) (combc real (fun nat nat) _let_0) (hAPP _let_9 _let_18 (hAPP (fun _let_0 _let_10) (fun _let_9 _let_18) (combb _let_0 _let_10 real) _let_11) _let_1)) _let_17))))) Xa) (hAPP _let_0 real _let_12 (hAPP _let_0 _let_0 _let_15 (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_10 _let_11 (hAPP real _let_0 _let_1 Xa)) _let_16))))))))))))))))))))))))) ) 21.01/21.28 ( (hAPP int real (number_number_of real) min) ) 21.01/21.28 ( (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)))) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (one_one nat))))) ) 21.01/21.28 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( n ) 21.01/21.28 ( tn ) 21.01/21.28 ( (hAPP int nat nat_1 t) ) 21.01/21.28 ) 21.01/21.28 (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))) ) 21.01/21.28 ( int, nat ) 21.01/21.28 ( nat, int ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102537 $$unsorted) (BOUND_VARIABLE_102538 $$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_102538)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_102537)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_102538)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_102537) BOUND_VARIABLE_102538))))))) ) 21.01/21.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.28 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( 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))))))))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ( 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))) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_102577 $$unsorted) (BOUND_VARIABLE_102578 $$unsorted) (BOUND_VARIABLE_102579 $$unsorted) (BOUND_VARIABLE_102580 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ord X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_102578 BOUND_VARIABLE_102579)) BOUND_VARIABLE_102580))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_102577) BOUND_VARIABLE_102579))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) Y_1) X_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_102578 Y_1)) (hAPP X_b X_a BOUND_VARIABLE_102578 X_1)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_102578 BOUND_VARIABLE_102577)) BOUND_VARIABLE_102580)))) ) 21.01/21.28 ( int, int, (one_one 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)))), (hAPP int int (abs_abs int) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, int, min, bit0, pls, pls ) 21.01/21.28 ( int, int, (zero_zero int), bit0, pls, (one_one int) ) 21.01/21.28 ( int, int, s, bit1, min, pls ) 21.01/21.28 ( int, int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), bit1, min, min ) 21.01/21.28 ( int, int, t, (fact_fact int), (zero_zero int), t ) 21.01/21.28 ( int, int, m1, bit0, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.28 ( int, int, skv_4, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (abs_abs int) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, real, skv_5, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 21.01/21.28 ( nat, int, (zero_zero nat), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (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))) ) 21.01/21.28 ( real, real, pi, cos, skv_10, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( 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)))), (hAPP 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))) ) 21.01/21.28 ( real, real, (one_one real), cos, skv_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)))) ) 21.01/21.28 ( real, real, (zero_zero real), cos, skv_10, pi ) 21.01/21.28 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_10, skv_11 ) 21.01/21.28 ( 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))))), cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 21.01/21.28 ( 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_10, skv_10 ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N)) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N))))) ) 21.01/21.28 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( (zero_zero nat), n ) 21.01/21.28 ( (zero_zero nat), tn ) 21.01/21.28 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N))) (= M (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) M) N))) ) 21.01/21.28 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( (zero_zero nat), n ) 21.01/21.28 ( (zero_zero nat), tn ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102626 $$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) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_102626) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_102626) BOUND_VARIABLE_102626)))) ) 21.01/21.28 ( int, (one_one int) ) 21.01/21.28 ( 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)))) ) 21.01/21.28 ( 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) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.28 ( int, (hAPP int int (abs_abs int) w) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.01/21.28 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.28 ( int, (hAPP int int (abs_abs int) v) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( int, (hAPP int int (abs_abs int) skv_14) ) 21.01/21.28 ( int, (hAPP int int (abs_abs int) skv_20) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( nat, (one_one nat) ) 21.01/21.28 ( real, pi ) 21.01/21.28 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.01/21.28 ( complex, (hAPP real complex (of_real complex) pi) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (B_2 $$unsorted) (F $$unsorted) (Xa $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_b bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) Xa) A_2))) (not (= (ti X_b B_2) (hAPP X_a X_b F Xa))) (hBOOL (hAPP _let_1 bool (hAPP X_b (fun _let_1 bool) (member X_b) B_2) (hAPP _let_0 _let_1 (hAPP (fun X_a X_b) (fun _let_0 _let_1) (image X_a X_b) F) A_2)))))) ) 21.01/21.28 ( int, int, s1, (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int), zEven ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X $$unsorted)) (= (hAPP complex real re (hAPP complex complex cnj X)) (hAPP complex real re X)) ) 21.01/21.28 ( (zero_zero complex) ) 21.01/21.28 ( ii ) 21.01/21.28 ( (one_one complex) ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (= (hAPP real real cos X_1) (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) cos_coeff)) (hAPP real _let_0 (power_power real) X_1))))))) ) 21.01/21.28 ( (hAPP int real (number_number_of real) min) ) 21.01/21.28 ( pi ) 21.01/21.28 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.28 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.28 ( (zero_zero real) ) 21.01/21.28 ( (hAPP real 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))))) ) 21.01/21.28 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.01/21.28 ( (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)))) ) 21.01/21.28 ( (hAPP real real (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))))) ) 21.01/21.28 ( (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)))) ) 21.01/21.28 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.01/21.28 ( skv_10 ) 21.01/21.28 ) 21.01/21.28 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102716 $$unsorted) (BOUND_VARIABLE_102717 $$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 (ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_102716)) BOUND_VARIABLE_102717) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_102716) BOUND_VARIABLE_102717))))))) ) 21.01/21.28 ( int, pls, (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))) m1))) ) 21.01/21.28 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.28 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.28 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.28 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.01/21.28 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 21.01/21.28 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.01/21.28 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.01/21.28 ( int, y, v ) 21.01/21.28 ( int, y, w ) 21.01/21.28 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, sa, v ) 21.01/21.28 ( int, sa, w ) 21.01/21.28 ( int, x, v ) 21.01/21.28 ( int, x, w ) 21.01/21.28 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.01/21.28 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.28 ( int, r, v ) 21.01/21.28 ( int, r, w ) 21.01/21.28 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 21.01/21.28 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 21.01/21.28 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 21.01/21.28 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.28 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.01/21.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.01/21.29 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.29 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.01/21.29 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.01/21.29 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.01/21.29 ( 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)))))) ) 21.01/21.29 ( 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 ) 21.01/21.29 ( complex, ii, ii ) 21.01/21.29 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 21.01/21.29 ( 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 ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_102766 $$unsorted) (BOUND_VARIABLE_102767 $$unsorted) (BOUND_VARIABLE_102768 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_b))) (or (not (comm_semiring_1 X_b)) (not (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) BOUND_VARIABLE_102767))) (= _let_1 (hAPP _let_0 X_b (hAPP (fun X_a X_b) (fun _let_0 X_b) (big_co302546470etprod X_a X_b) BOUND_VARIABLE_102766) BOUND_VARIABLE_102767)) (not (= _let_1 (hAPP X_a X_b BOUND_VARIABLE_102766 BOUND_VARIABLE_102768))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_102768) BOUND_VARIABLE_102767)))))) ) 21.01/21.29 ( nat, bool, (even_odd_even nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)), (zero_zero nat) ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_a $$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)))) ) 21.01/21.29 ( rat ) 21.01/21.29 ( int ) 21.01/21.29 ( (fun int int) ) 21.01/21.29 ( nat ) 21.01/21.29 ( bool ) 21.01/21.29 ( real ) 21.01/21.29 ( (fun nat real) ) 21.01/21.29 ( (fun real real) ) 21.01/21.29 ( (filter nat) ) 21.01/21.29 ( complex ) 21.01/21.29 ( (fun int bool) ) 21.01/21.29 ( (product_prod int int) ) 21.01/21.29 ( (fun (product_prod int int) int) ) 21.01/21.29 ( (fun int (fun int bool)) ) 21.01/21.29 ( (fun nat bool) ) 21.01/21.29 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.01/21.29 ( (fun (product_prod int int) bool) ) 21.01/21.29 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.01/21.29 ( (fun real bool) ) 21.01/21.29 ( quickcheck_code_int ) 21.01/21.29 ( code_code_numeral ) 21.01/21.29 ( (product_prod real real) ) 21.01/21.29 ( (filter real) ) 21.01/21.29 ( (product_prod nat nat) ) 21.01/21.29 ( (fun nat rat) ) 21.01/21.29 ( (fun int (fun int (fun int bool))) ) 21.01/21.29 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.01/21.29 ( (fun int real) ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102859 $$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_102859)))) (hBOOL (hAPP X_a bool _let_0 (hAPP int X_a _let_1 BOUND_VARIABLE_102859))))))) ) 21.01/21.29 ( int, pls ) 21.01/21.29 ( int, (hAPP int int bit1 pls) ) 21.01/21.29 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.29 ( nat, pls ) 21.01/21.29 ( nat, (hAPP int int bit1 pls) ) 21.01/21.29 ( real, (hAPP int int bit1 pls) ) 21.01/21.29 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.01/21.29 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.01/21.29 ( complex, (hAPP int int bit1 pls) ) 21.01/21.29 ( quickcheck_code_int, pls ) 21.01/21.29 ( code_code_numeral, pls ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102881 $$unsorted) (BOUND_VARIABLE_102882 $$unsorted)) (let ((_let_0 (exp X_a))) (let ((_let_1 (fun X_a X_a))) (or (not (banach X_a)) (not (real_normed_field X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_102881)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_102882)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 (minus_minus X_a) BOUND_VARIABLE_102881) BOUND_VARIABLE_102882)))))) ) 21.01/21.29 ( 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) ) 21.01/21.29 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.29 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.29 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.29 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.01/21.29 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.01/21.29 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.01/21.29 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.01/21.29 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.01/21.29 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.01/21.29 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.01/21.29 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.01/21.29 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.01/21.29 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102897 $$unsorted) (BOUND_VARIABLE_102898 $$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 _let_3 BOUND_VARIABLE_102898)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_102897))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102897) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_102898) _let_2)))) (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_102897) BOUND_VARIABLE_102898))))))))) ) 21.01/21.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.29 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.01/21.29 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.01/21.29 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.01/21.29 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.01/21.29 ( 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))))))))) ) 21.01/21.29 ( 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))) ) 21.01/21.29 ( 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))) ) 21.01/21.29 ( 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))) ) 21.01/21.29 ) 21.01/21.29 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_3 $$unsorted) (B_2 $$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))) (= (and (= (ti X_a A_8) (ti X_a A_3)) (= (ti X_b B_2) (ti X_b B_7))) (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_3) B_2) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_8) B_7)))))) ) 21.01/21.29 ( int, int, pls, skv_20, pls, skv_20 ) 21.01/21.29 ( int, int, min, y, min, t ) 21.01/21.29 ( int, int, s, x, s, x ) 21.01/21.29 ( int, int, s, x, s, skv_14 ) 21.01/21.29 ( int, int, t, skv_20, t, skv_20 ) 21.01/21.29 ( int, int, v, r, v, m ) 21.01/21.29 ( int, int, v, r, v, r ) 21.01/21.29 ( int, int, x, skv_20, x, skv_20 ) 21.01/21.29 ( int, int, m1, skv_20, m1, skv_20 ) 21.01/21.29 ( int, int, skv_20, skv_20, skv_20, skv_20 ) 21.01/21.29 ( int, (fun int int), pred, s1, pred, s1 ) 21.01/21.29 ( int, (fun int int), pred, s1, pred, v ) 21.01/21.29 ( int, nat, tn, skv_20, tn, skv_20 ) 21.01/21.29 ( int, bool, fFalse, skv_20, fFalse, skv_20 ) 21.01/21.29 ( int, real, pi, skv_20, pi, skv_20 ) 21.01/21.29 ( int, (fun real real), cos, pls, cos, pls ) 21.01/21.29 ( int, (fun real real), cos, pls, cos, w ) 21.01/21.29 ( int, (fun real real), tan, sa, tan, m1 ) 21.01/21.29 ( int, (fun real real), arcsin, skv_20, arcsin, skv_20 ) 21.01/21.29 ( int, (fun nat nat), (fact_fact nat), skv_20, (fact_fact nat), skv_20 ) 21.01/21.29 ( int, (filter nat), sequentially, skv_20, sequentially, skv_20 ) 21.01/21.29 ( int, (fun int bool), zEven, skv_20, zEven, skv_20 ) 21.01/21.29 ( int, (fun int bool), twoSqu1091635170sum2sq, s, twoSqu1091635170sum2sq, min ) 21.01/21.29 ( int, (fun int (fun int int)), legacy_zgcd, skv_20, legacy_zgcd, skv_20 ) 21.01/21.29 ( int, (fun int (fun int int)), inv, skv_20, inv, skv_20 ) 21.01/21.29 ( int, (fun (product_prod int int) int), twoSqu1094008024sum2sq, min, twoSqu1094008024sum2sq, min ) 21.01/21.29 ( int, (fun (product_prod int int) int), twoSqu1094008024sum2sq, min, twoSqu1094008024sum2sq, s ) 21.01/21.29 ( int, (fun bool bool), fNot, m, fNot, r ) 21.01/21.29 ( int, (fun bool (fun bool bool)), fimplies, skv_20, fimplies, skv_20 ) 21.01/21.29 ( int, (fun int (fun int bool)), d22set, skv_20, d22set, skv_20 ) 21.01/21.29 ( int, (fun nat bool), prime, skv_20, prime, skv_20 ) 21.01/21.29 ( int, (fun real complex), cis, skv_20, cis, skv_20 ) 21.01/21.29 ( int, (fun nat (fun nat bool)), coprime, w, coprime, pls ) 21.01/21.29 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, skv_20, negDivAlg_rel, skv_20 ) 21.01/21.29 ( int, (fun int (fun (product_prod int int) bool)), int_ge_less_than, skv_20, int_ge_less_than, skv_20 ) 21.01/21.29 ( int, (fun nat (fun real real)), root, v, root, s1 ) 21.01/21.29 ( int, (fun real (fun real real)), powr, skv_20, powr, skv_20 ) 21.01/21.29 ( int, (fun complex complex), expi, skv_20, expi, skv_20 ) 21.01/21.29 ( int, (fun int nat), phi, skv_20, phi, skv_20 ) 21.01/21.29 ( int, (fun complex real), re, t, re, t ) 21.01/21.29 ( int, (fun complex real), re, t, re, y ) 21.01/21.29 ( int, (fun int (fun int (product_prod int int))), posDivAlg, skv_20, posDivAlg, skv_20 ) 21.01/21.29 ( int, (fun int (fun int (product_prod int int))), norm_frac, skv_14, norm_frac, x ) 21.01/21.29 ( int, (fun (product_prod nat nat) bool), pred_nat, skv_20, pred_nat, skv_20 ) 21.01/21.29 ( int, (fun (fun int bool) int), (the int), skv_20, (the int), skv_20 ) 21.01/21.29 ( int, (fun nat (fun nat (product_prod nat nat))), divmod_nat, skv_20, divmod_nat, skv_20 ) 21.01/21.29 ( int, (fun real (fun real complex)), complex_1, skv_20, complex_1, skv_20 ) 21.01/21.29 ( int, (fun int (fun int (fun int bool))), zcong, skv_20, zcong, skv_20 ) 21.01/21.29 ( int, (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, skv_20, pair_less, skv_20 ) 21.01/21.29 ( int, (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, skv_20, nat_gcd_rel, skv_20 ) 21.01/21.29 ( int, (fun (product_prod int int) rat), frct, skv_20, frct, skv_20 ) 21.01/21.29 ( int, (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), skv_20, (ord_gr676655987ssThan nat), skv_20 ) 21.01/21.29 ( int, (fun int (fun int (fun int (fun int bool)))), multInvPair, m1, multInvPair, sa ) 21.01/21.29 ( int, (fun int (fun int (fun int (fun int bool)))), multInvPair, m1, multInvPair, m1 ) 21.01/21.29 ( int, (fun int (fun nat nat)), nat_aux, skv_20, nat_aux, skv_20 ) 21.01/21.29 ( int, (fun nat (fun nat (product_prod int int))), bezw, skv_20, bezw, skv_20 ) 21.01/21.29 ( int, (fun int (list int)), quickc666637781d_zero, skv_20, quickc666637781d_zero, skv_20 ) 21.01/21.29 ( int, (fun quickcheck_code_int nat), quickcheck_nat_of, skv_20, quickcheck_nat_of, skv_20 ) 21.01/21.29 ( int, (fun (fun real bool) real), (complete_Sup_Sup real), skv_20, (complete_Sup_Sup real), skv_20 ) 21.01/21.29 ( int, (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, skv_20, divmod_int_rel, skv_20 ) 21.01/21.29 ( int, (fun code_code_numeral nat), code_c271388182l_size, skv_20, code_c271388182l_size, skv_20 ) 21.01/21.29 ( int, (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, skv_20, divmod_nat_rel, skv_20 ) 21.01/21.29 ( int, (fun code_code_numeral int), code_int_of, skv_20, code_int_of, skv_20 ) 21.01/21.29 ( (fun int int), (fun int (fun int int)), multInv, zfact, multInv, succ ) 21.01/21.29 ( (fun int int), (fun nat bool), (even_odd_even nat), (fact_fact int), (even_odd_even nat), bit1 ) 21.01/21.29 ( (fun int int), (fun nat bool), (even_odd_even nat), (fact_fact int), (even_odd_even nat), (fact_fact int) ) 21.01/21.29 ( (fun int int), (fun int (fun (product_prod int int) bool)), int_ge_less_than2, bit1, int_ge_less_than2, (fact_fact int) ) 21.01/21.29 ( (fun int int), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, succ, code_nat_of_aux, succ ) 21.01/21.29 ( (fun int int), (fun code_code_numeral (fun nat nat)), code_nat_of_aux, succ, code_nat_of_aux, zfact ) 21.01/21.29 ( (fun int int), (fun int (fun int (fun int bool))), wset, pred, wset, bit0 ) 21.01/21.29 ( (fun int int), (fun int (fun int (fun int bool))), wset, pred, wset, pred ) 21.01/21.29 ( (fun int int), (fun real nat), natfloor, bit0, natfloor, pred ) 21.01/21.29 ( nat, (fun (fun int bool) bool), nat_nat_set, n, nat_nat_set, n ) 21.01/21.29 ( nat, (fun (fun int bool) bool), nat_nat_set, n, nat_nat_set, tn ) 21.01/21.29 ( nat, (fun int (fun int (fun int bool))), zcongm, tn, zcongm, n ) 21.01/21.29 ( bool, (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, fTrue, upto_rel, fTrue ) 21.01/21.29 ( bool, (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, fTrue, upto_rel, fFalse ) 21.01/21.29 ( bool, (fun int (fun int (product_prod int int))), negDivAlg, fFalse, negDivAlg, fTrue ) 21.01/21.29 ( real, int, pls, pi, pls, pi ) 21.01/21.29 ( real, int, min, pi, min, pi ) 21.01/21.29 ( real, int, s, pi, s, pi ) 21.01/21.29 ( real, int, t, pi, t, pi ) 21.01/21.29 ( real, int, x, pi, x, pi ) 21.01/21.29 ( real, int, m1, pi, m1, pi ) 21.01/21.29 ( real, int, skv_20, pi, skv_20, pi ) 21.01/21.29 ( real, nat, tn, pi, tn, pi ) 21.01/21.29 ( real, bool, fFalse, pi, fFalse, pi ) 21.01/21.29 ( real, real, pi, pi, pi, pi ) 21.01/21.29 ( real, (fun nat real), (real_1 nat), pi, (real_1 nat), pi ) 21.01/21.29 ( real, (fun nat real), cos_coeff, pi, cos_coeff, pi ) 21.01/21.29 ( real, (fun real real), cos, pi, cos, pi ) 21.01/21.29 ( real, (fun real real), arcsin, pi, arcsin, pi ) 21.01/21.29 ( real, (fun real real), arccos, pi, arccos, pi ) 21.01/21.29 ( real, (fun nat nat), (fact_fact nat), pi, (fact_fact nat), pi ) 21.01/21.29 ( real, (filter nat), sequentially, pi, sequentially, pi ) 21.01/21.29 ( real, (fun int bool), zEven, pi, zEven, pi ) 21.01/21.29 ( real, (fun int bool), nat_neg, pi, nat_neg, pi ) 21.01/21.29 ( real, (fun int (fun int int)), legacy_zgcd, pi, legacy_zgcd, pi ) 21.01/21.29 ( real, (fun int (fun int int)), inv, pi, inv, pi ) 21.01/21.29 ( real, (fun int (fun int int)), int_gcd, pi, int_gcd, pi ) 21.01/21.29 ( real, (fun bool (fun bool bool)), fimplies, pi, fimplies, pi ) 21.01/21.29 ( real, (fun int (fun int bool)), d22set, pi, d22set, pi ) 21.01/21.29 ( real, (fun int (fun int bool)), quickc1265749348ro_rel, pi, quickc1265749348ro_rel, pi ) 21.01/21.29 ( real, (fun nat bool), prime, pi, prime, pi ) 21.01/21.29 ( real, (fun real complex), cis, pi, cis, pi ) 21.01/21.29 ( real, (fun nat 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(fun int (fun int (fun int bool))), zcong, ii, zcong, ii ) 21.11/21.29 ( complex, (fun int (fun int (fun int bool))), bnorRset, ii, bnorRset, ii ) 21.11/21.29 ( complex, (fun int (fun int (fun int bool))), zcongm, ii, zcongm, ii ) 21.11/21.29 ( complex, (fun real nat), natceiling, ii, natceiling, ii ) 21.11/21.29 ( complex, (fun real nat), natfloor, ii, natfloor, ii ) 21.11/21.29 ( complex, (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, ii, pair_less, ii ) 21.11/21.29 ( complex, (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, ii, pair_leq, ii ) 21.11/21.29 ( complex, (fun int real), (real_1 int), ii, (real_1 int), ii ) 21.11/21.29 ( complex, (fun quickcheck_code_int int), quickcheck_int_of, ii, quickcheck_int_of, ii ) 21.11/21.29 ( complex, (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, ii, quickc495462417de_int, ii ) 21.11/21.29 ( complex, (fun complex nat), (size_size complex), ii, (size_size complex), ii ) 21.11/21.29 ( complex, (fun complex nat), complex_size, ii, complex_size, ii ) 21.11/21.29 ( complex, (fun (fun nat rat) bool), vanishes, ii, vanishes, ii ) 21.11/21.29 ( complex, (fun int (fun int (fun (fun int bool) bool))), setS, ii, setS, ii ) 21.11/21.29 ( complex, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, ii, xzgcda, ii ) 21.11/21.29 ( complex, (fun rat real), ratreal, ii, ratreal, ii ) 21.11/21.29 ( complex, (fun int (fun int (fun int (fun int bool)))), multInvPair, ii, multInvPair, ii ) 21.11/21.29 ( complex, (fun (fun int bool) (fun int (fun int int))), rRset2norRR, ii, rRset2norRR, ii ) 21.11/21.29 ( complex, (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, ii, bolzano_bisect, ii ) 21.11/21.29 ( complex, (fun rat 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sequentially, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int bool), zEven, (even_odd_even int), zEven, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int bool), nat_neg, (even_odd_even int), nat_neg, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int int)), legacy_zgcd, (even_odd_even int), legacy_zgcd, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int int)), inv, (even_odd_even int), inv, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun bool (fun bool bool)), fimplies, (even_odd_even int), fimplies, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int bool)), d22set, (even_odd_even int), d22set, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun nat bool), prime, (even_odd_even int), prime, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun real complex), cis, (even_odd_even int), cis, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (let ((_let_0 (product_prod int int))) (fun _let_0 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int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int (product_prod int int))), posDivAlg, (even_odd_even int), posDivAlg, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int (product_prod int int))), norm_frac, (even_odd_even int), norm_frac, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun (product_prod nat nat) bool), pred_nat, (even_odd_even int), pred_nat, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun (fun int bool) int), (the int), (even_odd_even int), (the int), (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun nat (fun nat (product_prod nat nat))), divmod_nat, (even_odd_even int), divmod_nat, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun real (fun real complex)), complex_1, (even_odd_even int), complex_1, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (fun int (fun int (fun int bool))), zcong, (even_odd_even int), zcong, (even_odd_even int) ) 21.11/21.29 ( (fun int bool), (let ((_let_0 (product_prod nat nat))) (fun 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(fun nat (product_prod int int))), bezw, (even_odd_even int), bezw, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun int (list int)), quickc666637781d_zero, (even_odd_even int), quickc666637781d_zero, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun quickcheck_code_int nat), quickcheck_nat_of, (even_odd_even int), quickcheck_nat_of, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun (fun real bool) real), (complete_Sup_Sup real), (even_odd_even int), (complete_Sup_Sup real), (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, (even_odd_even int), divmod_int_rel, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun code_code_numeral nat), code_c271388182l_size, (even_odd_even int), code_c271388182l_size, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, (even_odd_even int), divmod_nat_rel, (even_odd_even int) ) 21.11/21.30 ( (fun int bool), (fun code_code_numeral int), code_int_of, (even_odd_even int), code_int_of, (even_odd_even int) ) 21.11/21.30 ( (fun int (fun int int)), int, pls, nat_tsub, pls, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), int, s, nat_tsub, s, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), int, t, nat_tsub, t, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), int, x, nat_tsub, x, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), int, m1, nat_tsub, m1, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), int, skv_20, nat_tsub, skv_20, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int int), bit1, z3div, bit1, legacy_zgcd ) 21.11/21.30 ( (fun int (fun int int)), (fun int int), bit1, z3div, bit1, z3div ) 21.11/21.30 ( (fun int (fun int int)), (fun int int), (fact_fact int), inv, (fact_fact int), int_gcd ) 21.11/21.30 ( (fun int (fun int int)), nat, tn, nat_tsub, tn, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), bool, fFalse, nat_tsub, fFalse, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), real, pi, nat_tsub, pi, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun real real), sin, multInv, sin, (gcd_gcd int) ) 21.11/21.30 ( (fun int (fun int int)), (fun real real), arcsin, nat_tsub, arcsin, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun real real), arccos, nat_tsub, arccos, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun nat nat), (fact_fact nat), nat_tsub, (fact_fact nat), nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (filter nat), sequentially, nat_tsub, sequentially, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int bool), zEven, nat_tsub, zEven, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int bool), nat_neg, nat_tsub, nat_neg, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int bool), nat_is_nat, legendre, nat_is_nat, legendre ) 21.11/21.30 ( (fun int (fun int int)), (fun int bool), nat_is_nat, legendre, nat_is_nat, z3mod ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int int)), legacy_zgcd, nat_tsub, legacy_zgcd, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int int)), inv, nat_tsub, inv, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int int)), int_gcd, legacy_zgcd, int_gcd, z3div ) 21.11/21.30 ( (fun int (fun int int)), (fun bool (fun bool bool)), fdisj, (gcd_gcd int), fdisj, (gcd_gcd int) ) 21.11/21.30 ( (fun int (fun int int)), (fun bool (fun bool bool)), fdisj, (gcd_gcd int), fdisj, multInv ) 21.11/21.30 ( (fun int (fun int int)), (fun bool (fun bool bool)), fimplies, nat_tsub, fimplies, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int bool)), d22set, nat_tsub, d22set, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int bool)), sr, z3mod, sr, legendre ) 21.11/21.30 ( (fun int (fun int int)), (fun nat bool), prime, nat_tsub, prime, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun real complex), cis, nat_tsub, cis, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun (product_prod int int) bool), frac_1, int_lcm, frac_1, standardRes ) 21.11/21.30 ( (fun int (fun int int)), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, nat_tsub, negDivAlg_rel, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun (product_prod int int) bool)), int_ge_less_than, nat_tsub, int_ge_less_than, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun real (fun real real)), powr, nat_tsub, powr, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun complex complex), expi, nat_tsub, expi, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int nat), phi, nat_tsub, phi, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun complex real), im, nat_tsub, im, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int (product_prod int int))), posDivAlg, nat_tsub, posDivAlg, nat_tsub ) 21.11/21.30 ( (fun int (fun int int)), (fun int (fun int (product_prod int int))), norm_frac, nat_tsub, norm_frac, nat_tsub ) 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bool), nat, n, vanishes, n, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), nat, tn, vanishes, tn, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), bool, fFalse, vanishes, fFalse, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), real, pi, vanishes, pi, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat real), (real_1 nat), vanishes, (real_1 nat), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat real), cos_coeff, vanishes, cos_coeff, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat real), sin_coeff, vanishes, sin_coeff, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real real), cos, vanishes, cos, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real real), tan, vanishes, tan, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real real), arctan, vanishes, arctan, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real real), arcsin, vanishes, arcsin, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real real), arccos, vanishes, arccos, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat nat), suc, vanishes, suc, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat nat), (fact_fact nat), vanishes, (fact_fact nat), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat nat), fact, vanishes, fact, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int bool), zEven, vanishes, zEven, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int bool), nat_neg, vanishes, nat_neg, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int bool), twoSqu1091635170sum2sq, vanishes, twoSqu1091635170sum2sq, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int int)), legacy_zgcd, vanishes, legacy_zgcd, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int int)), inv, vanishes, inv, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int int)), legendre, vanishes, legendre, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int int)), z3mod, vanishes, z3mod, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int int)), int_gcd, vanishes, int_gcd, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (product_prod int int) int), twoSqu1094008024sum2sq, vanishes, twoSqu1094008024sum2sq, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun bool bool), fNot, vanishes, fNot, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, vanishes, is_RRset, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun bool (fun bool bool)), fconj, vanishes, fconj, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun bool (fun bool bool)), fimplies, vanishes, fimplies, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int bool)), sr, vanishes, sr, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int bool)), quickc1265749348ro_rel, vanishes, quickc1265749348ro_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat bool), (even_odd_even nat), vanishes, (even_odd_even nat), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat bool), prime, vanishes, prime, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real complex), cis, vanishes, cis, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat (fun nat bool)), coprime, vanishes, coprime, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, vanishes, ratrel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, vanishes, posDivAlg_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, vanishes, negDivAlg_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, vanishes, lazy_small_lazy_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, vanishes, norm_frac_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun (product_prod int int) bool)), int_ge_less_than2, vanishes, int_ge_less_than2, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, vanishes, xzgcd, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex complex), expi, vanishes, expi, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat (fun nat nat)), (gcd_gcd nat), vanishes, (gcd_gcd nat), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun (fun int bool) bool)), resSet, vanishes, resSet, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int nat), phi, vanishes, phi, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex real), re, vanishes, re, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex real), im, vanishes, im, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex real), arg, vanishes, arg, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), posDivAlg, vanishes, posDivAlg, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), negDivAlg, vanishes, negDivAlg, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (product_prod int int))), norm_frac, vanishes, norm_frac, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (product_prod nat nat) bool), pred_nat, vanishes, pred_nat, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat (fun nat (product_prod nat nat))), divmod_nat, vanishes, divmod_nat, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun real (fun real complex)), complex_1, vanishes, complex_1, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), zcong, vanishes, zcong, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), bnorRset, vanishes, bnorRset, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun int bool))), zcongm, vanishes, zcongm, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, vanishes, pair_less, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, vanishes, pair_leq, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int real), (real_1 int), vanishes, (real_1 int), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, vanishes, quickc495462417de_int, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, vanishes, nat_gcd_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex nat), (size_size complex), vanishes, (size_size complex), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun complex nat), complex_size, vanishes, complex_size, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (fun nat rat) bool), vanishes, vanishes, vanishes, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (product_prod int int) rat), frct, vanishes, frct, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun (fun int bool) bool))), setS, vanishes, setS, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, vanishes, xzgcda, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), vanishes, (ord_gr676655987ssThan nat), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun rat real), ratreal, vanishes, ratreal, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun int (fun int bool)))), multInvPair, vanishes, multInvPair, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (fun int bool) (fun int (fun int int))), rRset2norRR, vanishes, rRset2norRR, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, vanishes, bolzano_bisect, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun rat (product_prod int int)), quotient_of, vanishes, quotient_of, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun nat nat)), nat_aux, vanishes, nat_aux, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun nat (fun nat (product_prod int int))), bezw, vanishes, bezw, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (list int)), quickc666637781d_zero, vanishes, quickc666637781d_zero, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun quickcheck_code_int nat), quickcheck_nat_of, vanishes, quickcheck_nat_of, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun (fun real bool) real), (complete_Sup_Sup real), vanishes, (complete_Sup_Sup real), vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, vanishes, divmod_int_rel, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun code_code_numeral nat), code_c271388182l_size, vanishes, code_c271388182l_size, vanishes ) 21.11/21.33 ( (fun (fun nat rat) bool), (fun code_code_numeral nat), (size_size code_code_numeral), vanishes, code_c271388182l_size, vanishes ) 21.11/21.33 ( (fun (product_prod int int) rat), int, pls, frct, pls, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), int, s, frct, s, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), int, t, frct, t, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), int, x, frct, x, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), int, m1, frct, m1, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), int, skv_20, frct, skv_20, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), nat, tn, frct, tn, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), bool, fFalse, frct, fFalse, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), real, pi, frct, pi, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat real), (real_1 nat), frct, (real_1 nat), frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real real), cos, frct, cos, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real real), arcsin, frct, arcsin, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real real), arccos, frct, arccos, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat nat), (fact_fact nat), frct, (fact_fact nat), frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (filter nat), sequentially, frct, sequentially, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int bool), zEven, frct, zEven, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int bool), nat_neg, frct, nat_neg, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int int)), legacy_zgcd, frct, legacy_zgcd, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int int)), inv, frct, inv, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun bool (fun bool bool)), fimplies, frct, fimplies, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int bool)), d22set, frct, d22set, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int bool)), quickc1265749348ro_rel, frct, quickc1265749348ro_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat bool), prime, frct, prime, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real complex), cis, frct, cis, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat (fun nat bool)), coprime, frct, coprime, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, frct, negDivAlg_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, frct, lazy_small_lazy_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, frct, norm_frac_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun (product_prod int int) bool)), int_ge_less_than, frct, int_ge_less_than, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real (fun real real)), powr, frct, powr, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun complex complex), expi, frct, expi, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int nat), phi, frct, phi, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun complex real), im, frct, im, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int (product_prod int int))), posDivAlg, frct, posDivAlg, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int (product_prod int int))), norm_frac, frct, norm_frac, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun (product_prod nat nat) bool), pred_nat, frct, pred_nat, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun (fun int bool) int), (the int), frct, (the int), frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat (fun nat (product_prod nat nat))), divmod_nat, frct, divmod_nat, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun real (fun real complex)), complex_1, frct, complex_1, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int (fun int bool))), zcong, frct, zcong, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, frct, pair_less, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, frct, nat_gcd_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun (product_prod int int) rat), frct, frct, frct, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), frct, (ord_gr676655987ssThan nat), frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, frct, bolzano_bisect, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun rat (product_prod int int)), quotient_of, frct, quotient_of, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun nat nat)), nat_aux, frct, nat_aux, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat (fun nat (product_prod int int))), bezw, frct, bezw, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (list int)), quickc666637781d_zero, frct, quickc666637781d_zero, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun quickcheck_code_int nat), quickcheck_nat_of, frct, quickcheck_nat_of, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun (fun real bool) real), (complete_Sup_Sup real), frct, (complete_Sup_Sup real), frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, frct, divmod_int_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun code_code_numeral nat), code_c271388182l_size, frct, code_c271388182l_size, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, frct, divmod_nat_rel, frct ) 21.11/21.33 ( (fun (product_prod int int) rat), (fun code_code_numeral int), code_int_of, frct, code_int_of, frct ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, pls, setS, pls, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, pls, setS, w, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, min, setS, min, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, s, setS, s, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, m, setS, m, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, t, setS, t, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, v, setS, v, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, r, setS, r, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), int, m1, setS, m1, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int int), bit1, setS, bit1, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int int), bit0, setS, bit0, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int int), (fact_fact int), setS, (fact_fact int), setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), nat, tn, setS, tn, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), bool, fFalse, setS, fFalse, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), real, pi, setS, pi, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat real), (real_1 nat), setS, (real_1 nat), setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat real), cos_coeff, setS, cos_coeff, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat real), sin_coeff, setS, sin_coeff, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun real real), cos, setS, cos, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun real real), tan, setS, tan, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun real real), arctan, setS, arctan, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun real real), arcsin, setS, arcsin, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun real real), arccos, setS, arccos, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat nat), suc, setS, suc, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat nat), (fact_fact nat), setS, (fact_fact nat), setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun nat nat), fact, setS, fact, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (filter nat), sequentially, setS, sequentially, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int bool), zEven, setS, zEven, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int bool), nat_neg, setS, nat_neg, setS ) 21.11/21.33 ( (fun int (fun int (fun (fun int bool) bool))), (fun int bool), twoSqu1091635170sum2sq, setS, twoSqu1091635170sum2sq, setS ) 21.11/21.33 ( (fun 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divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), divmod_nat_rel, (ord_gr676655987ssThan nat), divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun rat (product_prod int int)), quotient_of, divmod_nat_rel, quotient_of, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun int (fun nat nat)), nat_aux, divmod_nat_rel, nat_aux, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun nat (fun nat (product_prod int int))), bezw, divmod_nat_rel, bezw, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun int (list int)), quickc666637781d_zero, divmod_nat_rel, quickc666637781d_zero, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun quickcheck_code_int nat), quickcheck_nat_of, divmod_nat_rel, quickcheck_nat_of, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun (fun real bool) real), (complete_Sup_Sup real), divmod_nat_rel, (complete_Sup_Sup real), divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_nat_rel, divmod_int_rel, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun code_code_numeral nat), code_c271388182l_size, divmod_nat_rel, code_c271388182l_size, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel, divmod_nat_rel, divmod_nat_rel ) 21.11/21.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), (fun code_code_numeral int), code_int_of, divmod_nat_rel, code_int_of, divmod_nat_rel ) 21.11/21.35 ( (fun code_code_numeral int), int, pls, code_int_of, pls, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), int, s, code_int_of, s, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), int, t, code_int_of, t, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), int, x, code_int_of, x, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), int, m1, code_int_of, m1, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), int, skv_20, code_int_of, skv_20, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), nat, tn, code_int_of, tn, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), bool, fFalse, code_int_of, fFalse, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), real, pi, code_int_of, pi, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun real real), arcsin, code_int_of, arcsin, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun real real), arccos, code_int_of, arccos, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat nat), (fact_fact nat), code_int_of, (fact_fact nat), code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (filter nat), sequentially, code_int_of, sequentially, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int bool), zEven, code_int_of, zEven, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int bool), nat_neg, code_int_of, nat_neg, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int int)), legacy_zgcd, code_int_of, legacy_zgcd, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int int)), inv, code_int_of, inv, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun bool (fun bool bool)), fimplies, code_int_of, fimplies, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int bool)), d22set, code_int_of, d22set, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat bool), prime, code_int_of, prime, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun real complex), cis, code_int_of, cis, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, code_int_of, negDivAlg_rel, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun (product_prod int int) bool)), int_ge_less_than, code_int_of, int_ge_less_than, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun real (fun real real)), powr, code_int_of, powr, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun complex complex), expi, code_int_of, expi, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int nat), phi, code_int_of, phi, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun complex real), im, code_int_of, im, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int (product_prod int int))), posDivAlg, code_int_of, posDivAlg, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int (product_prod int int))), norm_frac, code_int_of, norm_frac, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun (product_prod nat nat) bool), pred_nat, code_int_of, pred_nat, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun (fun int bool) int), (the int), code_int_of, (the int), code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat (fun nat (product_prod nat nat))), divmod_nat, code_int_of, divmod_nat, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun real (fun real complex)), complex_1, code_int_of, complex_1, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int (fun int bool))), zcong, code_int_of, zcong, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, code_int_of, pair_less, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, code_int_of, nat_gcd_rel, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun (product_prod int int) rat), frct, code_int_of, frct, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), code_int_of, (ord_gr676655987ssThan nat), code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun nat nat)), nat_aux, code_int_of, nat_aux, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat (fun nat (product_prod int int))), bezw, code_int_of, bezw, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (list int)), quickc666637781d_zero, code_int_of, quickc666637781d_zero, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun quickcheck_code_int nat), quickcheck_nat_of, code_int_of, quickcheck_nat_of, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun (fun real bool) real), (complete_Sup_Sup real), code_int_of, (complete_Sup_Sup real), code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, code_int_of, divmod_int_rel, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun code_code_numeral nat), code_c271388182l_size, code_int_of, code_c271388182l_size, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, code_int_of, divmod_nat_rel, code_int_of ) 21.11/21.35 ( (fun code_code_numeral int), (fun code_code_numeral int), code_int_of, code_int_of, code_int_of, code_int_of ) 21.11/21.35 ) 21.11/21.35 (instantiation (forall ((R_3 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (or (not (= (hAPP rat _let_0 quotient_of R_3) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) P_5) Q_3)))) ) 21.11/21.35 ( (one_one rat), (one_one int), (one_one int) ) 21.11/21.35 ( (zero_zero rat), (zero_zero int), (one_one int) ) 21.11/21.35 ) 21.11/21.35 (instantiation (forall ((Z_1 $$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))))) ) 21.11/21.35 ( (zero_zero complex) ) 21.11/21.35 ( ii ) 21.11/21.35 ( (one_one complex) ) 21.11/21.35 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.35 ( (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)) ) 21.11/21.35 ) 21.11/21.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_102991 $$unsorted) (BOUND_VARIABLE_102992 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (= (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (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_102991 N_1)) BOUND_VARIABLE_102992))) R_1))) )) ))) ) (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_102991) BOUND_VARIABLE_102992) sequentially))))) ) 21.11/21.35 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.11/21.35 ) 21.11/21.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103045 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_103045)) (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_103045))))) ) 21.11/21.35 ( complex, (one_one real) ) 21.11/21.35 ) 21.11/21.35 (instantiation (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_2) Na))) (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 Na)))) (not (forall ((I_2 $$unsorted)) (or (not (= (hAPP nat int F I_2) (ti int K))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_2) Na)))) ))))) ) 21.11/21.35 ( min, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.35 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.35 ( (zero_zero int), (semiring_1_of_nat int), (one_one nat) ) 21.11/21.35 ( (zero_zero int), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.35 ( (zero_zero int), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.35 ) 21.11/21.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103159 $$unsorted) (BOUND_VARIABLE_103166 $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun int (fun int bool)))) (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_103166) _let_0)))) (let ((_let_17 (hAPP int X_a _let_3 BOUND_VARIABLE_103166))) (or (not (ring_1 X_a)) (and (or (not (= _let_0 (ti int BOUND_VARIABLE_103159))) (= (zero_zero X_a) (hAPP int X_a _let_3 BOUND_VARIABLE_103159))) (or (= _let_0 (ti int BOUND_VARIABLE_103166)) (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_103166))))) (or _let_16 (= _let_17 (hAPP _let_1 X_a (hAPP _let_5 (fun _let_1 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_2 _let_2 (combc int int bool) (fequal int)) _let_0)))) _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_1 (hAPP int (fun int _let_1) divmod_int BOUND_VARIABLE_103166) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))))))))))))))))))) ) 21.11/21.36 ( rat, s1, s1 ) 21.11/21.36 ( int, m, m ) 21.11/21.36 ( real, r, r ) 21.11/21.36 ( complex, v, v ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (comple44059174attice T_1)) (comple44059174attice (fun T_2 T_1))) ) 21.11/21.36 ( rat, real ) 21.11/21.36 ( rat, (product_prod int int) ) 21.11/21.36 ( int, rat ) 21.11/21.36 ( int, int ) 21.11/21.36 ( int, (fun int int) ) 21.11/21.36 ( int, nat ) 21.11/21.36 ( int, bool ) 21.11/21.36 ( int, real ) 21.11/21.36 ( int, (fun nat real) ) 21.11/21.36 ( int, (fun real real) ) 21.11/21.36 ( int, (fun nat nat) ) 21.11/21.36 ( int, (fun int rat) ) 21.11/21.36 ( int, (fun int bool) ) 21.11/21.36 ( int, (product_prod int int) ) 21.11/21.36 ( int, (fun (product_prod int int) int) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 21.11/21.36 ( int, (fun nat int) ) 21.11/21.36 ( int, (fun bool bool) ) 21.11/21.36 ( int, (fun int (fun bool bool)) ) 21.11/21.36 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( int, (fun int (fun int bool)) ) 21.11/21.36 ( int, (fun nat bool) ) 21.11/21.36 ( int, (fun (product_prod int int) bool) ) 21.11/21.36 ( int, (fun int (fun (product_prod int int) bool)) ) 21.11/21.36 ( int, quickcheck_code_int ) 21.11/21.36 ( int, (fun (fun int bool) bool) ) 21.11/21.36 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 21.11/21.36 ( int, (product_prod int (product_prod int int)) ) 21.11/21.36 ( int, (fun int (product_prod int (product_prod int int))) ) 21.11/21.36 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 21.11/21.36 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 21.11/21.36 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 21.11/21.36 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 21.11/21.36 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 21.11/21.36 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 21.11/21.36 ( int, (fun nat (fun bool bool)) ) 21.11/21.36 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( int, (fun int (product_prod int int)) ) 21.11/21.36 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 21.11/21.36 ( int, (fun int (fun (fun int bool) bool)) ) 21.11/21.36 ( int, (fun (fun int int) (fun int bool)) ) 21.11/21.36 ( int, (list int) ) 21.11/21.36 ( int, (fun int (fun int (fun int bool))) ) 21.11/21.36 ( int, (fun int real) ) 21.11/21.36 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun int int), (fun int int) ) 21.11/21.36 ( (fun int int), (fun int bool) ) 21.11/21.36 ( (fun int int), (fun int (fun int int)) ) 21.11/21.36 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun int int), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 21.11/21.36 ( nat, rat ) 21.11/21.36 ( nat, int ) 21.11/21.36 ( nat, (fun int int) ) 21.11/21.36 ( nat, nat ) 21.11/21.36 ( nat, bool ) 21.11/21.36 ( nat, real ) 21.11/21.36 ( nat, (fun real real) ) 21.11/21.36 ( nat, (fun nat nat) ) 21.11/21.36 ( nat, complex ) 21.11/21.36 ( nat, (product_prod int int) ) 21.11/21.36 ( nat, (fun bool bool) ) 21.11/21.36 ( nat, (fun nat bool) ) 21.11/21.36 ( nat, (fun nat (fun nat bool)) ) 21.11/21.36 ( nat, (fun nat (product_prod int int)) ) 21.11/21.36 ( nat, (product_prod real real) ) 21.11/21.36 ( nat, (product_prod nat nat) ) 21.11/21.36 ( nat, (fun (product_prod nat nat) bool) ) 21.11/21.36 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 21.11/21.36 ( nat, (fun nat (product_prod nat nat)) ) 21.11/21.36 ( bool, bool ) 21.11/21.36 ( bool, (fun bool bool) ) 21.11/21.36 ( real, nat ) 21.11/21.36 ( real, bool ) 21.11/21.36 ( real, real ) 21.11/21.36 ( real, (fun nat real) ) 21.11/21.36 ( real, (fun real real) ) 21.11/21.36 ( real, (fun (filter nat) bool) ) 21.11/21.36 ( real, complex ) 21.11/21.36 ( real, (fun int bool) ) 21.11/21.36 ( real, (fun bool bool) ) 21.11/21.36 ( real, (fun int (fun int bool)) ) 21.11/21.36 ( real, (fun real complex) ) 21.11/21.36 ( real, (fun real bool) ) 21.11/21.36 ( real, (fun nat (product_prod real real)) ) 21.11/21.36 ( real, (fun real (fun nat (product_prod real real))) ) 21.11/21.36 ( real, (fun (filter real) bool) ) 21.11/21.36 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 21.11/21.36 ( real, (fun int (fun int (fun bool bool))) ) 21.11/21.36 ( real, (fun int (fun nat bool)) ) 21.11/21.36 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 21.11/21.36 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( real, (fun int (fun nat (fun bool bool))) ) 21.11/21.36 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 21.11/21.36 ( real, (fun (fun nat real) (fun nat bool)) ) 21.11/21.36 ( real, (fun (fun int real) (fun int bool)) ) 21.11/21.36 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 21.11/21.36 ( (fun nat real), (fun nat real) ) 21.11/21.36 ( (fun nat real), (fun nat bool) ) 21.11/21.36 ( (fun nat real), (fun nat (fun real real)) ) 21.11/21.36 ( (fun nat real), (fun int (fun nat real)) ) 21.11/21.36 ( (fun real real), (fun real real) ) 21.11/21.36 ( (fun real real), (fun real (fun real bool)) ) 21.11/21.36 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun real real), (fun real (fun real real)) ) 21.11/21.36 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun nat nat), (fun nat real) ) 21.11/21.36 ( (fun nat nat), (fun nat (fun nat bool)) ) 21.11/21.36 ( (fun nat nat), (fun nat (fun nat nat)) ) 21.11/21.36 ( (filter nat), bool ) 21.11/21.36 ( complex, nat ) 21.11/21.36 ( complex, real ) 21.11/21.36 ( complex, complex ) 21.11/21.36 ( (fun int bool), int ) 21.11/21.36 ( (fun int bool), bool ) 21.11/21.36 ( (fun int bool), (fun int bool) ) 21.11/21.36 ( (fun int bool), (fun int (fun int int)) ) 21.11/21.36 ( (fun int bool), (fun int (fun bool bool)) ) 21.11/21.36 ( (fun int bool), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 21.11/21.36 ( (fun int bool), (fun real (fun int (fun int bool))) ) 21.11/21.36 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 21.11/21.36 ( (product_prod int int), rat ) 21.11/21.36 ( (product_prod int int), int ) 21.11/21.36 ( (product_prod int int), (fun int int) ) 21.11/21.36 ( (product_prod int int), bool ) 21.11/21.36 ( (product_prod int int), (fun int bool) ) 21.11/21.36 ( (product_prod int int), (product_prod int int) ) 21.11/21.36 ( (product_prod int int), (fun (product_prod int int) int) ) 21.11/21.36 ( (product_prod int int), (fun bool bool) ) 21.11/21.36 ( (product_prod int int), (fun (product_prod int int) bool) ) 21.11/21.36 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 21.11/21.36 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 21.11/21.36 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 21.11/21.36 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 21.11/21.36 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 21.11/21.36 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 21.11/21.36 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 21.11/21.36 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (fun int (fun int bool)), (fun int bool) ) 21.11/21.36 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 21.11/21.36 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 21.11/21.36 ( (fun nat bool), bool ) 21.11/21.36 ( (fun nat bool), (fun nat bool) ) 21.11/21.36 ( (fun nat bool), (fun nat (fun bool bool)) ) 21.11/21.36 ( (fun nat bool), (fun int (fun nat bool)) ) 21.11/21.36 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 21.11/21.36 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 21.11/21.36 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 21.11/21.36 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (fun real bool), real ) 21.11/21.36 ( (fun real bool), (fun real bool) ) 21.11/21.36 ( (fun real bool), (fun real (fun bool bool)) ) 21.11/21.36 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 21.11/21.36 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 21.11/21.36 ( quickcheck_code_int, int ) 21.11/21.36 ( quickcheck_code_int, nat ) 21.11/21.36 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 21.11/21.36 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 21.11/21.36 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 21.11/21.36 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 21.11/21.36 ( code_code_numeral, int ) 21.11/21.36 ( code_code_numeral, nat ) 21.11/21.36 ( code_code_numeral, (fun nat nat) ) 21.11/21.36 ( code_code_numeral, code_code_numeral ) 21.11/21.36 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 21.11/21.36 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 21.11/21.36 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 21.11/21.36 ( (product_prod real real), bool ) 21.11/21.36 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 21.11/21.36 ( (filter real), bool ) 21.11/21.36 ( (product_prod nat nat), bool ) 21.11/21.36 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 21.11/21.36 ( (fun nat rat), bool ) 21.11/21.36 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 21.11/21.36 ( (fun int real), (fun int bool) ) 21.11/21.36 ( (fun int real), (fun int real) ) 21.11/21.36 ( (fun int real), (fun int (fun real real)) ) 21.11/21.36 ( (fun int real), (fun int (fun int real)) ) 21.11/21.36 ( (fun real (fun int bool)), (fun real bool) ) 21.11/21.36 ( (fun int (fun nat bool)), (fun int bool) ) 21.11/21.36 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 21.11/21.36 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 21.11/21.36 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 21.11/21.36 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 21.11/21.36 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 21.11/21.36 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 21.11/21.36 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 21.11/21.36 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 21.11/21.36 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 21.11/21.36 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 21.11/21.36 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 21.11/21.36 ( (fun int (fun int real)), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 21.11/21.36 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 21.11/21.36 ) 21.11/21.36 (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 int nat nat_1 (hAPP int int _let_1 _let_0)) (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)))))))))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( t ) 21.11/21.36 ( y ) 21.11/21.36 ( x ) 21.11/21.36 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.11/21.36 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.11/21.36 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.11/21.36 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.11/21.36 ( (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))) m1))) ) 21.11/21.36 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X $$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 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)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_2))))) ) 21.11/21.36 ( pi ) 21.11/21.36 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (zero_zero real) ) 21.11/21.36 ( (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))))) ) 21.11/21.36 ( (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) ) 21.11/21.36 ( (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))))) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.11/21.36 ( skv_10 ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_103245 $$unsorted)) (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_103245))) (or (not (monoid_mult X_b)) (not (number X_b)) (= (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)))) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (times_times X_b) _let_0) _let_0)))) ) 21.11/21.36 ( int, pls ) 21.11/21.36 ( int, (hAPP int int bit1 pls) ) 21.11/21.36 ( int, min ) 21.11/21.36 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.36 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.11/21.36 ( nat, pls ) 21.11/21.36 ( nat, (hAPP int int bit1 pls) ) 21.11/21.36 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.36 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.11/21.36 ( real, min ) 21.11/21.36 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.36 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.11/21.36 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.36 ( 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)))))))) ) 21.11/21.36 ( complex, min ) 21.11/21.36 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.36 ( quickcheck_code_int, pls ) 21.11/21.36 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.11/21.36 ( quickcheck_code_int, (one_one int) ) 21.11/21.36 ( code_code_numeral, pls ) 21.11/21.36 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103271 $$unsorted) (BOUND_VARIABLE_103272 $$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_103272) (one_one X_a))) BOUND_VARIABLE_103271) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103271) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_103272) BOUND_VARIABLE_103271))))))) ) 21.11/21.36 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.11/21.36 ( 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) ) 21.11/21.36 ( 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))) ) 21.11/21.36 ( int, v, y ) 21.11/21.36 ( int, v, sa ) 21.11/21.36 ( int, v, x ) 21.11/21.36 ( int, v, r ) 21.11/21.36 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.11/21.36 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.11/21.36 ( int, w, y ) 21.11/21.36 ( int, w, sa ) 21.11/21.36 ( int, w, x ) 21.11/21.36 ( int, w, r ) 21.11/21.36 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.11/21.36 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.11/21.36 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.11/21.36 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( int, m1, (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) ) 21.11/21.36 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.36 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))), (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) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.36 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( int, skv_21, (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) ) 21.11/21.36 ( int, skv_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))) ) 21.11/21.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( 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))))) ) 21.11/21.36 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( 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)))) ) 21.11/21.36 ( complex, ii, ii ) 21.11/21.36 ( 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)) ) 21.11/21.36 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (ord_less_eq int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_1 _let_0) Na))) (= (ti int Na) (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_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) (hAPP int (fun int bool) (ord_less int) _let_0))) (hAPP int (fun int bool) (hAPP _let_4 _let_4 (combc int int bool) _let_1) Na)))))))))))) ) 21.11/21.36 ( pls ) 21.11/21.36 ( (one_one int) ) 21.11/21.36 ( min ) 21.11/21.36 ( s ) 21.11/21.36 ( s1 ) 21.11/21.36 ( m ) 21.11/21.36 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( t ) 21.11/21.36 ( v ) 21.11/21.36 ( w ) 21.11/21.36 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.36 ( y ) 21.11/21.36 ( sa ) 21.11/21.36 ( x ) 21.11/21.36 ( r ) 21.11/21.36 ( m1 ) 21.11/21.36 ( skv_4 ) 21.11/21.36 ( skv_5 ) 21.11/21.36 ( skv_14 ) 21.11/21.36 ( skv_20 ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (ord_less nat))) (let ((_let_3 (div_div nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_2 (zero_zero nat)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_2 M) N)) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_3 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N)) (hAPP nat nat (hAPP nat _let_0 _let_3 M) N))))))) ) 21.11/21.36 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( (zero_zero nat), n ) 21.11/21.36 ( (zero_zero nat), tn ) 21.11/21.36 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) B_2))) (not (forall ((X_1 $$unsorted)) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_3) X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (zero_zero real))))) )))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F B_2)) (hAPP real real F A_3)))))) ) 21.11/21.36 ( cos, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.11/21.36 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_a $$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)))) ) 21.11/21.36 ( int ) 21.11/21.36 ( nat ) 21.11/21.36 ) 21.11/21.36 (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))) ) 21.11/21.36 ( rat, int ) 21.11/21.36 ( rat, nat ) 21.11/21.36 ( rat, (product_prod int int) ) 21.11/21.36 ( int, int ) 21.11/21.36 ( int, nat ) 21.11/21.36 ( int, (fun int bool) ) 21.11/21.36 ( int, (product_prod int int) ) 21.11/21.36 ( int, quickcheck_code_int ) 21.11/21.36 ( int, code_code_numeral ) 21.11/21.36 ( (fun int int), int ) 21.11/21.36 ( (fun int int), (fun int int) ) 21.11/21.36 ( (fun int int), nat ) 21.11/21.36 ( (fun int int), (product_prod int int) ) 21.11/21.36 ( nat, int ) 21.11/21.36 ( nat, nat ) 21.11/21.36 ( nat, real ) 21.11/21.36 ( nat, complex ) 21.11/21.36 ( nat, quickcheck_code_int ) 21.11/21.36 ( nat, code_code_numeral ) 21.11/21.36 ( bool, int ) 21.11/21.36 ( bool, nat ) 21.11/21.36 ( bool, bool ) 21.11/21.36 ( bool, real ) 21.11/21.36 ( bool, (filter nat) ) 21.11/21.36 ( bool, (fun int bool) ) 21.11/21.36 ( bool, (product_prod int int) ) 21.11/21.36 ( bool, (fun nat bool) ) 21.11/21.36 ( bool, (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.11/21.36 ( bool, (product_prod real real) ) 21.11/21.36 ( bool, (filter real) ) 21.11/21.36 ( bool, (product_prod nat nat) ) 21.11/21.36 ( bool, (fun nat rat) ) 21.11/21.36 ( bool, (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.11/21.36 ( real, rat ) 21.11/21.36 ( real, int ) 21.11/21.36 ( real, nat ) 21.11/21.36 ( real, real ) 21.11/21.36 ( real, complex ) 21.11/21.36 ( real, (fun real bool) ) 21.11/21.36 ( (fun nat real), int ) 21.11/21.36 ( (fun nat real), real ) 21.11/21.36 ( (fun nat real), (fun nat real) ) 21.11/21.36 ( (fun nat real), (fun nat nat) ) 21.11/21.36 ( (fun real real), int ) 21.11/21.36 ( (fun real real), nat ) 21.11/21.36 ( (fun real real), real ) 21.11/21.36 ( (fun real real), (fun real real) ) 21.11/21.36 ( (fun nat nat), int ) 21.11/21.36 ( (fun nat nat), nat ) 21.11/21.36 ( (fun nat nat), code_code_numeral ) 21.11/21.36 ( (fun (filter nat) bool), real ) 21.11/21.36 ( (fun int rat), int ) 21.11/21.36 ( complex, nat ) 21.11/21.36 ( complex, real ) 21.11/21.36 ( complex, complex ) 21.11/21.36 ( (fun int bool), int ) 21.11/21.36 ( (fun int bool), (fun int int) ) 21.11/21.36 ( (fun int bool), real ) 21.11/21.36 ( (fun int bool), (fun int bool) ) 21.11/21.36 ( (fun int bool), (product_prod int int) ) 21.11/21.36 ( (fun int bool), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int bool), (fun int real) ) 21.11/21.36 ( (fun int bool), (fun int (fun nat bool)) ) 21.11/21.36 ( (fun int (fun int int)), (fun int int) ) 21.11/21.36 ( (fun int (fun int int)), (fun int bool) ) 21.11/21.36 ( (product_prod int int), rat ) 21.11/21.36 ( (product_prod int int), int 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int) int) ) 21.11/21.36 ( (fun int (fun (product_prod int int) bool)), int ) 21.11/21.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) int) ) 21.11/21.36 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (product_prod int int) ) 21.11/21.36 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))), (fun (product_prod int int) (fun int bool)) ) 21.11/21.36 ( (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)))) ) 21.11/21.36 ( (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 _let_0 int))) ) 21.11/21.36 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (fun int int) ) 21.11/21.36 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)), (product_prod int int) ) 21.11/21.36 ( (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)) ) 21.11/21.36 ( (fun (product_prod int int) (fun int int)), (fun (product_prod int int) int) ) 21.11/21.36 ( (fun real bool), real ) 21.11/21.36 ( (fun real bool), (fun real bool) ) 21.11/21.36 ( (fun real bool), (fun real (fun int bool)) ) 21.11/21.36 ( quickcheck_code_int, int ) 21.11/21.36 ( (fun (fun int bool) bool), int ) 21.11/21.36 ( (fun real (fun real bool)), (fun real real) ) 21.11/21.36 ( (fun nat (fun real real)), (fun nat real) ) 21.11/21.36 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), int ) 21.11/21.36 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)), (fun real real) ) 21.11/21.36 ( (fun real (fun real real)), (fun real real) ) 21.11/21.36 ( code_code_numeral, code_code_numeral ) 21.11/21.36 ( (fun nat (product_prod int int)), nat ) 21.11/21.36 ( (product_prod int (product_prod int int)), int ) 21.11/21.36 ( (fun int (product_prod int (product_prod int int))), int ) 21.11/21.36 ( (fun int (fun int (product_prod int (product_prod int int)))), int ) 21.11/21.36 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))), int ) 21.11/21.36 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))), int ) 21.11/21.36 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))), int ) 21.11/21.36 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))), int ) 21.11/21.36 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), int ) 21.11/21.36 ( (fun nat (fun bool bool)), int ) 21.11/21.36 ( (fun nat (fun bool bool)), (fun nat bool) ) 21.11/21.36 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), int ) 21.11/21.36 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun nat (fun bool bool)) ) 21.11/21.36 ( (fun nat (fun nat nat)), (fun nat nat) ) 21.11/21.36 ( (fun int (product_prod int int)), int ) 21.11/21.36 ( (product_prod real real), nat ) 21.11/21.36 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), int ) 21.11/21.36 ( (fun nat (product_prod real real)), real ) 21.11/21.36 ( (fun real (fun nat (product_prod real real))), real ) 21.11/21.36 ( (fun real (fun real (fun nat (product_prod real real)))), (fun (product_prod real real) bool) ) 21.11/21.36 ( (fun int (fun (fun int bool) bool)), int ) 21.11/21.36 ( (fun (filter real) bool), real ) 21.11/21.36 ( (fun (fun int int) (fun int bool)), int ) 21.11/21.36 ( (fun (fun int int) (fun int bool)), (fun int bool) ) 21.11/21.36 ( (list int), int ) 21.11/21.36 ( (product_prod nat nat), nat ) 21.11/21.36 ( (fun (product_prod nat nat) bool), nat ) 21.11/21.36 ( (fun (product_prod nat nat) bool), (product_prod nat nat) ) 21.11/21.36 ( (fun nat (fun (product_prod nat nat) bool)), nat ) 21.11/21.36 ( (fun nat (product_prod nat nat)), nat ) 21.11/21.36 ( (product_prod code_code_numeral code_code_numeral), code_code_numeral ) 21.11/21.36 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_code_numeral ) 21.11/21.36 ( (fun int (fun (fun int int) (fun int bool))), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int (fun int (fun int bool))), int ) 21.11/21.36 ( (fun int (fun int (fun int bool))), (fun int (fun int int)) ) 21.11/21.36 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 21.11/21.36 ( (fun real (fun bool bool)), (fun real bool) ) 21.11/21.36 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), real ) 21.11/21.36 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int (fun bool bool))) ) 21.11/21.36 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))), real ) 21.11/21.36 ( (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))) ) 21.11/21.36 ( (fun int (fun int (fun bool bool))), real ) 21.11/21.36 ( (fun int (fun int (fun bool bool))), (fun int (fun int bool)) ) 21.11/21.36 ( (fun int real), int ) 21.11/21.36 ( (fun int real), (fun int real) ) 21.11/21.36 ( (product_prod quickcheck_code_int quickcheck_code_int), quickcheck_code_int ) 21.11/21.36 ( (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickcheck_code_int ) 21.11/21.36 ( (fun real (fun int bool)), (fun real (fun int (fun nat bool))) ) 21.11/21.36 ( (fun real (fun int bool)), (fun real (fun int (fun int bool))) ) 21.11/21.36 ( (fun int (fun nat bool)), real ) 21.11/21.36 ( (fun int (fun nat bool)), (fun nat bool) ) 21.11/21.36 ( (fun int (fun nat bool)), (fun int (fun nat real)) ) 21.11/21.36 ( (fun real (fun int (fun nat bool))), (fun nat bool) ) 21.11/21.36 ( (fun real (fun int (fun nat bool))), (fun int (fun nat real)) ) 21.11/21.36 ( (let ((_let_0 (fun nat bool))) (fun 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real))) (fun int (fun _let_0 _let_0))), (fun int (fun real real)) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103443 $$unsorted) (BOUND_VARIABLE_103444 $$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_103443) BOUND_VARIABLE_103444)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103444) BOUND_VARIABLE_103443))))) ) 21.11/21.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.11/21.36 ( 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)))) ) 21.11/21.36 ( 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))) ) 21.11/21.36 ( 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)))) ) 21.11/21.36 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.36 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( 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))))))))) ) 21.11/21.36 ( 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))) ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 21.11/21.36 ( 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))) ) 21.11/21.36 ( 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))) ) 21.11/21.36 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 21.11/21.36 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.11/21.36 ( 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) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted) (B_5 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun X_b _let_0))) (let ((_let_2 (product_Pair X_a X_b))) (or (not (= (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_6) B_5) (hAPP X_b _let_0 (hAPP X_a _let_1 _let_2 A_1) B))) (and (= (ti X_a A_6) (ti X_a A_1)) (= (ti X_b B_5) (ti X_b B))))))) ) 21.11/21.36 ( int, int, (one_one int), (one_one int), (zero_zero int), (one_one int) ) 21.11/21.36 ( int, int, (zero_zero int), (one_one int), (one_one int), (one_one int) ) 21.11/21.36 ( int, int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 21.11/21.36 ( int, int, (zero_zero int), (one_one int), s, (one_one int) ) 21.11/21.36 ( int, int, s, (one_one int), (one_one int), (one_one int) ) 21.11/21.36 ) 21.11/21.36 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103476 $$unsorted) (BOUND_VARIABLE_103477 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (exp X_a))) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_103476) BOUND_VARIABLE_103477)) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) (hAPP X_a X_a _let_1 BOUND_VARIABLE_103476)) (hAPP X_a X_a _let_1 BOUND_VARIABLE_103477)))))) ) 21.11/21.36 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.11/21.36 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.36 ( 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) ) 21.11/21.36 ( 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) ) 21.11/21.36 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.11/21.36 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.36 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.11/21.36 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.11/21.37 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.11/21.37 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.11/21.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( nat, (one_one nat), (one_one nat) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103531 $$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_103531)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_103531))) ) 21.11/21.37 ( int, (zero_zero nat) ) 21.11/21.37 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (one_one nat) ) 21.11/21.37 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, n ) 21.11/21.37 ( real, (zero_zero nat) ) 21.11/21.37 ( real, (one_one nat) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((C $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (abs_abs real) C)) (one_one real)))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) (hAPP real _let_0 (power_power real) C)) (zero_zero real)) sequentially))))) ) 21.11/21.37 ( (hAPP int real (number_number_of real) min) ) 21.11/21.37 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((Na $$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)) Na)) (hAPP nat nat (fact_fact nat) Na))) ) 21.11/21.37 ( (zero_zero nat) ) 21.11/21.37 ( (one_one nat) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103554 $$unsorted) (BOUND_VARIABLE_103555 $$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_103555))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_103554))) (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_103555) BOUND_VARIABLE_103554))))) ) 21.11/21.37 ( 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)))) ) 21.11/21.37 ( 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) ) 21.11/21.37 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.11/21.37 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.11/21.37 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.37 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.11/21.37 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.11/21.37 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.11/21.37 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.11/21.37 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.11/21.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( nat, (one_one nat), (one_one nat) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (div_mod nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N))))) ) 21.11/21.37 ( (one_one nat), (hAPP int nat nat_1 t) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103626 $$unsorted) (BOUND_VARIABLE_103627 $$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_103627))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_103626)) BOUND_VARIABLE_103627) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_103626) BOUND_VARIABLE_103627))))) ) 21.11/21.37 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((P_1 $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (ord_less nat))) (let ((_let_1 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 Na) Ma)))) (let ((_let_2 (not _let_1))) (or (and (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) _let_0 Ma) Na)) _let_2) (and (= Ma Na) _let_2) (and (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) _let_0 Na) Ma)) _let_2) _let_1)))) ) 21.11/21.37 ( (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.11/21.37 ( (ord_less nat), n, (zero_zero nat) ) 21.11/21.37 ( (ord_less nat), tn, (zero_zero nat) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int pred K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) min)) ) 21.11/21.37 ( pls ) 21.11/21.37 ( (one_one int) ) 21.11/21.37 ( min ) 21.11/21.37 ( (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)))) ) 21.11/21.37 ( (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) ) 21.11/21.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.11/21.37 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.11/21.37 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.11/21.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103716 $$unsorted)) (or (not (number_ring X_a)) (not (field X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_103716) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) (ti X_a BOUND_VARIABLE_103716))) ) 21.11/21.37 ( int, pls ) 21.11/21.37 ( int, min ) 21.11/21.37 ( int, s ) 21.11/21.37 ( int, s1 ) 21.11/21.37 ( int, m ) 21.11/21.37 ( int, t ) 21.11/21.37 ( int, v ) 21.11/21.37 ( int, w ) 21.11/21.37 ( int, y ) 21.11/21.37 ( int, sa ) 21.11/21.37 ( int, x ) 21.11/21.37 ( int, r ) 21.11/21.37 ( int, m1 ) 21.11/21.37 ( int, skv_14 ) 21.11/21.37 ( int, skv_20 ) 21.11/21.37 ( (fun int int), bit1 ) 21.11/21.37 ( (fun int int), bit0 ) 21.11/21.37 ( (fun int int), succ ) 21.11/21.37 ( (fun int int), pred ) 21.11/21.37 ( (fun int int), (fact_fact int) ) 21.11/21.37 ( (fun int int), zfact ) 21.11/21.37 ( nat, n ) 21.11/21.37 ( nat, tn ) 21.11/21.37 ( bool, fTrue ) 21.11/21.37 ( bool, fFalse ) 21.11/21.37 ( real, pi ) 21.11/21.37 ( real, (one_one real) ) 21.11/21.37 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.37 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.11/21.37 ( (fun nat real), (real_1 nat) ) 21.11/21.37 ( (fun nat real), cos_coeff ) 21.11/21.37 ( (fun nat real), sin_coeff ) 21.11/21.37 ( (fun real real), sin ) 21.11/21.37 ( (fun real real), cos ) 21.11/21.37 ( (fun real real), sqrt ) 21.11/21.37 ( (fun real real), tan ) 21.11/21.37 ( (fun real real), ln ) 21.11/21.37 ( (fun real real), arctan ) 21.11/21.37 ( (fun real real), arcsin ) 21.11/21.37 ( (fun real real), arccos ) 21.11/21.37 ( (fun nat nat), suc ) 21.11/21.37 ( (fun nat nat), (fact_fact nat) ) 21.11/21.37 ( (fun nat nat), nat_size ) 21.11/21.37 ( (fun nat nat), (size_size nat) ) 21.11/21.37 ( (fun nat nat), fact ) 21.11/21.37 ( (filter nat), sequentially ) 21.11/21.37 ( (fun int (fun int rat)), fract ) 21.11/21.37 ( complex, ii ) 21.11/21.37 ( (fun int bool), zOdd ) 21.11/21.37 ( (fun int bool), zprime ) 21.11/21.37 ( (fun int bool), zEven ) 21.11/21.37 ( (fun int bool), nat_neg ) 21.11/21.37 ( (fun int bool), nat_is_nat ) 21.11/21.37 ( (fun int bool), (even_odd_even int) ) 21.11/21.37 ( (fun int bool), twoSqu1091635170sum2sq ) 21.11/21.37 ( (fun int (fun int int)), legacy_zgcd ) 21.11/21.37 ( (fun int (fun int int)), (gcd_gcd int) ) 21.11/21.37 ( (fun int (fun int int)), inv ) 21.11/21.37 ( (fun int (fun int int)), multInv ) 21.11/21.37 ( (fun int (fun int int)), legendre ) 21.11/21.37 ( (fun int (fun int int)), standardRes ) 21.11/21.37 ( (fun int (fun int int)), nat_tsub ) 21.11/21.37 ( (fun int (fun int int)), z3div ) 21.11/21.37 ( (fun int (fun int int)), z3mod ) 21.11/21.37 ( (fun int (fun int int)), int_lcm ) 21.11/21.37 ( (fun int (fun int int)), int_gcd ) 21.11/21.37 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.11/21.37 ( (fun bool bool), fNot ) 21.11/21.37 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.11/21.37 ( (fun bool (fun bool bool)), fconj ) 21.11/21.37 ( (fun bool (fun bool bool)), fdisj ) 21.11/21.37 ( (fun bool (fun bool bool)), fimplies ) 21.11/21.37 ( (fun int (fun int bool)), quadRes ) 21.11/21.37 ( (fun int (fun int bool)), d22set ) 21.11/21.37 ( (fun int (fun int bool)), norRRset ) 21.11/21.37 ( (fun int (fun int bool)), sRStar ) 21.11/21.37 ( (fun int (fun int bool)), sr ) 21.11/21.37 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.11/21.37 ( (fun nat bool), (even_odd_even nat) ) 21.11/21.37 ( (fun nat bool), prime ) 21.11/21.37 ( (fun real complex), cis ) 21.11/21.37 ( (fun nat (fun nat bool)), coprime ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.11/21.37 ( (fun (product_prod int int) bool), frac_1 ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.11/21.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.11/21.37 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.11/21.37 ( (fun (fun int bool) bool), nat_nat_set ) 21.11/21.37 ( (fun nat (fun real real)), root ) 21.11/21.37 ( (fun real (fun real real)), log ) 21.11/21.37 ( (fun real (fun real real)), powr ) 21.11/21.37 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.11/21.37 ( (fun complex complex), cnj ) 21.11/21.37 ( (fun complex complex), expi ) 21.11/21.37 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.11/21.37 ( (fun nat (fun nat nat)), nat_gcd ) 21.11/21.37 ( (fun nat (fun nat nat)), nat_lcm ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.11/21.37 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.11/21.37 ( (fun int (fun (fun int bool) bool)), resSet ) 21.11/21.37 ( (fun int nat), nat_1 ) 21.11/21.37 ( (fun int nat), phi ) 21.11/21.37 ( (fun complex real), re ) 21.11/21.37 ( (fun complex real), im ) 21.11/21.37 ( (fun complex real), arg ) 21.11/21.37 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.11/21.37 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.11/21.37 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.11/21.37 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.11/21.37 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.11/21.37 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.11/21.37 ( (fun (product_prod nat nat) bool), pred_nat ) 21.11/21.37 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.11/21.37 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.11/21.37 ( (fun (fun int bool) int), (the int) ) 21.11/21.37 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.11/21.37 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.11/21.37 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.11/21.37 ( (fun real (fun real complex)), rcis ) 21.11/21.37 ( (fun real (fun real complex)), complex_1 ) 21.11/21.37 ( (fun int (fun int (fun int bool))), zcong ) 21.11/21.37 ( (fun int (fun int (fun int bool))), wset ) 21.11/21.37 ( (fun int (fun int (fun int bool))), noXRRset ) 21.11/21.37 ( (fun int (fun int (fun int bool))), bnorRset ) 21.11/21.37 ( (fun int (fun int (fun int bool))), zcongm ) 21.11/21.37 ( (fun real nat), natceiling ) 21.11/21.37 ( (fun real nat), natfloor ) 21.11/21.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.11/21.37 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.11/21.37 ( (fun int real), (real_1 int) ) 21.11/21.37 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.11/21.37 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.11/21.37 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.11/21.37 ( (fun complex nat), (size_size complex) ) 21.11/21.37 ( (fun complex nat), complex_size ) 21.11/21.37 ( (fun (fun nat rat) bool), vanishes ) 21.11/21.37 ( (fun (product_prod int int) rat), frct ) 21.11/21.37 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.11/21.37 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.11/21.37 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.11/21.37 ( (fun rat real), ratreal ) 21.11/21.37 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.11/21.37 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.11/21.37 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.11/21.37 ( (fun rat (product_prod int int)), quotient_of ) 21.11/21.37 ( (fun int (fun nat nat)), nat_aux ) 21.11/21.37 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.11/21.37 ( (fun int (list int)), quickc666637781d_zero ) 21.11/21.37 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.11/21.37 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.11/21.37 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.11/21.37 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.11/21.37 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.11/21.37 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.11/21.37 ( (fun code_code_numeral int), code_int_of ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((Va $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) Va))) (= (or (hBOOL (hAPP int bool _let_1 V_1)) (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 Va)) (hAPP int nat _let_0 V_1)))))) ) 21.11/21.37 ( (one_one int), t ) 21.11/21.37 ( min, pls ) 21.11/21.37 ( min, min ) 21.11/21.37 ( (zero_zero int), pls ) 21.11/21.37 ( (zero_zero int), (one_one int) ) 21.11/21.37 ( (zero_zero int), min ) 21.11/21.37 ( (zero_zero int), s ) 21.11/21.37 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.37 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.37 ( (zero_zero int), skv_4 ) 21.11/21.37 ( (zero_zero int), skv_5 ) 21.11/21.37 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103760 $$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_103760)) (ring_1_Ints X_a))))) ) 21.11/21.37 ( real, (one_one int) ) 21.11/21.37 ( real, (zero_zero int) ) 21.11/21.37 ) 21.11/21.37 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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 int))) (let ((_let_2 (power_power int))) (let ((_let_3 (abs_abs int))) (= (= (hAPP nat int (hAPP int _let_1 _let_2 A_3) _let_0) (hAPP nat int (hAPP int _let_1 _let_2 B_2) _let_0)) (= (hAPP int int _let_3 A_3) (hAPP int int _let_3 B_2))))))) ) 21.11/21.37 ( s, s1 ) 21.11/21.37 ( s, w ) 21.11/21.37 ( s1, s ) 21.11/21.37 ( s1, s1 ) 21.11/21.37 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.11/21.37 ( v, v ) 21.11/21.37 ( v, y ) 21.11/21.37 ( w, s1 ) 21.11/21.37 ( y, v ) 21.11/21.37 ( y, x ) 21.11/21.37 ( x, v ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.37 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.11/21.37 ( skv_6, skv_7 ) 21.11/21.37 ( skv_6, skv_16 ) 21.11/21.37 ( skv_7, skv_6 ) 21.11/21.37 ( skv_7, skv_7 ) 21.11/21.37 ( skv_16, skv_7 ) 21.11/21.37 ( skv_23, skv_24 ) 21.11/21.37 ( skv_24, skv_23 ) 21.11/21.37 ( skv_24, skv_24 ) 21.11/21.37 ) 21.11/21.38 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) M))) (or (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N)))) (hBOOL (hAPP nat bool _let_0 N)) (= M N))) ) 21.11/21.38 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X)) (hAPP real real (exp real) X)))))) ) 21.11/21.38 ( pi ) 21.11/21.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( skv_10 ) 21.11/21.38 ( skv_11 ) 21.11/21.38 ( skv_15 ) 21.11/21.38 ( skv_18 ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)) (one_one X_a))) ) 21.11/21.38 ( rat ) 21.11/21.38 ( int ) 21.11/21.38 ( nat ) 21.11/21.38 ( real ) 21.11/21.38 ( complex ) 21.11/21.38 ( quickcheck_code_int ) 21.11/21.38 ( code_code_numeral ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_103874 $$unsorted) (BOUND_VARIABLE_103875 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (field X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_103874) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_103875)) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_103874) BOUND_VARIABLE_103875)))) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.38 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( 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))))))))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ) 21.11/21.38 (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)))) ) 21.11/21.38 ( rat ) 21.11/21.38 ( int ) 21.11/21.38 ( (fun int int) ) 21.11/21.38 ( nat ) 21.11/21.38 ( bool ) 21.11/21.38 ( real ) 21.11/21.38 ( (fun real real) ) 21.11/21.38 ( (fun nat nat) ) 21.11/21.38 ( complex ) 21.11/21.38 ( (product_prod int int) ) 21.11/21.38 ( (fun bool bool) ) 21.11/21.38 ( (fun nat bool) ) 21.11/21.38 ( (fun nat (fun nat bool)) ) 21.11/21.38 ( (fun nat (product_prod int int)) ) 21.11/21.38 ( (product_prod real real) ) 21.11/21.38 ( (product_prod nat nat) ) 21.11/21.38 ( (fun (product_prod nat nat) bool) ) 21.11/21.38 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.11/21.38 ( (fun nat (product_prod nat nat)) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 bool))) (let ((_let_4 (product_Pair int int))) (let ((_let_5 (hAPP int (fun int _let_2) posDivAlg A_3))) (let ((_let_6 (hAPP int _let_2 _let_5 B_2))) (let ((_let_7 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_3) B_2)))) (let ((_let_8 (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) _let_1)))) (or (not (hBOOL (hAPP _let_2 bool (hAPP (fun _let_2 _let_3) _let_3 (accp _let_2) posDivAlg_rel) (hAPP int _let_2 (hAPP int (fun int _let_2) _let_4 A_3) B_2)))) (and (or (and (not _let_7) (not _let_8)) (= (hAPP int _let_2 (hAPP int (fun int _let_2) _let_4 _let_1) A_3) _let_6)) (or _let_7 _let_8 (= _let_6 (hAPP _let_2 _let_2 (hAPP int (fun _let_2 _let_2) adjust B_2) (hAPP int _let_2 _let_5 (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_2)))))))))))))))) ) 21.11/21.38 ( (one_one int), (one_one int) ) 21.11/21.38 ( (one_one int), t ) 21.11/21.38 ( min, min ) 21.11/21.38 ( min, (zero_zero int) ) 21.11/21.38 ( (zero_zero int), pls ) 21.11/21.38 ( (zero_zero int), (one_one int) ) 21.11/21.38 ( (zero_zero int), min ) 21.11/21.38 ( (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))) ) 21.11/21.38 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( s, (one_one int) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((U $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat nat suc U) (hAPP _let_0 nat (finite_card nat) (hAPP nat _let_0 (ord_atMost nat) U)))) ) 21.11/21.38 ( (zero_zero nat) ) 21.11/21.38 ( (hAPP nat nat suc (zero_zero nat)) ) 21.11/21.38 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archimedean_ceiling X_a) (one_one X_a)))) ) 21.11/21.38 ( rat ) 21.11/21.38 ( int ) 21.11/21.38 ( nat ) 21.11/21.38 ( real ) 21.11/21.38 ( complex ) 21.11/21.38 ( quickcheck_code_int ) 21.11/21.38 ( code_code_numeral ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104020 $$unsorted) (BOUND_VARIABLE_104021 $$unsorted) (BOUND_VARIABLE_104022 $$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_104021) (ti X_a BOUND_VARIABLE_104022))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104022) BOUND_VARIABLE_104020))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104021) BOUND_VARIABLE_104020))))) ) 21.11/21.38 ( int, pls, r, (zero_zero int) ) 21.11/21.38 ( int, pls, m1, min ) 21.11/21.38 ( int, (one_one int), s1, (zero_zero int) ) 21.11/21.38 ( int, min, s, min ) 21.11/21.38 ( int, min, y, (zero_zero int) ) 21.11/21.38 ( int, s, pls, (zero_zero int) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), t, (zero_zero int) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m, (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)))) (hAPP int int (abs_abs int) w)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, (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)))) (hAPP int int (abs_abs int) v)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_14, (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_20, (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.11/21.38 ( int, t, v, (one_one int) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), min, (zero_zero int) ) 21.11/21.38 ( int, skv_4, w, (zero_zero int) ) 21.11/21.38 ( int, skv_5, x, (zero_zero int) ) 21.11/21.38 ( 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) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104072 $$unsorted) (BOUND_VARIABLE_104073 $$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_104072)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_104073))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104073) BOUND_VARIABLE_104072))))))) ) 21.11/21.38 ( int, pls, pls ) 21.11/21.38 ( int, pls, (one_one int) ) 21.11/21.38 ( int, pls, min ) 21.11/21.38 ( int, pls, (zero_zero int) ) 21.11/21.38 ( int, (one_one int), pls ) 21.11/21.38 ( int, (one_one int), (one_one int) ) 21.11/21.38 ( int, (one_one int), (zero_zero int) ) 21.11/21.38 ( int, min, min ) 21.11/21.38 ( int, min, (zero_zero int) ) 21.11/21.38 ( int, s, (zero_zero int) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.11/21.38 ( int, t, (one_one int) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( int, skv_4, (zero_zero int) ) 21.11/21.38 ( int, skv_5, (zero_zero int) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( real, pi, (zero_zero real) ) 21.11/21.38 ( 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)))) ) 21.11/21.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.11/21.38 ( 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) ) 21.11/21.38 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.11/21.38 ( real, skv_10, (zero_zero real) ) 21.11/21.38 ( real, skv_11, (zero_zero real) ) 21.11/21.38 ( real, skv_15, (zero_zero real) ) 21.11/21.38 ( real, skv_18, (zero_zero real) ) 21.11/21.38 ) 21.11/21.38 (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 d22set _let_1) (hAPP int _let_0 (hAPP int (fun int _let_0) wset _let_1) P_4))))) ) 21.11/21.38 ( (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)))) ) 21.11/21.38 ( (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))) ) 21.11/21.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( y ) 21.11/21.38 ( x ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.11/21.38 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.11/21.38 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.11/21.38 ( (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))) m1))) ) 21.11/21.38 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (hBOOL (hAPP X_a bool (iszero X_a) (zero_zero X_a)))) ) 21.11/21.38 ( rat ) 21.11/21.38 ( int ) 21.11/21.38 ( nat ) 21.11/21.38 ( real ) 21.11/21.38 ( complex ) 21.11/21.38 ( quickcheck_code_int ) 21.11/21.38 ( code_code_numeral ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (hAPP real real tan X_1)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1)))))) ))) ) 21.11/21.38 ( pi ) 21.11/21.38 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( skv_2 ) 21.11/21.38 ( skv_9 ) 21.11/21.38 ( skv_12 ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104138 $$unsorted) (BOUND_VARIABLE_104139 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (divisi14063676e_zero X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_104138) (hAPP X_a X_a _let_0 BOUND_VARIABLE_104139)) (= (ti X_a BOUND_VARIABLE_104138) (ti X_a BOUND_VARIABLE_104139))))) ) 21.11/21.38 ( real, (zero_zero real), (zero_zero real) ) 21.11/21.38 ( complex, ii, ii ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (one_one int)) B_2))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) A_3))) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_2) (hAPP int _let_0 d22set A_3))))) ) 21.11/21.38 ( pls, min ) 21.11/21.38 ( pls, (zero_zero int) ) 21.11/21.38 ( (one_one int), (zero_zero int) ) 21.11/21.38 ( min, min ) 21.11/21.38 ( min, (zero_zero int) ) 21.11/21.38 ( s, (zero_zero int) ) 21.11/21.38 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.11/21.38 ( t, (one_one int) ) 21.11/21.38 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( skv_4, (zero_zero int) ) 21.11/21.38 ( skv_5, (zero_zero int) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104186 $$unsorted) (BOUND_VARIABLE_104187 $$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_104186) BOUND_VARIABLE_104187)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_104187) BOUND_VARIABLE_104186)))) ) 21.11/21.38 ( int, pls, min ) 21.11/21.38 ( int, pls, (zero_zero int) ) 21.11/21.38 ( int, (one_one int), (zero_zero int) ) 21.11/21.38 ( int, (one_one int), t ) 21.11/21.38 ( int, min, min ) 21.11/21.38 ( int, min, (zero_zero int) ) 21.11/21.38 ( int, (zero_zero int), pls ) 21.11/21.38 ( int, (zero_zero int), (one_one int) ) 21.11/21.38 ( int, (zero_zero int), min ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( int, s, (zero_zero int) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.11/21.38 ( int, t, (one_one int) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.11/21.38 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( int, skv_4, (zero_zero int) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, skv_5, (zero_zero int) ) 21.11/21.38 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( nat, (zero_zero nat), n ) 21.11/21.38 ( nat, (zero_zero nat), tn ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( real, pi, (zero_zero real) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( 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)))) ) 21.11/21.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( 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) ) 21.11/21.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (zero_zero real), pi ) 21.11/21.38 ( 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)))) ) 21.11/21.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (zero_zero real), skv_2 ) 21.11/21.38 ( real, (zero_zero real), skv_9 ) 21.11/21.38 ( real, (zero_zero real), skv_12 ) 21.11/21.38 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.11/21.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.11/21.38 ( 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) ) 21.11/21.38 ( 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 ) 21.11/21.38 ( real, skv_10, (zero_zero real) ) 21.11/21.38 ( real, skv_11, (zero_zero real) ) 21.11/21.38 ( real, skv_15, (zero_zero real) ) 21.11/21.38 ( real, skv_18, (zero_zero real) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 M) N))))) ) 21.11/21.38 ( (zero_zero nat), (one_one nat) ) 21.11/21.38 ( (one_one nat), (one_one nat) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_1) (hAPP real int (archim2085082626_floor real) X)))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP int real (real_1 int) A_1)) X))) ) 21.11/21.38 ( (zero_zero int), pi ) 21.11/21.38 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( (zero_zero int), skv_10 ) 21.11/21.38 ( (zero_zero int), skv_11 ) 21.11/21.38 ( (zero_zero int), skv_15 ) 21.11/21.38 ( (zero_zero int), skv_18 ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104268 $$unsorted) (BOUND_VARIABLE_104269 $$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_104269))) (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_104269)) BOUND_VARIABLE_104268)))))))) ) 21.11/21.38 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((V $$unsorted)) (= (hAPP int real (real_1 int) (hAPP int int (number_number_of int) V)) (hAPP int real (number_number_of real) V)) ) 21.11/21.38 ( pls ) 21.11/21.38 ( (hAPP int int bit1 pls) ) 21.11/21.38 ( min ) 21.11/21.38 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.38 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.11/21.38 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.38 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104342 $$unsorted) (BOUND_VARIABLE_104343 $$unsorted) (BOUND_VARIABLE_104344 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (let ((_let_3 (hAPP nat nat suc BOUND_VARIABLE_104343))) (or (not (linordered_semidom X_a)) (not (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104344) _let_3) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_104342) _let_3))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_104342))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_104344))) (= (ti X_a BOUND_VARIABLE_104344) (ti X_a BOUND_VARIABLE_104342))))))) ) 21.11/21.38 ( int, s, (zero_zero nat), s1 ) 21.11/21.38 ( int, s1, (zero_zero nat), s1 ) 21.11/21.38 ( int, s1, (hAPP nat nat suc (zero_zero nat)), s ) 21.11/21.38 ( int, s1, (hAPP nat nat suc (zero_zero nat)), s1 ) 21.11/21.38 ( int, s1, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), s1 ) 21.11/21.38 ( int, v, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), w ) 21.11/21.38 ( int, w, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), w ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X $$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))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X))))) ) 21.11/21.38 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( (one_one real) ) 21.11/21.38 ( (zero_zero real) ) 21.11/21.38 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104390 $$unsorted) (BOUND_VARIABLE_104391 $$unsorted) (BOUND_VARIABLE_104392 $$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 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_104390) BOUND_VARIABLE_104392)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104391) BOUND_VARIABLE_104392)) (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_104390) BOUND_VARIABLE_104391)) BOUND_VARIABLE_104392)))))) ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), m1 ) 21.11/21.38 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), skv_3 ) 21.11/21.38 ( 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), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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 ) 21.11/21.38 ( 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), m1 ) 21.11/21.38 ( 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), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.11/21.38 ( 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_21 ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, v ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 21.11/21.38 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, w ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int real (ring_1_of_int real) Z_1) (hAPP complex real re (hAPP int complex (ring_1_of_int complex) Z_1))) ) 21.11/21.38 ( (one_one int) ) 21.11/21.38 ( (zero_zero int) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104420 $$unsorted) (BOUND_VARIABLE_104421 $$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_104420) BOUND_VARIABLE_104421)) (= (= (ti X_a BOUND_VARIABLE_104421) (ti X_a BOUND_VARIABLE_104420)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_104420) BOUND_VARIABLE_104421))))) ) 21.11/21.38 ( int, (one_one int), t ) 21.11/21.38 ( int, min, pls ) 21.11/21.38 ( int, min, min ) 21.11/21.38 ( int, min, (zero_zero int) ) 21.11/21.38 ( int, (zero_zero int), pls ) 21.11/21.38 ( int, (zero_zero int), (one_one int) ) 21.11/21.38 ( int, (zero_zero int), min ) 21.11/21.38 ( int, (zero_zero int), s ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (zero_zero int), skv_4 ) 21.11/21.38 ( int, (zero_zero int), skv_5 ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( nat, (zero_zero nat), n ) 21.11/21.38 ( nat, (zero_zero nat), tn ) 21.11/21.38 ( real, pi, (zero_zero real) ) 21.11/21.38 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (zero_zero real), pi ) 21.11/21.38 ( 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)))) ) 21.11/21.38 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( real, (zero_zero real), skv_2 ) 21.11/21.38 ( real, (zero_zero real), skv_9 ) 21.11/21.38 ( real, (zero_zero real), skv_10 ) 21.11/21.38 ( real, (zero_zero real), skv_11 ) 21.11/21.38 ( real, (zero_zero real), skv_12 ) 21.11/21.38 ( real, (zero_zero real), skv_15 ) 21.11/21.38 ( real, (zero_zero real), skv_18 ) 21.11/21.38 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.11/21.38 ( 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) ) 21.11/21.38 ( 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 ) 21.11/21.38 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd N) K_4))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N)))) (hBOOL (hAPP int bool _let_1 M))))) ) 21.11/21.38 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_21, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((W $$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)))) ) 21.11/21.38 ( (one_one int), t ) 21.11/21.38 ( min, min ) 21.11/21.38 ( min, (zero_zero int) ) 21.11/21.38 ( (zero_zero int), pls ) 21.11/21.38 ( (zero_zero int), (one_one int) ) 21.11/21.38 ( (zero_zero int), min ) 21.11/21.38 ( (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))) ) 21.11/21.38 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.38 ( 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))) ) 21.11/21.38 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104500 $$unsorted) (BOUND_VARIABLE_104501 $$unsorted) (BOUND_VARIABLE_104502 $$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_104500))) (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_104501)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_104502)) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_104501) BOUND_VARIABLE_104502))))))) ) 21.11/21.38 ( 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))), (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.11/21.38 ( 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))), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.11/21.38 ( int, sa, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.38 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.38 ( int, r, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.38 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.38 ( int, skv_13, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.38 ( int, skv_19, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C $$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)))) (= (zero_zero real) L) (not (forall ((R_1 $$unsorted)) (or (not (forall ((X_1 $$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) X_1))) R_1))) (= C X_1) (not (= (zero_zero real) (hAPP real real F X_1)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1)))) ))))) ) 21.11/21.38 ( (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)))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104552 $$unsorted) (BOUND_VARIABLE_104553 $$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_104552) BOUND_VARIABLE_104553))) (or (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_104552)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_104553)))))) ) 21.11/21.38 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ) 21.11/21.38 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104599 $$unsorted) (BOUND_VARIABLE_104600 $$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_104600)))) (or (not (linordered_idom X_a)) (= (or (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_104599)) (not _let_1)) _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_104599) BOUND_VARIABLE_104600))))))) ) 21.11/21.38 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.38 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104628 $$unsorted) (BOUND_VARIABLE_104629 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (= (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_104628) BOUND_VARIABLE_104629)) (and (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_104628)) (= (ti X_a BOUND_VARIABLE_104629) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_104628)))))) ) 21.11/21.39 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((Xa $$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) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) (one_one int))) zEven)))))) ) 21.11/21.39 ( (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)))) ) 21.11/21.39 ( y ) 21.11/21.39 ( x ) 21.11/21.39 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.11/21.39 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.11/21.39 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.11/21.39 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.11/21.39 ( (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))) m1))) ) 21.11/21.39 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104694 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (= (zero_zero X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_104694)) (= (zero_zero real) BOUND_VARIABLE_104694))) ) 21.11/21.39 ( complex, (hAPP int real (number_number_of real) min) ) 21.11/21.39 ( complex, pi ) 21.11/21.39 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104709 $$unsorted) (BOUND_VARIABLE_104710 $$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_104709) BOUND_VARIABLE_104710) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_104709) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_104710))))) ) 21.11/21.39 ( int, (one_one int), pls ) 21.11/21.39 ( 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)))), (hAPP int int (number_number_of int) min) ) 21.11/21.39 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.39 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.39 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.39 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.11/21.39 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.11/21.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.11/21.39 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.11/21.39 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.11/21.39 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.11/21.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.11/21.39 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.11/21.39 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.11/21.39 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((Xa $$unsorted)) (or (= (zero_zero real) (hAPP real real cos Xa)) (hBOOL (hAPP real bool (hAPP (fun real real) (fun real bool) (isCont real real) tan) Xa))) ) 21.11/21.39 ( pi ) 21.11/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.39 ( (zero_zero real) ) 21.11/21.39 ( (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))))) ) 21.11/21.39 ( (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) ) 21.11/21.39 ( (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))))) ) 21.11/21.39 ( (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)))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104774 $$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_104774)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_104774))))) ) 21.11/21.39 ( int, (zero_zero nat) ) 21.11/21.39 ( int, (hAPP nat nat suc (zero_zero nat)) ) 21.11/21.39 ( int, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.11/21.39 ( int, n ) 21.11/21.39 ( real, (zero_zero nat) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_104811 $$unsorted) (BOUND_VARIABLE_104812 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_104811) BOUND_VARIABLE_104812))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_104811)) (hAPP nat X_a _let_0 BOUND_VARIABLE_104812))))) ) 21.11/21.39 ( int, (zero_zero nat), (zero_zero nat) ) 21.11/21.39 ( int, (zero_zero nat), (one_one nat) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (hAPP int int bit0 L) (hAPP int int bit0 K)) (= (ti int L) (ti int K))) ) 21.11/21.39 ( pls, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.39 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.11/21.39 ( (hAPP int int bit1 pls), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.39 ( (hAPP int int bit1 pls), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.11/21.39 ( min, pls ) 21.11/21.39 ( min, min ) 21.11/21.39 ( min, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.39 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 21.11/21.39 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.11/21.39 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))), min ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_104866 $$unsorted) (BOUND_VARIABLE_104867 $$unsorted) (BOUND_VARIABLE_104868 $$unsorted) (BOUND_VARIABLE_104869 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_b _let_1))) (let ((_let_4 (tendsto X_a X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_104869))) (or (not (topological_space X_a)) (not (topological_space X_b)) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_104869)) (= (hAPP X_a X_b BOUND_VARIABLE_104867 X_1) (hAPP X_a X_b BOUND_VARIABLE_104868 X_1))) )) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_104868) BOUND_VARIABLE_104866) _let_5)) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_104867) BOUND_VARIABLE_104866) _let_5)))))))))) ) 21.11/21.39 ( 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)))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (let ((_let_0 (fun X_c X_a))) (let ((_let_1 (product_prod X_b X_c))) (= (hAPP _let_1 X_a (hAPP (fun X_b _let_0) (fun _let_1 X_a) (product_prod_case X_b X_c X_a) P_1) Z) (hAPP X_c X_a (hAPP X_b _let_0 P_1 (hAPP _let_1 X_b (product_fst X_b X_c) Z)) (hAPP _let_1 X_c (product_snd X_b X_c) Z))))) ) 21.11/21.39 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (fun _let_0 _let_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (let ((_let_5 (hAPP nat _let_0 (hAPP (fun int (fun nat int)) (fun nat _let_0) (combc int nat int) (power_power int)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP _let_0 _let_1 (hAPP _let_3 _let_4 (combc int _let_0 _let_0) (hAPP _let_1 _let_3 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_3) (combb _let_0 _let_2 int) (combb int int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), (let ((_let_0 (product_prod int int))) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) s) (one_one int))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (hAPP int (fun int _let_0) zcong X))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int _let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (hAPP int int _let_1 min)) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (one_one int)) P_5))))))) ) 21.11/21.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) min) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)))) ) 21.11/21.39 ( rat ) 21.11/21.39 ( int ) 21.11/21.39 ( nat ) 21.11/21.39 ( real ) 21.11/21.39 ( complex ) 21.11/21.39 ( quickcheck_code_int ) 21.11/21.39 ( code_code_numeral ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (zero_zero X_a)) (field_char_0_Rats X_a))))) ) 21.11/21.39 ( rat ) 21.11/21.39 ( int ) 21.11/21.39 ( nat ) 21.11/21.39 ( real ) 21.11/21.39 ( complex ) 21.11/21.39 ( quickcheck_code_int ) 21.11/21.39 ( code_code_numeral ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((K $$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)))) ) 21.11/21.39 ( (zero_zero nat) ) 21.11/21.39 ( (hAPP nat nat suc (zero_zero nat)) ) 21.11/21.39 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((R_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_3) (zero_zero real)))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (real_1 int))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP int real _let_0 N_1)) R_3))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) R_3) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_1) (one_one int))))))))) ))) ) 21.11/21.39 ( pi ) 21.11/21.39 ( (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)))) ) 21.11/21.39 ( (one_one real) ) 21.11/21.39 ( (zero_zero real) ) 21.11/21.39 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ( (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))))) ) 21.11/21.39 ( (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)) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105055 $$unsorted) (BOUND_VARIABLE_105056 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_a)) (= (ti X_a BOUND_VARIABLE_105056) (ti X_a BOUND_VARIABLE_105055)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_105055) BOUND_VARIABLE_105056))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_105055) BOUND_VARIABLE_105056)))) ) 21.11/21.39 ( int, (one_one int), t ) 21.11/21.39 ( int, min, pls ) 21.11/21.39 ( int, min, min ) 21.11/21.39 ( int, min, (zero_zero int) ) 21.11/21.39 ( int, (zero_zero int), pls ) 21.11/21.39 ( int, (zero_zero int), (one_one int) ) 21.11/21.39 ( int, (zero_zero int), min ) 21.11/21.39 ( int, (zero_zero int), s ) 21.11/21.39 ( 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))) ) 21.11/21.39 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.39 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.39 ( int, (zero_zero int), skv_4 ) 21.11/21.39 ( int, (zero_zero int), skv_5 ) 21.11/21.39 ( 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))) ) 21.11/21.39 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ( 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))) ) 21.11/21.39 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( 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))) ) 21.11/21.39 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.39 ( nat, (zero_zero nat), n ) 21.11/21.39 ( nat, (zero_zero nat), tn ) 21.11/21.39 ( real, pi, (zero_zero real) ) 21.11/21.39 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.11/21.39 ( 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))) ) 21.11/21.39 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ( real, (zero_zero real), pi ) 21.11/21.39 ( 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)))) ) 21.11/21.39 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ( real, (zero_zero real), skv_2 ) 21.11/21.39 ( real, (zero_zero real), skv_9 ) 21.11/21.39 ( real, (zero_zero real), skv_10 ) 21.11/21.39 ( real, (zero_zero real), skv_11 ) 21.11/21.39 ( real, (zero_zero real), skv_12 ) 21.11/21.39 ( real, (zero_zero real), skv_15 ) 21.11/21.39 ( real, (zero_zero real), skv_18 ) 21.11/21.39 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.11/21.39 ( 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) ) 21.11/21.39 ( 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 ) 21.11/21.39 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (zero_zero real))) (= (and (= _let_0 B_2) (= _let_0 A_3)) (= (zero_zero complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_3) B_2)))) ) 21.11/21.39 ( (one_one real), (zero_zero real) ) 21.11/21.39 ( (zero_zero real), (one_one real) ) 21.11/21.39 ( (zero_zero real), (zero_zero real) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((N $$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)))) (hBOOL (hAPP int bool _let_0 N)) (hBOOL (hAPP int bool _let_0 M)))) ) 21.11/21.39 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.11/21.39 ( skv_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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105205 $$unsorted) (BOUND_VARIABLE_105206 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105205) (hAPP X_a X_a _let_2 BOUND_VARIABLE_105206))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105206) (hAPP X_a X_a _let_2 BOUND_VARIABLE_105205)))))))) ) 21.11/21.39 ( int, pls, min ) 21.11/21.39 ( int, pls, (zero_zero int) ) 21.11/21.39 ( int, (one_one int), min ) 21.11/21.39 ( int, (one_one int), (zero_zero int) ) 21.11/21.39 ( int, min, pls ) 21.11/21.39 ( int, min, (one_one int) ) 21.11/21.39 ( int, (zero_zero int), pls ) 21.11/21.39 ( int, (zero_zero int), (one_one int) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105229 $$unsorted) (BOUND_VARIABLE_105230 $$unsorted) (BOUND_VARIABLE_105231 $$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 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (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_105229) BOUND_VARIABLE_105230)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_105231) BOUND_VARIABLE_105230)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_105230))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105229) BOUND_VARIABLE_105231))))))) ) 21.11/21.39 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((Y $$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)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (not (forall ((X_1 $$unsorted)) (or (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y_1))) (not (= Y (hAPP real real cos Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) pi))) (= X_1 Y_1)) )) (not (= Y (hAPP real real cos X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) pi))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X_1)))) ))))) ) 21.11/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.11/21.39 ( (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)))) ) 21.11/21.39 ( (zero_zero real) ) 21.11/21.39 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.11/21.39 ( skv_10 ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= Xa Ya) (= (hAPP real real sqrt Ya) (hAPP real real sqrt Xa))) ) 21.11/21.39 ( (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))) ) 21.11/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.11/21.39 ( (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))) ) 21.11/21.39 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.11/21.39 ( (zero_zero real), (zero_zero real) ) 21.11/21.39 ( (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))) ) 21.11/21.39 ) 21.11/21.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (summable X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 21.11/21.39 ( rat ) 21.11/21.39 ( int ) 21.11/21.39 ( (fun int int) ) 21.11/21.39 ( nat ) 21.11/21.39 ( bool ) 21.11/21.39 ( real ) 21.11/21.39 ( (fun real real) ) 21.11/21.39 ( (fun nat nat) ) 21.11/21.39 ( complex ) 21.11/21.39 ( (product_prod int int) ) 21.11/21.39 ( (fun bool bool) ) 21.11/21.39 ( (fun nat bool) ) 21.21/21.39 ( (fun nat (fun nat bool)) ) 21.21/21.39 ( quickcheck_code_int ) 21.21/21.39 ( code_code_numeral ) 21.21/21.39 ( (fun nat (product_prod int int)) ) 21.21/21.39 ( (product_prod real real) ) 21.21/21.39 ( (product_prod nat nat) ) 21.21/21.39 ( (fun (product_prod nat nat) bool) ) 21.21/21.39 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.21/21.39 ( (fun nat (product_prod nat nat)) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (fun int rat))) (let ((_let_1 (zero_zero int))) (= (hAPP int rat (hAPP int _let_0 fract A_1) _let_1) (hAPP int rat (hAPP int _let_0 fract _let_1) (one_one int))))) ) 21.21/21.39 ( (one_one int) ) 21.21/21.39 ( (zero_zero int) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105661 $$unsorted) (BOUND_VARIABLE_105662 $$unsorted) (BOUND_VARIABLE_105663 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_105661))) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_105663) (ti X_a BOUND_VARIABLE_105662))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_105663))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_105662)))) ) 21.21/21.39 ( int, (one_one int), m, m ) 21.21/21.39 ( int, min, r, r ) 21.21/21.39 ( int, (zero_zero int), s1, s1 ) 21.21/21.39 ( int, s, m1, m1 ) 21.21/21.39 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), s, s ) 21.21/21.39 ( int, t, v, v ) 21.21/21.39 ( int, m1, min, min ) 21.21/21.39 ( int, skv_4, sa, sa ) 21.21/21.39 ( int, skv_5, t, t ) 21.21/21.39 ( nat, (zero_zero nat), n, n ) 21.21/21.39 ( real, pi, pi, pi ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105692 $$unsorted) (BOUND_VARIABLE_105693 $$unsorted) (BOUND_VARIABLE_105694 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_105692))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_105693) BOUND_VARIABLE_105694))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_105692))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105692) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_105694)) (hAPP nat X_a _let_2 BOUND_VARIABLE_105693))))))) ) 21.21/21.39 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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))) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X $$unsorted)) (or (not (= (one_one real) (hAPP real real cos X))) (= (zero_zero real) (hAPP real real sin X))) ) 21.21/21.39 ( pi ) 21.21/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.39 ( (zero_zero real) ) 21.21/21.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.21/21.39 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.21/21.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.21/21.39 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.21/21.39 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.21/21.39 ( skv_10 ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((Va $$unsorted)) (= (= (zero_zero nat) (hAPP int nat (number_number_of nat) Va)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Va) pls))) ) 21.21/21.39 ( pls ) 21.21/21.39 ( (hAPP int int bit1 pls) ) 21.21/21.39 ( (one_one int) ) 21.21/21.39 ( min ) 21.21/21.39 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.21/21.39 ( (zero_zero int) ) 21.21/21.39 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.21/21.39 ( (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)))) (hAPP int int (abs_abs int) w)) ) 21.21/21.39 ( (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)))) (hAPP int int (abs_abs int) v)) ) 21.21/21.39 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.21/21.39 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((I_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (list int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) I_1))) (= (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int nat nat_1 I_1))) (one_one nat)) (hAPP _let_1 nat (size_size _let_1) (hAPP int _let_1 quickc666637781d_zero I_1)))))) ) 21.21/21.39 ( pls ) 21.21/21.39 ( (one_one int) ) 21.21/21.39 ( min ) 21.21/21.39 ( (zero_zero int) ) 21.21/21.39 ( s ) 21.21/21.39 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ( t ) 21.21/21.39 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.21/21.39 ( skv_4 ) 21.21/21.39 ( skv_5 ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root Na) Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0))))))) ) 21.21/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((B $$unsorted) (Q_3 $$unsorted) (R_3 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (ord_less int))) (let ((_let_4 (zero_zero int))) (let ((_let_5 (times_times int))) (let ((_let_6 (ord_less_eq int))) (let ((_let_7 (hAPP int _let_2 _let_6 _let_4))) (let ((_let_8 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_5 B_5) Q_5)) R_4))) (or (not (= _let_8 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_5 B) Q_3)) R_3))) (not (hBOOL (hAPP int bool _let_7 _let_8))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 R_4) B_5))) (not (hBOOL (hAPP int bool _let_7 R_3))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 _let_4) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_6 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_2 _let_6 Q_3) Q_5)))))))))))) ) 21.21/21.39 ( (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) ) 21.21/21.39 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.21/21.39 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 21.21/21.39 ( x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.21/21.39 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 21.21/21.39 ( r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.21/21.39 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.21/21.39 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (hilbert_Eps X_a))) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0))) ) 21.21/21.39 ( int ) 21.21/21.39 ( nat ) 21.21/21.39 ( bool ) 21.21/21.39 ( real ) 21.21/21.39 ( (filter nat) ) 21.21/21.39 ( (fun int bool) ) 21.21/21.39 ( (product_prod int int) ) 21.21/21.39 ( (fun nat bool) ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.21/21.39 ( (product_prod real real) ) 21.21/21.39 ( (filter real) ) 21.21/21.39 ( (product_prod nat nat) ) 21.21/21.39 ( (fun nat rat) ) 21.21/21.39 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105851 $$unsorted) (BOUND_VARIABLE_105852 $$unsorted) (BOUND_VARIABLE_105853 $$unsorted) (BOUND_VARIABLE_105854 $$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 (ord_less X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_105853) BOUND_VARIABLE_105854))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_105851) BOUND_VARIABLE_105852))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_105853))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_2) BOUND_VARIABLE_105851))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_105853) BOUND_VARIABLE_105851)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_105854) BOUND_VARIABLE_105852)))))))))) ) 21.21/21.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.39 ) 21.21/21.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105890 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_105890)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_105890))))) ) 21.21/21.39 ( rat, (zero_zero rat) ) 21.21/21.39 ( int, pls ) 21.21/21.39 ( int, min ) 21.21/21.39 ( int, s ) 21.21/21.39 ( int, s1 ) 21.21/21.39 ( int, m ) 21.21/21.39 ( int, t ) 21.21/21.39 ( int, v ) 21.21/21.39 ( int, w ) 21.21/21.39 ( int, y ) 21.21/21.39 ( int, sa ) 21.21/21.39 ( int, x ) 21.21/21.39 ( int, r ) 21.21/21.39 ( int, m1 ) 21.21/21.39 ( int, skv_14 ) 21.21/21.39 ( int, skv_20 ) 21.21/21.39 ( (fun int int), bit1 ) 21.21/21.39 ( (fun int int), bit0 ) 21.21/21.39 ( (fun int int), succ ) 21.21/21.39 ( (fun int int), pred ) 21.21/21.39 ( (fun int int), (fact_fact int) ) 21.21/21.39 ( (fun int int), zfact ) 21.21/21.39 ( nat, n ) 21.21/21.39 ( nat, tn ) 21.21/21.39 ( bool, fTrue ) 21.21/21.39 ( bool, fFalse ) 21.21/21.39 ( real, pi ) 21.21/21.39 ( real, (zero_zero real) ) 21.21/21.39 ( (fun nat real), (real_1 nat) ) 21.21/21.39 ( (fun nat real), cos_coeff ) 21.21/21.39 ( (fun nat real), sin_coeff ) 21.21/21.39 ( (fun real real), sin ) 21.21/21.39 ( (fun real real), cos ) 21.21/21.39 ( (fun real real), sqrt ) 21.21/21.39 ( (fun real real), tan ) 21.21/21.39 ( (fun real real), ln ) 21.21/21.39 ( (fun real real), arctan ) 21.21/21.39 ( (fun real real), arcsin ) 21.21/21.39 ( (fun real real), arccos ) 21.21/21.39 ( (fun nat nat), suc ) 21.21/21.39 ( (fun nat nat), (fact_fact nat) ) 21.21/21.39 ( (fun nat nat), nat_size ) 21.21/21.39 ( (fun nat nat), (size_size nat) ) 21.21/21.39 ( (fun nat nat), fact ) 21.21/21.39 ( (filter nat), sequentially ) 21.21/21.39 ( (fun int (fun int rat)), fract ) 21.21/21.39 ( complex, ii ) 21.21/21.39 ( (fun int bool), zOdd ) 21.21/21.39 ( (fun int bool), zprime ) 21.21/21.39 ( (fun int bool), zEven ) 21.21/21.39 ( (fun int bool), nat_neg ) 21.21/21.39 ( (fun int bool), nat_is_nat ) 21.21/21.39 ( (fun int bool), (even_odd_even int) ) 21.21/21.39 ( (fun int bool), twoSqu1091635170sum2sq ) 21.21/21.39 ( (fun int (fun int int)), legacy_zgcd ) 21.21/21.39 ( (fun int (fun int int)), (gcd_gcd int) ) 21.21/21.39 ( (fun int (fun int int)), inv ) 21.21/21.39 ( (fun int (fun int int)), multInv ) 21.21/21.39 ( (fun int (fun int int)), legendre ) 21.21/21.39 ( (fun int (fun int int)), standardRes ) 21.21/21.39 ( (fun int (fun int int)), nat_tsub ) 21.21/21.39 ( (fun int (fun int int)), z3div ) 21.21/21.39 ( (fun int (fun int int)), z3mod ) 21.21/21.39 ( (fun int (fun int int)), int_lcm ) 21.21/21.39 ( (fun int (fun int int)), int_gcd ) 21.21/21.39 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.21/21.39 ( (fun bool bool), fNot ) 21.21/21.39 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.21/21.39 ( (fun bool (fun bool bool)), fconj ) 21.21/21.39 ( (fun bool (fun bool bool)), fdisj ) 21.21/21.39 ( (fun bool (fun bool bool)), fimplies ) 21.21/21.39 ( (fun int (fun int bool)), quadRes ) 21.21/21.39 ( (fun int (fun int bool)), d22set ) 21.21/21.39 ( (fun int (fun int bool)), norRRset ) 21.21/21.39 ( (fun int (fun int bool)), sRStar ) 21.21/21.39 ( (fun int (fun int bool)), sr ) 21.21/21.39 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.21/21.39 ( (fun nat bool), (even_odd_even nat) ) 21.21/21.39 ( (fun nat bool), prime ) 21.21/21.39 ( (fun real complex), cis ) 21.21/21.39 ( (fun nat (fun nat bool)), coprime ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.21/21.39 ( (fun (product_prod int int) bool), frac_1 ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.21/21.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.21/21.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.21/21.39 ( (fun (fun int bool) bool), nat_nat_set ) 21.21/21.39 ( (fun nat (fun real real)), root ) 21.21/21.39 ( (fun real (fun real real)), log ) 21.21/21.39 ( (fun real (fun real real)), powr ) 21.21/21.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.21/21.39 ( (fun complex complex), cnj ) 21.21/21.39 ( (fun complex complex), expi ) 21.21/21.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.21/21.39 ( (fun nat (fun nat nat)), nat_gcd ) 21.21/21.39 ( (fun nat (fun nat nat)), nat_lcm ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.21/21.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.21/21.39 ( (fun int (fun (fun int bool) bool)), resSet ) 21.21/21.39 ( (fun int nat), nat_1 ) 21.21/21.39 ( (fun int nat), phi ) 21.21/21.39 ( (fun complex real), re ) 21.21/21.39 ( (fun complex real), im ) 21.21/21.39 ( (fun complex real), arg ) 21.21/21.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.21/21.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.21/21.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.21/21.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.21/21.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.21/21.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.21/21.39 ( (fun (product_prod nat nat) bool), pred_nat ) 21.21/21.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.21/21.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.21/21.39 ( (fun (fun int bool) int), (the int) ) 21.21/21.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.21/21.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.21/21.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.21/21.39 ( (fun real (fun real complex)), rcis ) 21.21/21.39 ( (fun real (fun real complex)), complex_1 ) 21.21/21.39 ( (fun int (fun int (fun int bool))), zcong ) 21.21/21.39 ( (fun int (fun int (fun int bool))), wset ) 21.21/21.39 ( (fun int (fun int (fun int bool))), noXRRset ) 21.21/21.39 ( (fun int (fun int (fun int bool))), bnorRset ) 21.21/21.39 ( (fun int (fun int (fun int bool))), zcongm ) 21.21/21.39 ( (fun real nat), natceiling ) 21.21/21.39 ( (fun real nat), natfloor ) 21.21/21.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.21/21.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.21/21.39 ( (fun int real), (real_1 int) ) 21.21/21.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.21/21.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.21/21.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.21/21.39 ( (fun complex nat), (size_size complex) ) 21.21/21.39 ( (fun complex nat), complex_size ) 21.21/21.39 ( (fun (fun nat rat) bool), vanishes ) 21.21/21.39 ( (fun (product_prod int int) rat), frct ) 21.21/21.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.21/21.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.21/21.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.21/21.39 ( (fun rat real), ratreal ) 21.21/21.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.21/21.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.21/21.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.21/21.39 ( (fun rat (product_prod int int)), quotient_of ) 21.21/21.39 ( (fun int (fun nat nat)), nat_aux ) 21.21/21.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.21/21.39 ( (fun int (list int)), quickc666637781d_zero ) 21.21/21.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.21/21.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.21/21.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.21/21.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.21/21.40 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.21/21.40 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.21/21.40 ( (fun code_code_numeral int), code_int_of ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105913 $$unsorted) (BOUND_VARIABLE_105914 $$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_105914) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_105913) _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_105914) BOUND_VARIABLE_105913))))))) ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( 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 bit1 (hAPP int int bit1 pls))) ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 21.21/21.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.21/21.40 ( 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) ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_105950 $$unsorted) (BOUND_VARIABLE_105951 $$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_105950) BOUND_VARIABLE_105951))) (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_105950) BOUND_VARIABLE_105951)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 _let_4) _let_4))) BOUND_VARIABLE_105951)))))))) ) 21.21/21.40 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.21/21.40 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.21/21.40 ( int, (one_one int), t ) 21.21/21.40 ( int, min, min ) 21.21/21.40 ( int, min, (zero_zero int) ) 21.21/21.40 ( int, (zero_zero int), pls ) 21.21/21.40 ( int, (zero_zero int), (one_one int) ) 21.21/21.40 ( int, (zero_zero int), min ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( 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)))), (one_one int) ) 21.21/21.40 ( 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) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.21/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.21/21.40 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.21/21.40 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.21/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( nat, (zero_zero nat), n ) 21.21/21.40 ( nat, (zero_zero nat), tn ) 21.21/21.40 ( nat, (one_one nat), (one_one nat) ) 21.21/21.40 ( real, pi, (zero_zero real) ) 21.21/21.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( real, (zero_zero real), pi ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( real, (zero_zero real), skv_2 ) 21.21/21.40 ( real, (zero_zero real), skv_9 ) 21.21/21.40 ( real, (zero_zero real), skv_12 ) 21.21/21.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.21/21.40 ( 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) ) 21.21/21.40 ( 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 ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((N $$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))) (not (= _let_0 (hAPP int int (fact_fact int) N))))) ) 21.21/21.40 ( pls ) 21.21/21.40 ( (one_one int) ) 21.21/21.40 ( min ) 21.21/21.40 ( (zero_zero int) ) 21.21/21.40 ( s ) 21.21/21.40 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.21/21.40 ( skv_4 ) 21.21/21.40 ( skv_5 ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= _let_0 (hAPP real real (hAPP nat (fun real real) root N) _let_0)))) ) 21.21/21.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( n ) 21.21/21.40 ( tn ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$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)))))) ) 21.21/21.40 ( int, rat, int, fract, (fact_fact int), (one_one int) ) 21.21/21.40 ( int, rat, int, fract, (fact_fact int), (zero_zero int) ) 21.21/21.40 ( int, int, int, (plus_plus int), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.21/21.40 ( int, int, int, (plus_plus int), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.21/21.40 ( int, bool, int, (ord_less int), bit1, min ) 21.21/21.40 ( int, bool, int, (ord_less int), bit0, (zero_zero int) ) 21.21/21.40 ( int, bool, int, (ord_less int), succ, min ) 21.21/21.40 ( int, bool, int, (ord_less int), pred, (zero_zero int) ) 21.21/21.40 ( int, bool, int, (ord_less int), (fact_fact int), (zero_zero int) ) 21.21/21.40 ( int, bool, int, (ord_less_eq int), bit1, min ) 21.21/21.40 ( int, bool, int, (ord_less_eq int), bit0, (zero_zero int) ) 21.21/21.40 ( int, bool, int, (ord_less_eq int), succ, min ) 21.21/21.40 ( int, bool, int, (ord_less_eq int), pred, (zero_zero int) ) 21.21/21.40 ( int, bool, int, (ord_less_eq int), (fact_fact int), (zero_zero int) ) 21.21/21.40 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (one_one int) ) 21.21/21.40 ( int, (product_prod int int), int, (product_Pair int int), (fact_fact int), (zero_zero int) ) 21.21/21.40 ( nat, nat, nat, (plus_plus nat), (fact_fact nat), (one_one nat) ) 21.21/21.40 ( real, bool, real, (ord_less real), sin, pi ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( real, complex, real, complex_1, cos, (zero_zero real) ) 21.21/21.40 ( real, complex, real, complex_1, (sgn_sgn real), (zero_zero real) ) 21.21/21.40 ( real, complex, real, complex_1, ln, (one_one real) ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= M (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N)))) ) 21.21/21.40 ( (one_one nat), (hAPP int nat nat_1 t) ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$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))))))) ) 21.21/21.40 ( rat ) 21.21/21.40 ( int ) 21.21/21.40 ( (fun int int) ) 21.21/21.40 ( nat ) 21.21/21.40 ( bool ) 21.21/21.40 ( real ) 21.21/21.40 ( (fun real real) ) 21.21/21.40 ( (fun nat nat) ) 21.21/21.40 ( complex ) 21.21/21.40 ( (product_prod int int) ) 21.21/21.40 ( (fun bool bool) ) 21.21/21.40 ( (fun nat bool) ) 21.21/21.40 ( (fun nat (fun nat bool)) ) 21.21/21.40 ( quickcheck_code_int ) 21.21/21.40 ( code_code_numeral ) 21.21/21.40 ( (fun nat (product_prod int int)) ) 21.21/21.40 ( (product_prod real real) ) 21.21/21.40 ( (product_prod nat nat) ) 21.21/21.40 ( (fun (product_prod nat nat) bool) ) 21.21/21.40 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.21/21.40 ( (fun nat (product_prod nat nat)) ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((F $$unsorted)) (let ((_let_0 (fun nat real))) (or (not (hBOOL (hAPP _let_0 bool (summable real) F))) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP nat real F N_1))) )) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) (hAPP _let_0 real (suminf real) F))))) ) 21.21/21.40 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106089 $$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_106089)) (= (one_one X_a) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_106089)))) ) 21.21/21.40 ( rat, (zero_zero rat) ) 21.21/21.40 ( int, pls ) 21.21/21.40 ( int, (one_one int) ) 21.21/21.40 ( int, min ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.21/21.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( nat, n ) 21.21/21.40 ( nat, tn ) 21.21/21.40 ( real, pi ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( real, (zero_zero real) ) 21.21/21.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( real, skv_2 ) 21.21/21.40 ( real, skv_9 ) 21.21/21.40 ( real, skv_12 ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106107 $$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)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_106107)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106107) _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_106107)))))))) ) 21.21/21.40 ( int, pls ) 21.21/21.40 ( int, (one_one int) ) 21.21/21.40 ( int, min ) 21.21/21.40 ( int, (zero_zero int) ) 21.21/21.40 ( 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))) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.21/21.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.21/21.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.21/21.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.21/21.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.21/21.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( nat, n ) 21.21/21.40 ( nat, tn ) 21.21/21.40 ( real, pi ) 21.21/21.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( real, (zero_zero real) ) 21.21/21.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( real, skv_2 ) 21.21/21.40 ( real, skv_9 ) 21.21/21.40 ( real, skv_10 ) 21.21/21.40 ( real, skv_12 ) 21.21/21.40 ( complex, ii ) 21.21/21.40 ) 21.21/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106155 $$unsorted) (BOUND_VARIABLE_106156 $$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_106156) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_106155) _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_106156) BOUND_VARIABLE_106155)) _let_3))))))) ) 21.21/21.40 ( 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)))) ) 21.21/21.40 ( 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) ) 21.21/21.40 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.21/21.40 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.21/21.40 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.21/21.40 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.21/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.21/21.40 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.21/21.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.21/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.22/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.22/21.40 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.22/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.22/21.40 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.22/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( nat, (one_one nat), (one_one nat) ) 21.22/21.40 ) 21.22/21.40 (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)))))) ) 21.22/21.40 ( (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)))) ) 21.22/21.40 ( y ) 21.22/21.40 ( x ) 21.22/21.40 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.22/21.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.22/21.40 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.22/21.40 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.22/21.40 ( (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))) m1))) ) 21.22/21.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.22/21.40 ) 21.22/21.40 (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_1 $$unsorted) (Y_1 $$unsorted)) (or (not (= (hAPP X_c _let_0 (hAPP X_b (fun X_c _let_0) (product_Pair X_b X_c) X_1) Y_1) (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_1) Y_1))))) )))) ) 21.22/21.40 ( int, int, int, twoSqu1091635170sum2sq, (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))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (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))) ) 21.22/21.40 ( 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_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (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))) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((M $$unsorted) (Y $$unsorted) (X $$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))) (not (hBOOL (hAPP int bool _let_2 Y))) (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) Y) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) M))) (= (ti int X) (ti int Y)))))) ) 21.22/21.40 ( (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))), s, s1 ) 21.22/21.40 ( (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))), (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)))) ) 21.22/21.40 ( (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))), (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( (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))), (hAPP int int (number_number_of int) min), (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)))) ) 21.22/21.40 ( (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))), (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( (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_4, s1 ) 21.22/21.40 ( (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_5, s1 ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real cos X)) (hAPP real real cos (hAPP real real (hAPP real (fun real real) (plus_plus real) X) pi))) ) 21.22/21.40 ( (zero_zero real) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) V))) (or (hBOOL (hAPP int bool nat_neg _let_0)) (= (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) V)) _let_0))) ) 21.22/21.40 ( pls ) 21.22/21.40 ( (hAPP int int bit1 pls) ) 21.22/21.40 ( min ) 21.22/21.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat (number_number_of nat) V)))) ) 21.22/21.40 ( pls ) 21.22/21.40 ( (hAPP int int bit1 pls) ) 21.22/21.40 ( min ) 21.22/21.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X)) X))))) ) 21.22/21.40 ( (one_one real) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (inverse_divide real) X) Y) (hAPP real real (hAPP real _let_0 (times_times real) X) (hAPP real real (inverse_inverse real) Y)))) ) 21.22/21.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 21.22/21.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106284 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int bit1 pls)) BOUND_VARIABLE_106284)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_106284))))) ) 21.22/21.40 ( int, pls ) 21.22/21.40 ( int, (hAPP int int bit1 pls) ) 21.22/21.40 ( int, min ) 21.22/21.40 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.40 ( nat, pls ) 21.22/21.40 ( nat, (hAPP int int bit1 pls) ) 21.22/21.40 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.40 ( real, min ) 21.22/21.40 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.40 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.22/21.40 ( complex, min ) 21.22/21.40 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.40 ( quickcheck_code_int, pls ) 21.22/21.40 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.22/21.40 ( quickcheck_code_int, (one_one int) ) 21.22/21.40 ( code_code_numeral, pls ) 21.22/21.40 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.22/21.40 ) 21.22/21.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106306 $$unsorted) (BOUND_VARIABLE_106307 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_106307)) (= (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_106306) BOUND_VARIABLE_106307)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_106306)) (hAPP X_a real _let_0 BOUND_VARIABLE_106307))))) ) 21.22/21.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.40 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.40 ( 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))))))))) ) 21.22/21.40 ( 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))) ) 21.22/21.40 ( 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))) ) 21.22/21.40 ( 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))) ) 21.22/21.40 ) 21.22/21.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106333 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ring_11004092258visors X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_106333)) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_106333) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.41 ( int, pls ) 21.22/21.41 ( int, min ) 21.22/21.41 ( int, s ) 21.22/21.41 ( int, s1 ) 21.22/21.41 ( int, m ) 21.22/21.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( int, t ) 21.22/21.41 ( int, v ) 21.22/21.41 ( int, w ) 21.22/21.41 ( int, y ) 21.22/21.41 ( int, sa ) 21.22/21.41 ( int, x ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.22/21.41 ( int, r ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.22/21.41 ( int, m1 ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.41 ( int, skv_6 ) 21.22/21.41 ( int, skv_7 ) 21.22/21.41 ( int, skv_14 ) 21.22/21.41 ( int, skv_16 ) 21.22/21.41 ( int, skv_20 ) 21.22/21.41 ( int, skv_23 ) 21.22/21.41 ( int, skv_24 ) 21.22/21.41 ( (fun int int), bit1 ) 21.22/21.41 ( (fun int int), bit0 ) 21.22/21.41 ( (fun int int), succ ) 21.22/21.41 ( (fun int int), pred ) 21.22/21.41 ( (fun int int), (fact_fact int) ) 21.22/21.41 ( (fun int int), zfact ) 21.22/21.41 ( nat, n ) 21.22/21.41 ( nat, tn ) 21.22/21.41 ( bool, fTrue ) 21.22/21.41 ( bool, fFalse ) 21.22/21.41 ( real, (hAPP int real (number_number_of real) min) ) 21.22/21.41 ( real, pi ) 21.22/21.41 ( 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)))) ) 21.22/21.41 ( (fun nat real), (real_1 nat) ) 21.22/21.41 ( (fun nat real), cos_coeff ) 21.22/21.41 ( (fun nat real), sin_coeff ) 21.22/21.41 ( (fun real real), sin ) 21.22/21.41 ( (fun real real), cos ) 21.22/21.41 ( (fun real real), sqrt ) 21.22/21.41 ( (fun real real), tan ) 21.22/21.41 ( (fun real real), ln ) 21.22/21.41 ( (fun real real), arctan ) 21.22/21.41 ( (fun real real), arcsin ) 21.22/21.41 ( (fun real real), arccos ) 21.22/21.41 ( (fun nat nat), suc ) 21.22/21.41 ( (fun nat nat), (fact_fact nat) ) 21.22/21.41 ( (fun nat nat), nat_size ) 21.22/21.41 ( (fun nat nat), (size_size nat) ) 21.22/21.41 ( (fun nat nat), fact ) 21.22/21.41 ( (filter nat), sequentially ) 21.22/21.41 ( (fun int (fun int rat)), fract ) 21.22/21.41 ( complex, ii ) 21.22/21.41 ( (fun int bool), zOdd ) 21.22/21.41 ( (fun int bool), zprime ) 21.22/21.41 ( (fun int bool), zEven ) 21.22/21.41 ( (fun int bool), nat_neg ) 21.22/21.41 ( (fun int bool), nat_is_nat ) 21.22/21.41 ( (fun int bool), (even_odd_even int) ) 21.22/21.41 ( (fun int bool), twoSqu1091635170sum2sq ) 21.22/21.41 ( (fun int (fun int int)), legacy_zgcd ) 21.22/21.41 ( (fun int (fun int int)), (gcd_gcd int) ) 21.22/21.41 ( (fun int (fun int int)), inv ) 21.22/21.41 ( (fun int (fun int int)), multInv ) 21.22/21.41 ( (fun int (fun int int)), legendre ) 21.22/21.41 ( (fun int (fun int int)), standardRes ) 21.22/21.41 ( (fun int (fun int int)), nat_tsub ) 21.22/21.41 ( (fun int (fun int int)), z3div ) 21.22/21.41 ( (fun int (fun int int)), z3mod ) 21.22/21.41 ( (fun int (fun int int)), int_lcm ) 21.22/21.41 ( (fun int (fun int int)), int_gcd ) 21.22/21.41 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.22/21.41 ( (fun bool bool), fNot ) 21.22/21.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.22/21.41 ( (fun bool (fun bool bool)), fconj ) 21.22/21.41 ( (fun bool (fun bool bool)), fdisj ) 21.22/21.41 ( (fun bool (fun bool bool)), fimplies ) 21.22/21.41 ( (fun int (fun int bool)), quadRes ) 21.22/21.41 ( (fun int (fun int bool)), d22set ) 21.22/21.41 ( (fun int (fun int bool)), norRRset ) 21.22/21.41 ( (fun int (fun int bool)), sRStar ) 21.22/21.41 ( (fun int (fun int bool)), sr ) 21.22/21.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.22/21.41 ( (fun nat bool), (even_odd_even nat) ) 21.22/21.41 ( (fun nat bool), prime ) 21.22/21.41 ( (fun real complex), cis ) 21.22/21.41 ( (fun nat (fun nat bool)), coprime ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.22/21.41 ( (fun (product_prod int int) bool), frac_1 ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.22/21.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.22/21.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.22/21.41 ( (fun (fun int bool) bool), nat_nat_set ) 21.22/21.41 ( (fun nat (fun real real)), root ) 21.22/21.41 ( (fun real (fun real real)), log ) 21.22/21.41 ( (fun real (fun real real)), powr ) 21.22/21.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.22/21.41 ( (fun complex complex), cnj ) 21.22/21.41 ( (fun complex complex), expi ) 21.22/21.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.22/21.41 ( (fun nat (fun nat nat)), nat_gcd ) 21.22/21.41 ( (fun nat (fun nat nat)), nat_lcm ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.22/21.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.22/21.41 ( (fun int (fun (fun int bool) bool)), resSet ) 21.22/21.41 ( (fun int nat), nat_1 ) 21.22/21.41 ( (fun int nat), phi ) 21.22/21.41 ( (fun complex real), re ) 21.22/21.41 ( (fun complex real), im ) 21.22/21.41 ( (fun complex real), arg ) 21.22/21.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.22/21.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.22/21.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.22/21.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.22/21.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.22/21.41 ( (fun (product_prod nat nat) bool), pred_nat ) 21.22/21.41 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.22/21.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.22/21.41 ( (fun (fun int bool) int), (the int) ) 21.22/21.41 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.22/21.41 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.22/21.41 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.22/21.41 ( (fun real (fun real complex)), rcis ) 21.22/21.41 ( (fun real (fun real complex)), complex_1 ) 21.22/21.41 ( (fun int (fun int (fun int bool))), zcong ) 21.22/21.41 ( (fun int (fun int (fun int bool))), wset ) 21.22/21.41 ( (fun int (fun int (fun int bool))), noXRRset ) 21.22/21.41 ( (fun int (fun int (fun int bool))), bnorRset ) 21.22/21.41 ( (fun int (fun int (fun int bool))), zcongm ) 21.22/21.41 ( (fun real nat), natceiling ) 21.22/21.41 ( (fun real nat), natfloor ) 21.22/21.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.22/21.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.22/21.41 ( (fun int real), (real_1 int) ) 21.22/21.41 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.22/21.41 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.22/21.41 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.22/21.41 ( (fun complex nat), (size_size complex) ) 21.22/21.41 ( (fun complex nat), complex_size ) 21.22/21.41 ( (fun (fun nat rat) bool), vanishes ) 21.22/21.41 ( (fun (product_prod int int) rat), frct ) 21.22/21.41 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.22/21.41 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.22/21.41 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.22/21.41 ( (fun rat real), ratreal ) 21.22/21.41 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.22/21.41 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.22/21.41 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.22/21.41 ( (fun rat (product_prod int int)), quotient_of ) 21.22/21.41 ( (fun int (fun nat nat)), nat_aux ) 21.22/21.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.22/21.41 ( (fun int (list int)), quickc666637781d_zero ) 21.22/21.41 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.22/21.41 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.22/21.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.22/21.41 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.22/21.41 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.22/21.41 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.22/21.41 ( (fun code_code_numeral int), code_int_of ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((Na $$unsorted) (Ma $$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))) (= (and (= _let_0 (ti int Na)) (= _let_0 (ti int Ma))) (= _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) Ma) Na))))) ) 21.22/21.41 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.22/21.41 ( 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))) ) 21.22/21.41 ( v, y ) 21.22/21.41 ( v, sa ) 21.22/21.41 ( v, x ) 21.22/21.41 ( v, r ) 21.22/21.41 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.22/21.41 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.22/21.41 ( w, y ) 21.22/21.41 ( w, sa ) 21.22/21.41 ( w, x ) 21.22/21.41 ( w, r ) 21.22/21.41 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.22/21.41 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.22/21.41 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.22/21.41 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.41 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.41 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( skv_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))) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zEven))) (not (forall ((K_1 $$unsorted)) (not (= (ti int Xa) (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))) )))) ) 21.22/21.41 ( (one_one int) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_0 (plus_plus int))) (let ((_let_1 (hAPP int (fun int int) (times_times int) W))) (= (hAPP int int _let_1 (hAPP int int (hAPP int (fun int int) _let_0 Z1) Z2)) (hAPP int int (hAPP int (fun int int) _let_0 (hAPP int int _let_1 Z1)) (hAPP int int _let_1 Z2))))) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.22/21.41 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.41 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.22/21.41 ( sa, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.41 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( r, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.41 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.41 ( skv_13, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.41 ( skv_19, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.41 ) 21.22/21.41 (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)))) ) 21.22/21.41 ( rat ) 21.22/21.41 ( int ) 21.22/21.41 ( (fun int int) ) 21.22/21.41 ( nat ) 21.22/21.41 ( bool ) 21.22/21.41 ( real ) 21.22/21.41 ( (fun nat real) ) 21.22/21.41 ( (fun real real) ) 21.22/21.41 ( complex ) 21.22/21.41 ( (fun int bool) ) 21.22/21.41 ( (product_prod int int) ) 21.22/21.41 ( (fun (product_prod int int) int) ) 21.22/21.41 ( (fun int (fun int bool)) ) 21.22/21.41 ( (fun nat bool) ) 21.22/21.41 ( (fun (product_prod int int) bool) ) 21.22/21.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.22/21.41 ( (fun real bool) ) 21.22/21.41 ( quickcheck_code_int ) 21.22/21.41 ( code_code_numeral ) 21.22/21.41 ( (fun int (fun int (fun int bool))) ) 21.22/21.41 ( (fun int real) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106410 $$unsorted) (BOUND_VARIABLE_106411 $$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)) (= (and (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_106411))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106410) _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_106410) BOUND_VARIABLE_106411)) _let_2))))))) ) 21.22/21.41 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) Xa))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) ln) Xa) (hAPP real real (inverse_inverse real) Xa))))) ) 21.22/21.41 ( pi ) 21.22/21.41 ( (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)))) ) 21.22/21.41 ( (zero_zero real) ) 21.22/21.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( skv_2 ) 21.22/21.41 ( skv_9 ) 21.22/21.41 ( skv_12 ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106464 $$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_106464) _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_106464)) _let_3))))))) ) 21.22/21.41 ( int, pls ) 21.22/21.41 ( int, (one_one int) ) 21.22/21.41 ( int, min ) 21.22/21.41 ( 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)))) ) 21.22/21.41 ( real, (one_one real) ) 21.22/21.41 ( 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) ) 21.22/21.41 ( complex, ii ) 21.22/21.41 ( complex, (one_one complex) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106490 $$unsorted) (BOUND_VARIABLE_106491 $$unsorted) (BOUND_VARIABLE_106492 $$unsorted) (BOUND_VARIABLE_106493 $$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_106492) BOUND_VARIABLE_106493) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106490) BOUND_VARIABLE_106491))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_106490) BOUND_VARIABLE_106491)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_106492) BOUND_VARIABLE_106493)))))))) ) 21.22/21.41 ( 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), (hAPP nat int (hAPP 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) ) 21.22/21.41 ( 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), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.41 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.41 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.22/21.41 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP nat int (hAPP 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) ) 21.22/21.41 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.41 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.41 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.41 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.22/21.41 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.41 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.22/21.41 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.41 ( nat, (hAPP int nat nat_1 t), (one_one nat), (hAPP int nat nat_1 t), (one_one nat) ) 21.22/21.41 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.22/21.41 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106520 $$unsorted) (BOUND_VARIABLE_106521 $$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) (times_times int) BOUND_VARIABLE_106520) BOUND_VARIABLE_106521)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_106520)) (hAPP int X_a _let_0 BOUND_VARIABLE_106521))))) ) 21.22/21.41 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.22/21.41 ( nat, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.22/21.41 ( quickcheck_code_int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.22/21.41 ( code_code_numeral, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (number_number_of rat))) (= (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)) (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int _let_1 K_4)) (hAPP int int _let_1 L_4))))))) ) 21.22/21.41 ( pls, (hAPP int int bit1 pls) ) 21.22/21.41 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit0 K_4) (hAPP int int pred (hAPP int int bit1 K_4))) ) 21.22/21.41 ( pls ) 21.22/21.41 ( (hAPP int int bit1 pls) ) 21.22/21.41 ( min ) 21.22/21.41 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.41 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.41 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.41 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.22/21.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 21.22/21.41 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 21.22/21.41 ) 21.22/21.41 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 rat frct P_5) (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)))) ) 21.22/21.42 ( (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))) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (= (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) sin_coeff)) (hAPP real _let_0 (power_power real) Xa))) (hAPP real real sin Xa))))) ) 21.22/21.42 ( (hAPP int real (number_number_of real) min) ) 21.22/21.42 ( pi ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( (zero_zero real) ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.22/21.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((Z_1 $$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)))) ) 21.22/21.42 ( (zero_zero complex) ) 21.22/21.42 ( ii ) 21.22/21.42 ( (one_one complex) ) 21.22/21.42 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.42 ( (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)) ) 21.22/21.42 ) 21.22/21.42 (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))))))) ) 21.22/21.42 ( (one_one int), t ) 21.22/21.42 ( min, min ) 21.22/21.42 ( min, (zero_zero int) ) 21.22/21.42 ( (zero_zero int), pls ) 21.22/21.42 ( (zero_zero int), (one_one int) ) 21.22/21.42 ( (zero_zero int), min ) 21.22/21.42 ( (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))) ) 21.22/21.42 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.42 ) 21.22/21.42 (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 int) A_1) B)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B) (zero_zero int))) (= (hAPP int _let_1 _let_2 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)))))))) ) 21.22/21.42 ( (one_one int), t ) 21.22/21.42 ( min, min ) 21.22/21.42 ( min, (zero_zero int) ) 21.22/21.42 ( (zero_zero int), pls ) 21.22/21.42 ( (zero_zero int), (one_one int) ) 21.22/21.42 ( (zero_zero int), min ) 21.22/21.42 ( (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))) ) 21.22/21.42 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) Na))) (= (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Na) (hAPP nat nat suc Ma))) (= Ma Na)))) ) 21.22/21.42 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (ab_semigroup_add X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 21.22/21.42 ( rat ) 21.22/21.42 ( int ) 21.22/21.42 ( (fun int int) ) 21.22/21.42 ( nat ) 21.22/21.42 ( bool ) 21.22/21.42 ( real ) 21.22/21.42 ( (fun nat real) ) 21.22/21.42 ( (fun real real) ) 21.22/21.42 ( complex ) 21.22/21.42 ( (fun int bool) ) 21.22/21.42 ( (product_prod int int) ) 21.22/21.42 ( (fun (product_prod int int) int) ) 21.22/21.42 ( (fun int (fun int bool)) ) 21.22/21.42 ( (fun nat bool) ) 21.22/21.42 ( (fun (product_prod int int) bool) ) 21.22/21.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.22/21.42 ( (fun real bool) ) 21.22/21.42 ( quickcheck_code_int ) 21.22/21.42 ( code_code_numeral ) 21.22/21.42 ( (fun int (fun int (fun int bool))) ) 21.22/21.42 ( (fun int real) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106900 $$unsorted)) (let ((_let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_106900) (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)))) ) 21.22/21.42 ( int, s ) 21.22/21.42 ( int, s1 ) 21.22/21.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.42 ( int, v ) 21.22/21.42 ( int, w ) 21.22/21.42 ( int, y ) 21.22/21.42 ( int, x ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.42 ( int, skv_6 ) 21.22/21.42 ( int, skv_7 ) 21.22/21.42 ( int, skv_16 ) 21.22/21.42 ( int, skv_23 ) 21.22/21.42 ( int, skv_24 ) 21.22/21.42 ( real, (hAPP int real (number_number_of real) min) ) 21.22/21.42 ( 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)))) ) 21.22/21.42 ( complex, ii ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106918 $$unsorted) (BOUND_VARIABLE_106919 $$unsorted) (BOUND_VARIABLE_106920 $$unsorted) (BOUND_VARIABLE_106921 $$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))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_106920) BOUND_VARIABLE_106921))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_106918) BOUND_VARIABLE_106919))) (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_106920) BOUND_VARIABLE_106918)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_106921) BOUND_VARIABLE_106919)))))))) ) 21.22/21.42 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one 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) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N))) (not (forall ((K_1 $$unsorted)) (not (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) K_1)))) ))) ) 21.22/21.42 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.42 ( (zero_zero nat), n ) 21.22/21.42 ( (zero_zero nat), tn ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_106993 $$unsorted) (BOUND_VARIABLE_106994 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (linordered_idom X_a)) (= (and (= _let_1 (ti X_a BOUND_VARIABLE_106993)) (= _let_1 (ti X_a BOUND_VARIABLE_106994))) (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 (fun X_a X_a) (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_106993) _let_0)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_106994) _let_0))) _let_1)))))))) ) 21.22/21.42 ( int, v, w ) 21.22/21.42 ( int, x, y ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.22/21.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.42 ( int, skv_6, skv_7 ) 21.22/21.42 ( int, skv_23, skv_24 ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107020 $$unsorted) (BOUND_VARIABLE_107021 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_107020)) (hAPP int X_a _let_0 BOUND_VARIABLE_107021)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_107020) (hAPP int int (uminus_uminus int) BOUND_VARIABLE_107021)))))) ) 21.22/21.42 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 21.22/21.42 ) 21.22/21.42 (instantiation (forall ((X $$unsorted)) (= (hAPP real real cos (hAPP real real (uminus_uminus real) X)) (hAPP real real cos X)) ) 21.22/21.42 ( (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)))) ) 21.22/21.42 ( (one_one real) ) 21.22/21.42 ( (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) ) 21.22/21.42 ) 21.22/21.42 (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 int int (hAPP int (fun int int) (minus_minus int) P_4) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 sRStar P_4)))))) ) 21.22/21.42 ( (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)))) ) 21.22/21.42 ( y ) 21.22/21.42 ( x ) 21.22/21.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.22/21.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.22/21.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.22/21.42 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.22/21.42 ( (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))) m1))) ) 21.22/21.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.22/21.42 ) 21.22/21.42 (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)))) ) 21.22/21.42 ( int, rat, int, fract, (one_one int), (one_one int) ) 21.22/21.42 ( int, rat, int, fract, (one_one int), (zero_zero int) ) 21.22/21.42 ( 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)))) ) 21.22/21.42 ( 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) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.22/21.42 ( int, int, int, (plus_plus int), v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.22/21.42 ( int, int, int, (plus_plus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.42 ( 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)))) ) 21.22/21.42 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.42 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.22/21.42 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.22/21.42 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.22/21.42 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.22/21.42 ( 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))) ) 21.22/21.42 ( int, int, int, (times_times int), v, y ) 21.22/21.42 ( int, int, int, (times_times int), v, sa ) 21.22/21.42 ( int, int, int, (times_times int), v, x ) 21.22/21.42 ( int, int, int, (times_times int), v, r ) 21.22/21.42 ( int, int, int, (times_times int), v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.22/21.42 ( int, int, int, (times_times int), v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.22/21.42 ( int, int, int, (times_times int), w, y ) 21.22/21.42 ( int, int, int, (times_times int), w, sa ) 21.22/21.42 ( int, int, int, (times_times int), w, x ) 21.22/21.42 ( int, int, int, (times_times int), w, r ) 21.22/21.42 ( 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_let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.22/21.42 ( int, int, nat, (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.22/21.42 ( int, int, nat, (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.42 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 21.22/21.42 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 21.22/21.42 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 21.22/21.42 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 21.22/21.42 ( int, int, nat, (power_power int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 21.22/21.42 ( int, bool, int, (ord_less int), pls, (zero_zero int) ) 21.22/21.42 ( int, bool, int, (ord_less int), (one_one int), (zero_zero int) ) 21.22/21.42 ( int, bool, int, (ord_less int), min, min ) 21.22/21.42 ( int, bool, int, (ord_less int), min, (zero_zero int) ) 21.22/21.42 ( int, bool, int, (ord_less int), (zero_zero int), min ) 21.22/21.42 ( 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))), (zero_zero int) ) 21.22/21.42 ( 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 ) 21.22/21.42 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.43 ( 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 ) 21.22/21.43 ( 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 ) 21.22/21.43 ( 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_5 ) 21.22/21.43 ( int, bool, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.22/21.43 ( int, bool, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.22/21.43 ( int, bool, int, (ord_less int), t, (one_one int) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), pls, min ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), pls, (zero_zero int) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), (one_one int), (zero_zero int) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), min, min ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), min, (zero_zero int) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), s, (zero_zero int) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), t, (one_one int) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), skv_4, (zero_zero int) ) 21.22/21.43 ( int, bool, int, (ord_less_eq int), skv_5, (zero_zero int) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( int, bool, int, quadRes, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.43 ( int, bool, int, (dvd_dvd int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.43 ( int, bool, int, (dvd_dvd int), (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.43 ( 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 ) 21.22/21.43 ( 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 ) 21.22/21.43 ( 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_5 ) 21.22/21.43 ( 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) ) 21.22/21.43 ( int, bool, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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) ) 21.22/21.43 ( int, bool, (fun int bool), (member int), zEven, (one_one int) ) 21.22/21.43 ( int, (fun int bool), int, zcong, s, s1 ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.43 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min), (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)))) ) 21.22/21.43 ( int, (fun int bool), int, zcong, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.43 ( int, (fun int bool), int, zcong, skv_4, s1 ) 21.22/21.43 ( int, (fun int bool), int, zcong, skv_5, s1 ) 21.22/21.43 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (one_one int) ) 21.22/21.43 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), (zero_zero int) ) 21.22/21.43 ( int, (product_prod int int), int, (product_Pair int int), (one_one int), s ) 21.22/21.43 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 21.22/21.43 ( nat, nat, nat, (minus_minus nat), (one_one nat), (hAPP int nat nat_1 t) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( nat, bool, nat, (ord_less nat), n, (zero_zero nat) ) 21.22/21.43 ( nat, bool, nat, (ord_less nat), tn, (zero_zero nat) ) 21.22/21.43 ( 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))) ) 21.22/21.43 ( nat, real, real, root, (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.43 ( nat, real, real, root, (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.43 ( 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))) ) 21.22/21.43 ( real, bool, real, (ord_less real), pi, (zero_zero real) ) 21.22/21.43 ( 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)) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( real, bool, real, (ord_less real), (zero_zero real), pi ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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))))) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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 ) 21.22/21.43 ( real, bool, real, (ord_less real), skv_2, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less real), skv_9, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less real), skv_12, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), pi, (zero_zero real) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), skv_10, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), skv_11, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), skv_15, (zero_zero real) ) 21.22/21.43 ( real, bool, real, (ord_less_eq real), skv_18, (zero_zero real) ) 21.22/21.43 ( real, bool, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), sequentially, (zero_zero real) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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))) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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 ) 21.22/21.43 ( 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 ) 21.22/21.43 ( real, real, real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( 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) ) 21.22/21.43 ( real, real, real, (times_times real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.43 ( 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))))) ) 21.22/21.43 ( real, real, real, (times_times real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.43 ( 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)))) ) 21.22/21.43 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.22/21.43 ( real, complex, real, complex_1, (one_one real), (zero_zero real) ) 21.22/21.43 ( real, complex, real, complex_1, (zero_zero real), (one_one real) ) 21.22/21.43 ( real, complex, real, complex_1, (zero_zero real), (zero_zero real) ) 21.22/21.43 ( (fun nat real), bool, real, (sums real), (one_one real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))) ) 21.22/21.43 ( (fun nat real), (fun nat real), (fun nat nat), (combb nat real nat), suc, (real_1 nat) ) 21.22/21.43 ( (fun nat real), (fun nat real), (fun nat nat), (combb nat real nat), suc, (hAPP real (fun nat 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_let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 21.22/21.43 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))), (inverse_inverse real) ) 21.22/21.43 ( (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))) ) 21.22/21.43 ( complex, complex, nat, (power_power complex), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 21.22/21.43 ( complex, complex, complex, (times_times complex), ii, ii ) 21.22/21.43 ( 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)) ) 21.22/21.43 ( 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))) ) 21.22/21.43 ( (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_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))) ) 21.22/21.43 ( (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))))))) ) 21.22/21.43 ( (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) ) 21.22/21.43 ( (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) ) 21.22/21.43 ( (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) ) 21.22/21.43 ( (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 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int int int) ) 21.22/21.43 ( (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) ) 21.22/21.43 ( (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) ) 21.22/21.43 ( (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 ) 21.22/21.43 ( (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 ) 21.22/21.43 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))), fNot ) 21.22/21.43 ( (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 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))))))) ) 21.22/21.43 ( (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 ) 21.22/21.43 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP _let_3 _let_3 (hAPP (fun bool bool) (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))), fconj ) 21.22/21.43 ( (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 ) 21.22/21.43 ( (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 ) 21.22/21.43 ( (fun int (fun int bool)), (fun int bool), int, (combc int int bool), (zero_zero int), (fequal int) ) 21.22/21.43 ( (fun int (fun int bool)), (fun (product_prod int int) (fun int bool)), (fun 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bool)))) (let ((_let_6 (fun _let_2 _let_1))) (let ((_let_7 (fun _let_3 _let_6))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_3 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_6))) (let ((_let_12 (fun _let_3 _let_3))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_3 _let_8))) (let ((_let_15 (fun _let_2 _let_0))) (let ((_let_16 (hAPP _let_3 _let_15 (hAPP (fun int _let_0) (fun _let_3 _let_15) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_3))) (hAPP _let_8 _let_5 (hAPP _let_10 (fun _let_8 _let_5) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_6 _let_9) (fun _let_11 _let_10) (combb _let_6 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_7 (fun _let_8 _let_11) (combb _let_3 _let_6 _let_2) (hAPP (fun int _let_1) _let_7 (combb int _let_1 _let_2) (fequal int))) (hAPP _let_3 _let_8 (hAPP _let_13 _let_14 (combc _let_2 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_let_23 (hAPP (fun _let_6 _let_15) (fun _let_7 _let_23) (combb _let_6 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_13 _let_20 (hAPP _let_25 (fun _let_13 _let_20) (combc int _let_13 _let_13) (hAPP _let_14 _let_25 (hAPP (fun _let_0 _let_24) (fun _let_14 _let_25) (combb _let_0 _let_24 int) (combb real real int)) (hAPP _let_13 _let_14 (hAPP (fun real _let_0) (fun _let_13 _let_14) (combb real _let_0 int) (inverse_divide real)) _let_5))) _let_5))))))))))))))))))))))))))))))) ) 21.22/21.44 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun 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_let_17) (combb (fun int (fun int bool)) _let_9 real) (hAPP _let_4 _let_11 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_18 _let_15 (hAPP _let_20 (fun _let_18 _let_15) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_21 _let_20 (hAPP (fun _let_14 _let_19) (fun _let_21 _let_20) (combb _let_14 _let_19 real) (combb _let_12 (fun int bool) int)) (hAPP _let_7 _let_21 (hAPP (fun _let_6 _let_14) (fun _let_7 _let_21) (combb _let_6 _let_14 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_18 (hAPP _let_23 (fun _let_12 _let_18) (combc int _let_12 _let_12) (hAPP _let_13 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_13 _let_23) (combb _let_0 _let_22 int) (combb real real int)) (hAPP _let_12 _let_13 (hAPP (fun real _let_0) (fun _let_12 _let_13) (combb real _let_0 int) (inverse_divide real)) _let_5))) _let_5)))))))))))))))))))))))))))), (let ((_let_0 (fun int bool))) (combc int _let_0 _let_0)) ) 21.22/21.44 ( (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_0))) (let ((_let_4 (fun int _let_2))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (fun int _let_5))) (hAPP _let_2 _let_4 (hAPP _let_6 (fun _let_2 _let_4) (combc int _let_2 _let_2) (hAPP _let_3 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_3 _let_6) (combb _let_0 _let_5 int) (combb real real int)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (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 real) (fun int bool)))) (let ((_let_3 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun real _let_2))) (hAPP _let_5 _let_4 (hAPP (fun _let_2 _let_3) (fun _let_5 _let_4) (combb _let_2 _let_3 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_5) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real))))))))) ) 21.22/21.44 ( (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 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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) ) 21.22/21.44 ) 21.22/21.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107093 $$unsorted) (BOUND_VARIABLE_107094 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_107093))) (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_107094))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_107094) (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_107094) (ti int BOUND_VARIABLE_107093))))) ) 21.22/21.44 ( real, (zero_zero int), pi ) 21.22/21.44 ( 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)))) ) 21.22/21.44 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.44 ( real, (zero_zero int), skv_10 ) 21.22/21.44 ( real, (zero_zero int), skv_11 ) 21.22/21.44 ( real, (zero_zero int), skv_15 ) 21.22/21.44 ( real, (zero_zero int), skv_18 ) 21.22/21.44 ) 21.22/21.44 (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))))) ) 21.22/21.44 ( (one_one int), t ) 21.22/21.44 ( min, min ) 21.22/21.44 ( min, (zero_zero int) ) 21.22/21.44 ( (zero_zero int), pls ) 21.22/21.44 ( (zero_zero int), (one_one int) ) 21.22/21.44 ( (zero_zero int), min ) 21.22/21.44 ( (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))) ) 21.22/21.44 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.44 ( 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))) ) 21.22/21.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.44 ( 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))) ) 21.22/21.44 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.44 ( 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))) ) 21.22/21.44 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.22/21.44 ) 21.22/21.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107187 $$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_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_107187)) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_107187) pls)))) ) 21.22/21.44 ( int, pls ) 21.22/21.44 ( int, (hAPP int int bit1 pls) ) 21.22/21.44 ( int, min ) 21.22/21.44 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.44 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.44 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.44 ( nat, pls ) 21.22/21.44 ( nat, (hAPP int int bit1 pls) ) 21.22/21.44 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.44 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.44 ( real, min ) 21.22/21.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.44 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.44 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.44 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.44 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.44 ( 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)))))))) ) 21.22/21.44 ( complex, min ) 21.22/21.44 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.44 ( quickcheck_code_int, pls ) 21.22/21.44 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.22/21.44 ( quickcheck_code_int, (one_one int) ) 21.22/21.44 ( code_code_numeral, pls ) 21.22/21.44 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.22/21.44 ) 21.22/21.44 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_0) X))) (hAPP real real (uminus_uminus real) X))))))) ) 21.22/21.44 ( pi ) 21.22/21.44 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.44 ( (one_one real) ) 21.22/21.44 ( (zero_zero real) ) 21.22/21.44 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.44 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.22/21.44 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.22/21.44 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.22/21.44 ( skv_10 ) 21.22/21.44 ( skv_11 ) 21.22/21.44 ( skv_15 ) 21.22/21.44 ( skv_18 ) 21.22/21.44 ) 21.22/21.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107282 $$unsorted) (BOUND_VARIABLE_107283 $$unsorted) (BOUND_VARIABLE_107284 $$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 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107283) BOUND_VARIABLE_107284))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_107282))) (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_107283) BOUND_VARIABLE_107282)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_107284) BOUND_VARIABLE_107282)))))))) ) 21.22/21.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) Y))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X)) (hAPP real nat natceiling Y)))) ) 21.22/21.45 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.22/21.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( (zero_zero real), pi ) 21.22/21.45 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( (zero_zero real), skv_10 ) 21.22/21.45 ( (zero_zero real), skv_11 ) 21.22/21.45 ( (zero_zero real), skv_15 ) 21.22/21.45 ( (zero_zero real), skv_18 ) 21.22/21.45 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.22/21.45 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((M $$unsorted) (X $$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) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X) _let_1) M))) (= _let_1 (ti int X))))) ) 21.22/21.45 ( pls, (zero_zero int) ) 21.22/21.45 ( (one_one int), (zero_zero int) ) 21.22/21.45 ( min, min ) 21.22/21.45 ( min, (zero_zero int) ) 21.22/21.45 ( (zero_zero int), min ) 21.22/21.45 ( (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))), (zero_zero int) ) 21.22/21.45 ( (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))), s ) 21.22/21.45 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( (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))), t ) 21.22/21.45 ( (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))), skv_4 ) 21.22/21.45 ( (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))), skv_5 ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.22/21.45 ( t, (one_one int) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_107417 $$unsorted) (BOUND_VARIABLE_107418 $$unsorted) (BOUND_VARIABLE_107419 $$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 (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_1) BOUND_VARIABLE_107419)) S_1))) (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_107419)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_107417 X_1)) BOUND_VARIABLE_107418)) R_1))))) ))) ))) )) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_107417) BOUND_VARIABLE_107418) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_107419)))))) ) 21.22/21.45 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107467 $$unsorted) (BOUND_VARIABLE_107468 $$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_107468) BOUND_VARIABLE_107467)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_107467) BOUND_VARIABLE_107468)))))) ) 21.22/21.45 ( int, pls, (zero_zero int) ) 21.22/21.45 ( int, (one_one int), (zero_zero int) ) 21.22/21.45 ( int, (one_one int), t ) 21.22/21.45 ( int, min, pls ) 21.22/21.45 ( int, min, min ) 21.22/21.45 ( int, min, (zero_zero int) ) 21.22/21.45 ( int, (zero_zero int), pls ) 21.22/21.45 ( int, (zero_zero int), (one_one int) ) 21.22/21.45 ( int, (zero_zero int), min ) 21.22/21.45 ( int, (zero_zero int), s ) 21.22/21.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.45 ( int, (zero_zero int), skv_4 ) 21.22/21.45 ( int, (zero_zero int), skv_5 ) 21.22/21.45 ( 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))), (zero_zero int) ) 21.22/21.45 ( 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))), s ) 21.22/21.45 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 ) 21.22/21.45 ( 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_4 ) 21.22/21.45 ( 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_5 ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.22/21.45 ( int, t, (one_one int) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.22/21.45 ( nat, n, (zero_zero nat) ) 21.22/21.45 ( nat, tn, (zero_zero nat) ) 21.22/21.45 ( real, pi, (zero_zero real) ) 21.22/21.45 ( 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)) ) 21.22/21.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.22/21.45 ( 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)))) ) 21.22/21.45 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( 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) ) 21.22/21.45 ( real, (zero_zero real), pi ) 21.22/21.45 ( 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)))) ) 21.22/21.45 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( 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))))) ) 21.22/21.45 ( real, (zero_zero real), skv_10 ) 21.22/21.45 ( real, (zero_zero real), skv_11 ) 21.22/21.45 ( real, (zero_zero real), skv_15 ) 21.22/21.45 ( real, (zero_zero real), skv_18 ) 21.22/21.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.22/21.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.22/21.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.22/21.45 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.22/21.45 ( real, skv_2, (zero_zero real) ) 21.22/21.45 ( real, skv_9, (zero_zero real) ) 21.22/21.45 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( real, skv_12, (zero_zero real) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107492 $$unsorted) (BOUND_VARIABLE_107493 $$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_107492) BOUND_VARIABLE_107493))) (= (= (ti X_a BOUND_VARIABLE_107492) (ti X_a BOUND_VARIABLE_107493)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107493) BOUND_VARIABLE_107492)))))) ) 21.22/21.45 ( int, pls, min ) 21.22/21.45 ( int, pls, (zero_zero int) ) 21.22/21.45 ( int, (one_one int), (zero_zero int) ) 21.22/21.45 ( int, (one_one int), t ) 21.22/21.45 ( int, min, pls ) 21.22/21.45 ( int, min, min ) 21.22/21.45 ( int, min, (zero_zero int) ) 21.22/21.45 ( int, (zero_zero int), pls ) 21.22/21.45 ( int, (zero_zero int), (one_one int) ) 21.22/21.45 ( int, (zero_zero int), min ) 21.22/21.45 ( int, (zero_zero int), s ) 21.22/21.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.45 ( int, (zero_zero int), skv_4 ) 21.22/21.45 ( int, (zero_zero int), skv_5 ) 21.22/21.45 ( int, s, (zero_zero int) ) 21.22/21.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.22/21.45 ( int, t, (one_one int) ) 21.22/21.45 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( int, skv_4, (zero_zero int) ) 21.22/21.45 ( int, skv_5, (zero_zero int) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( real, pi, (zero_zero real) ) 21.22/21.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.22/21.45 ( 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)))) ) 21.22/21.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.22/21.45 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( 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) ) 21.22/21.45 ( real, (zero_zero real), pi ) 21.22/21.45 ( 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)))) ) 21.22/21.45 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( real, (zero_zero real), skv_10 ) 21.22/21.45 ( real, (zero_zero real), skv_11 ) 21.22/21.45 ( real, (zero_zero real), skv_15 ) 21.22/21.45 ( real, (zero_zero real), skv_18 ) 21.22/21.45 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.22/21.45 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.22/21.45 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( real, skv_10, (zero_zero real) ) 21.22/21.45 ( real, skv_11, (zero_zero real) ) 21.22/21.45 ( real, skv_15, (zero_zero real) ) 21.22/21.45 ( real, skv_18, (zero_zero real) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (= (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) Na)) (and (= _let_0 Ma) (= _let_0 Na)))) ) 21.22/21.45 ( (one_one nat), (one_one nat) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((Z $$unsorted) (Wa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ord_less_eq int))) (or (and (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) Wa))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 _let_1) Z)))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 Wa) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 Wa)) (hAPP int nat nat_1 Z)))))))) ) 21.22/21.45 ( pls, min ) 21.22/21.45 ( pls, (zero_zero int) ) 21.22/21.45 ( (one_one int), (zero_zero int) ) 21.22/21.45 ( min, min ) 21.22/21.45 ( min, (zero_zero int) ) 21.22/21.45 ( s, (zero_zero int) ) 21.22/21.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.22/21.45 ( t, (one_one int) ) 21.22/21.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.45 ( skv_4, (zero_zero int) ) 21.22/21.45 ( skv_5, (zero_zero int) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107565 $$unsorted) (BOUND_VARIABLE_107566 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_107565))) (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_107565) (hAPP nat X_a _let_0 BOUND_VARIABLE_107566)) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_107566))))) ) 21.22/21.45 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, v, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, w, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, y, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, x, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, skv_6, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, skv_7, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, skv_16, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, skv_23, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( int, skv_24, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat nat))) (let ((_let_4 (zero_zero real))) (= _let_4 (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (hAPP bool (fun real _let_2) (if real) (hAPP nat bool (even_odd_even nat) Na)) _let_4) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)) (hAPP nat nat (hAPP nat _let_3 (div_div nat) (hAPP nat nat (hAPP nat _let_3 (minus_minus nat) Na) (hAPP nat nat suc (zero_zero nat)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) Na))))) (hAPP nat real (hAPP real _let_0 _let_1 _let_4) Na)))))))) ) 21.22/21.45 ( (zero_zero nat) ) 21.22/21.45 ( (one_one nat) ) 21.22/21.45 ( (hAPP int nat nat_1 t) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X $$unsorted)) (= (hAPP int real (ring_1_of_int real) X) (hAPP int real (number_number_of real) X)) ) 21.22/21.45 ( (one_one int) ) 21.22/21.45 ( min ) 21.22/21.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.45 ( (zero_zero int) ) 21.22/21.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.45 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.45 ( (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)))))))) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (P $$unsorted)) (= (hAPP X_a X_a (combi X_a) P) (ti X_a P)) ) 21.22/21.45 ( int, pls ) 21.22/21.45 ( int, min ) 21.22/21.45 ( int, s ) 21.22/21.45 ( int, s1 ) 21.22/21.45 ( int, m ) 21.22/21.45 ( int, t ) 21.22/21.45 ( int, v ) 21.22/21.45 ( int, w ) 21.22/21.45 ( int, y ) 21.22/21.45 ( int, sa ) 21.22/21.45 ( int, x ) 21.22/21.45 ( int, r ) 21.22/21.45 ( int, m1 ) 21.22/21.45 ( int, skv_14 ) 21.22/21.45 ( int, skv_20 ) 21.22/21.45 ( (fun int int), bit1 ) 21.22/21.45 ( (fun int int), bit0 ) 21.22/21.45 ( (fun int int), succ ) 21.22/21.45 ( (fun int int), pred ) 21.22/21.45 ( (fun int int), (fact_fact int) ) 21.22/21.45 ( (fun int int), zfact ) 21.22/21.45 ( nat, n ) 21.22/21.45 ( nat, tn ) 21.22/21.45 ( bool, fTrue ) 21.22/21.45 ( bool, fFalse ) 21.22/21.45 ( real, pi ) 21.22/21.45 ( (fun nat real), (real_1 nat) ) 21.22/21.45 ( (fun nat real), cos_coeff ) 21.22/21.45 ( (fun nat real), sin_coeff ) 21.22/21.45 ( (fun real real), sin ) 21.22/21.45 ( (fun real real), cos ) 21.22/21.45 ( (fun real real), sqrt ) 21.22/21.45 ( (fun real real), tan ) 21.22/21.45 ( (fun real real), ln ) 21.22/21.45 ( (fun real real), arctan ) 21.22/21.45 ( (fun real real), arcsin ) 21.22/21.45 ( (fun real real), arccos ) 21.22/21.45 ( (fun nat nat), suc ) 21.22/21.45 ( (fun nat nat), (fact_fact nat) ) 21.22/21.45 ( (fun nat nat), nat_size ) 21.22/21.45 ( (fun nat nat), (size_size nat) ) 21.22/21.45 ( (fun nat nat), fact ) 21.22/21.45 ( (filter nat), sequentially ) 21.22/21.45 ( (fun int (fun int rat)), fract ) 21.22/21.45 ( complex, ii ) 21.22/21.45 ( (fun int bool), zOdd ) 21.22/21.45 ( (fun int bool), zprime ) 21.22/21.45 ( (fun int bool), zEven ) 21.22/21.45 ( (fun int bool), nat_neg ) 21.22/21.45 ( (fun int bool), nat_is_nat ) 21.22/21.45 ( (fun int bool), (even_odd_even int) ) 21.22/21.45 ( (fun int bool), twoSqu1091635170sum2sq ) 21.22/21.45 ( (fun int (fun int int)), legacy_zgcd ) 21.22/21.45 ( (fun int (fun int int)), (gcd_gcd int) ) 21.22/21.45 ( (fun int (fun int int)), inv ) 21.22/21.45 ( (fun int (fun int int)), multInv ) 21.22/21.45 ( (fun int (fun int int)), legendre ) 21.22/21.45 ( (fun int (fun int int)), standardRes ) 21.22/21.45 ( (fun int (fun int int)), nat_tsub ) 21.22/21.45 ( (fun int (fun int int)), z3div ) 21.22/21.45 ( (fun int (fun int int)), z3mod ) 21.22/21.45 ( (fun int (fun int int)), int_lcm ) 21.22/21.45 ( (fun int (fun int int)), int_gcd ) 21.22/21.45 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.22/21.45 ( (fun bool bool), fNot ) 21.22/21.45 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.22/21.45 ( (fun bool (fun bool bool)), fconj ) 21.22/21.45 ( (fun bool (fun bool bool)), fdisj ) 21.22/21.45 ( (fun bool (fun bool bool)), fimplies ) 21.22/21.45 ( (fun int (fun int bool)), quadRes ) 21.22/21.45 ( (fun int (fun int bool)), d22set ) 21.22/21.45 ( (fun int (fun int bool)), norRRset ) 21.22/21.45 ( (fun int (fun int bool)), sRStar ) 21.22/21.45 ( (fun int (fun int bool)), sr ) 21.22/21.45 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.22/21.45 ( (fun nat bool), (even_odd_even nat) ) 21.22/21.45 ( (fun nat bool), prime ) 21.22/21.45 ( (fun real complex), cis ) 21.22/21.45 ( (fun nat (fun nat bool)), coprime ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.22/21.45 ( (fun (product_prod int int) bool), frac_1 ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.22/21.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.22/21.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.22/21.45 ( (fun (fun int bool) bool), nat_nat_set ) 21.22/21.45 ( (fun nat (fun real real)), root ) 21.22/21.45 ( (fun real (fun real real)), log ) 21.22/21.45 ( (fun real (fun real real)), powr ) 21.22/21.45 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.22/21.45 ( (fun complex complex), cnj ) 21.22/21.45 ( (fun complex complex), expi ) 21.22/21.45 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.22/21.45 ( (fun nat (fun nat nat)), nat_gcd ) 21.22/21.45 ( (fun nat (fun nat nat)), nat_lcm ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.22/21.45 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.22/21.45 ( (fun int (fun (fun int bool) bool)), resSet ) 21.22/21.45 ( (fun int nat), nat_1 ) 21.22/21.45 ( (fun int nat), phi ) 21.22/21.45 ( (fun complex real), re ) 21.22/21.45 ( (fun complex real), im ) 21.22/21.45 ( (fun complex real), arg ) 21.22/21.45 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.22/21.45 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.22/21.45 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.22/21.45 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.22/21.45 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.22/21.45 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.22/21.45 ( (fun (product_prod nat nat) bool), pred_nat ) 21.22/21.45 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.22/21.45 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.22/21.45 ( (fun (fun int bool) int), (the int) ) 21.22/21.45 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.22/21.45 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.22/21.45 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.22/21.45 ( (fun real (fun real complex)), rcis ) 21.22/21.45 ( (fun real (fun real complex)), complex_1 ) 21.22/21.45 ( (fun int (fun int (fun int bool))), zcong ) 21.22/21.45 ( (fun int (fun int (fun int bool))), wset ) 21.22/21.45 ( (fun int (fun int (fun int bool))), noXRRset ) 21.22/21.45 ( (fun int (fun int (fun int bool))), bnorRset ) 21.22/21.45 ( (fun int (fun int (fun int bool))), zcongm ) 21.22/21.45 ( (fun real nat), natceiling ) 21.22/21.45 ( (fun real nat), natfloor ) 21.22/21.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.22/21.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.22/21.45 ( (fun int real), (real_1 int) ) 21.22/21.45 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.22/21.45 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.22/21.45 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.22/21.45 ( (fun complex nat), (size_size complex) ) 21.22/21.45 ( (fun complex nat), complex_size ) 21.22/21.45 ( (fun (fun nat rat) bool), vanishes ) 21.22/21.45 ( (fun (product_prod int int) rat), frct ) 21.22/21.45 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.22/21.45 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.22/21.45 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.22/21.45 ( (fun rat real), ratreal ) 21.22/21.45 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.22/21.45 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.22/21.45 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.22/21.45 ( (fun rat (product_prod int int)), quotient_of ) 21.22/21.45 ( (fun int (fun nat nat)), nat_aux ) 21.22/21.45 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.22/21.45 ( (fun int (list int)), quickc666637781d_zero ) 21.22/21.45 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.22/21.45 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.22/21.45 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.22/21.45 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.22/21.45 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.22/21.45 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.22/21.45 ( (fun code_code_numeral int), code_int_of ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107609 $$unsorted) (BOUND_VARIABLE_107610 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_107609)) (hAPP int X_a _let_0 BOUND_VARIABLE_107610)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_107609) BOUND_VARIABLE_107610))))) ) 21.22/21.45 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107629 $$unsorted) (BOUND_VARIABLE_107630 $$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_107630) BOUND_VARIABLE_107629) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_107629) BOUND_VARIABLE_107630))))) ) 21.22/21.45 ( 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)))) ) 21.22/21.45 ( 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) ) 21.22/21.45 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.22/21.45 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.45 ( 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)))), (one_one int) ) 21.22/21.45 ( 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) ) 21.22/21.45 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.22/21.45 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.22/21.45 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.22/21.45 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.22/21.45 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.22/21.45 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.22/21.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.45 ( nat, (one_one nat), (one_one nat) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) (zero_zero nat)) (zero_zero X_a))) ) 21.22/21.45 ( rat ) 21.22/21.45 ( int ) 21.22/21.45 ( nat ) 21.22/21.45 ( real ) 21.22/21.45 ( complex ) 21.22/21.45 ( quickcheck_code_int ) 21.22/21.45 ( code_code_numeral ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((Y $$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)) _let_0))) (= (hAPP real real sin (hAPP real real arccos Y)) (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) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 21.22/21.45 ( (hAPP int real (number_number_of real) min) ) 21.22/21.45 ( (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)))) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) V))) ) 21.22/21.45 ( pls ) 21.22/21.45 ( (hAPP int int bit1 pls) ) 21.22/21.45 ( min ) 21.22/21.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.45 ) 21.22/21.45 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) X) Y)) (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP int real _let_0 X)) (hAPP int real _let_0 Y)))) ) 21.22/21.45 ( (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)))), (hAPP int int (number_number_of int) min) ) 21.22/21.45 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.45 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.22/21.46 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.46 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real ln X)) _let_0)))))) ) 21.22/21.46 ( pi ) 21.22/21.46 ( (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)))) ) 21.22/21.46 ( (one_one real) ) 21.22/21.46 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( skv_2 ) 21.22/21.46 ( skv_9 ) 21.22/21.46 ( skv_12 ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X $$unsorted)) (or (not (= (zero_zero real) (hAPP real real sin X))) (= (one_one real) (hAPP real real (abs_abs real) (hAPP real real cos X)))) ) 21.22/21.46 ( pi ) 21.22/21.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (zero_zero real) ) 21.22/21.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.22/21.46 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.22/21.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.22/21.46 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.22/21.46 ( skv_10 ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107862 $$unsorted) (BOUND_VARIABLE_107863 $$unsorted) (BOUND_VARIABLE_107874 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (power_power X_a))) (let ((_let_3 (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_107862))) (or (not (power X_a)) (and (or (= _let_0 BOUND_VARIABLE_107863) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_107862) (hAPP nat X_a _let_3 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) BOUND_VARIABLE_107863) (one_one nat)))) (hAPP nat X_a _let_3 BOUND_VARIABLE_107863))) (= (one_one X_a) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_107874) _let_0)))))))) ) 21.22/21.46 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int nat nat_1 t), s1 ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((I $$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 (hAPP int _let_0 (ord_less_eq int) K) I)) (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) I) K))))))) ) 21.22/21.46 ( pls, min ) 21.22/21.46 ( pls, (zero_zero int) ) 21.22/21.46 ( (one_one int), (zero_zero int) ) 21.22/21.46 ( min, min ) 21.22/21.46 ( min, (zero_zero int) ) 21.22/21.46 ( s, (zero_zero int) ) 21.22/21.46 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.22/21.46 ( t, (one_one int) ) 21.22/21.46 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.22/21.46 ( skv_4, (zero_zero int) ) 21.22/21.46 ( skv_5, (zero_zero int) ) 21.22/21.46 ) 21.22/21.46 (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)))) ) 21.22/21.46 ( rat ) 21.22/21.46 ( int ) 21.22/21.46 ( nat ) 21.22/21.46 ( bool ) 21.22/21.46 ( real ) 21.22/21.46 ( (filter nat) ) 21.22/21.46 ( (fun int bool) ) 21.22/21.46 ( (product_prod int int) ) 21.22/21.46 ( (fun nat bool) ) 21.22/21.46 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.22/21.46 ( quickcheck_code_int ) 21.22/21.46 ( code_code_numeral ) 21.22/21.46 ( (product_prod real real) ) 21.22/21.46 ( (filter real) ) 21.22/21.46 ( (product_prod nat nat) ) 21.22/21.46 ( (fun nat rat) ) 21.22/21.46 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (refl X_a))) (= _let_0 (ti (fun (fun (product_prod X_a X_a) bool) bool) _let_0))) ) 21.22/21.46 ( int ) 21.22/21.46 ( nat ) 21.22/21.46 ( real ) 21.22/21.46 ( (product_prod int int) ) 21.22/21.46 ( quickcheck_code_int ) 21.22/21.46 ( code_code_numeral ) 21.22/21.46 ( (product_prod nat nat) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Ma $$unsorted) (Z $$unsorted)) (= (= (hAPP nat int (semiring_1_of_nat int) Ma) (ti int Z)) (and (= Ma (hAPP int nat nat_1 Z)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z)))) ) 21.22/21.46 ( (zero_zero nat), s1 ) 21.22/21.46 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), r ) 21.22/21.46 ( (one_one nat), min ) 21.22/21.46 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), m ) 21.22/21.46 ( n, v ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) N) M))) (= (hAPP int int (hAPP int _let_0 (times_times int) N) (hAPP int int (hAPP int _let_0 (div_div int) M) N)) (ti int M)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_107949 $$unsorted) (BOUND_VARIABLE_107950 $$unsorted) (BOUND_VARIABLE_107951 $$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_107949))) (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_107950) BOUND_VARIABLE_107951)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_107950)) BOUND_VARIABLE_107951)))))) ) 21.22/21.46 ( 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))) ) 21.22/21.46 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun nat _let_2))) (let ((_let_5 (fun _let_0 _let_0))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (hAPP (fun real _let_2) (fun _let_0 _let_4) (combb real _let_2 nat) (times_times real)))) (let ((_let_8 (fun (fun nat nat) _let_0))) (let ((_let_9 (combb nat real nat))) (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) Xa)) _let_3))) (= (hAPP real real arctan Xa) (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 _let_7 (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)))) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 _let_7 (hAPP _let_0 _let_0 (hAPP _let_2 _let_5 (combb real real nat) (hAPP real _let_2 (inverse_divide real) _let_3)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_8 _let_9 (real_1 nat)) _let_11)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_8 _let_9 (hAPP real _let_0 _let_1 Xa)) _let_11)))))))))))))))))) ) 21.22/21.46 ( (hAPP int real (number_number_of real) min) ) 21.22/21.46 ( (one_one real) ) 21.22/21.46 ( (zero_zero real) ) 21.22/21.46 ( (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)))) ) 21.22/21.46 ( (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))))) ) 21.22/21.46 ( (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)))))))))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (ord_less_eq int))) (let ((_let_5 (number_number_of int))) (let ((_let_6 (fun _let_3 bool))) (let ((_let_7 (product_Pair int int))) (let ((_let_8 (hAPP int int (hAPP int _let_0 (plus_plus int) A_3) B_2))) (let ((_let_9 (hAPP int (fun int _let_3) negDivAlg A_3))) (let ((_let_10 (hAPP int _let_3 _let_9 B_2))) (let ((_let_11 (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 _let_2) _let_8)))) (let ((_let_12 (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 B_2) _let_2)))) (or (not (hBOOL (hAPP _let_3 bool (hAPP (fun _let_3 _let_6) _let_6 (accp _let_3) negDivAlg_rel) (hAPP int _let_3 (hAPP int (fun int _let_3) _let_7 A_3) B_2)))) (and (or (and (not _let_11) (not _let_12)) (= _let_10 (hAPP int _let_3 (hAPP int (fun int _let_3) _let_7 (hAPP int int _let_5 min)) _let_8))) (or _let_11 _let_12 (= _let_10 (hAPP _let_3 _let_3 (hAPP int (fun _let_3 _let_3) adjust B_2) (hAPP int _let_3 _let_9 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_5 (hAPP int int bit0 (hAPP int int bit1 pls)))) B_2)))))))))))))))))))) ) 21.22/21.46 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.22/21.46 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.46 ( (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)))), (one_one int) ) 21.22/21.46 ( (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) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.22/21.46 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108090 $$unsorted) (BOUND_VARIABLE_108091 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_108090) BOUND_VARIABLE_108091) sequentially)) (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (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_108090 N_1)) BOUND_VARIABLE_108091)) R_1))) )) ))) )))) ) 21.22/21.46 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108211 $$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_108211) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_108211)) (one_one int))))) ) 21.22/21.46 ( 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)))) ) 21.22/21.46 ( int, y ) 21.22/21.46 ( int, x ) 21.22/21.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.22/21.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.22/21.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.22/21.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.22/21.46 ( 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))) m1))) ) 21.22/21.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.22/21.46 ( nat, (hAPP int nat nat_1 t) ) 21.22/21.46 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.22/21.46 ( code_code_numeral, (zero_zero code_code_numeral) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((N $$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) _let_1)) N)))) ) 21.22/21.46 ( (one_one int) ) 21.22/21.46 ( (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)))) ) 21.22/21.46 ( (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) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.22/21.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.22/21.46 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (product_prod nat nat))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun nat _let_2))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) Na)) (= (zero_zero nat) Na) (= (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat Ma) Na) (hAPP _let_1 _let_1 (hAPP _let_3 (fun _let_1 _let_1) (product_prod_case nat nat _let_1) (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb nat _let_2 nat) (product_Pair nat nat)) suc)) (hAPP nat _let_1 (hAPP nat _let_2 divmod_nat (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) Ma) Na)) Na)))))))) ) 21.22/21.46 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (zero_zero nat), n ) 21.22/21.46 ( (zero_zero nat), tn ) 21.22/21.46 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (product_prod nat nat))) (let ((_let_1 (fun nat _let_0))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) Na))) (= (hAPP nat _let_0 (hAPP nat _let_1 divmod_nat Ma) Na) (hAPP nat _let_0 (hAPP nat _let_1 (product_Pair nat nat) (zero_zero nat)) Ma))))) ) 21.22/21.46 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (zero_zero nat), n ) 21.22/21.46 ( (zero_zero nat), tn ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Y $$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)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (= Y (hAPP real real sin (hAPP real real arcsin Y)))))) ) 21.22/21.46 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (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)))) ) 21.22/21.46 ( (zero_zero real) ) 21.22/21.46 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( skv_10 ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= X (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N) X)) N))) ) 21.22/21.46 ( (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))) ) 21.22/21.46 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (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))) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((Xa $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) A_3) B_2))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X_1))) )) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) (zero_zero real))))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) B_2))) (= (hAPP real real F A_3) (hAPP real real F Xa))))) ) 21.22/21.46 ( pi, arctan, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.46 ( (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)))), (hAPP real real (hAPP 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))) ) 21.22/21.46 ( (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)))), tan, (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)))) ) 21.22/21.46 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sin, (zero_zero real), pi ) 21.22/21.46 ( skv_10, cos, (zero_zero real), skv_2 ) 21.22/21.46 ( skv_11, sqrt, (zero_zero real), skv_9 ) 21.22/21.46 ( skv_15, (inverse_inverse real), (zero_zero real), skv_12 ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108344 $$unsorted) (BOUND_VARIABLE_108345 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_108344)) (hAPP int X_a _let_0 BOUND_VARIABLE_108345)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_108344) BOUND_VARIABLE_108345))))) ) 21.22/21.46 ( int, (hAPP int int bit1 pls), pls ) 21.22/21.46 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108399 $$unsorted) (BOUND_VARIABLE_108400 $$unsorted) (BOUND_VARIABLE_108401 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_108401))) (let ((_let_3 (= _let_0 _let_2))) (let ((_let_4 (ti X_a BOUND_VARIABLE_108399))) (or (not (number X_a)) (not (field_inverse_zero X_a)) (= (and (or (not _let_3) (= _let_0 _let_4)) (or _let_3 (= (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_108399) _let_2) (ti X_a BOUND_VARIABLE_108400)))) (= _let_4 (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) BOUND_VARIABLE_108400) _let_2))))))))) ) 21.22/21.46 ( int, min, min, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.46 ( int, s, s, pls ) 21.22/21.46 ( int, s1, s1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( int, m, m, (hAPP int int bit1 pls) ) 21.22/21.46 ( int, v, v, min ) 21.22/21.46 ( int, r, r, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.46 ( nat, n, n, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.46 ( nat, tn, tn, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.46 ( real, pi, pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.46 ( complex, ii, ii, min ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((N $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) ) 21.22/21.46 ( (zero_zero nat) ) 21.22/21.46 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.46 ( (one_one nat) ) 21.22/21.46 ( n ) 21.22/21.46 ( tn ) 21.22/21.46 ) 21.22/21.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108457 $$unsorted) (BOUND_VARIABLE_108458 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (minus_minus X_a))) (let ((_let_4 (one_one X_a))) (let ((_let_5 (hAPP X_a _let_1 (power_power X_a) BOUND_VARIABLE_108458))) (or (not (field X_a)) (= _let_4 (ti X_a BOUND_VARIABLE_108458)) (= (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 (hAPP nat X_a _let_5 BOUND_VARIABLE_108457)) _let_4)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_108458) _let_4)) (hAPP _let_0 X_a (hAPP _let_1 (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_108457)))))))))) ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 21.22/21.46 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.22/21.46 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.22/21.46 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.22/21.46 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.22/21.46 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.22/21.46 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.22/21.46 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.22/21.46 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 21.22/21.46 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 21.22/21.46 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 21.22/21.46 ) 21.22/21.46 (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_b X_c P (hAPP X_a X_b Q R)) (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)))) ) 21.22/21.47 ( int, rat, rat, (sgn_sgn rat), (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 21.22/21.47 ( int, rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, rat, int, (hAPP int (fun int rat) fract (one_one int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( 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) ) 21.22/21.47 ( int, int, int, bit1, bit1, pls ) 21.22/21.47 ( int, int, int, bit1, bit1, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, bit1, bit1, min ) 21.22/21.47 ( int, int, int, bit1, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.22/21.47 ( 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))))) ) 21.22/21.47 ( 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)))))) ) 21.22/21.47 ( int, int, int, bit1, bit0, pls ) 21.22/21.47 ( int, int, int, bit1, bit0, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, bit1, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.22/21.47 ( int, int, int, (uminus_uminus int), bit1, min ) 21.22/21.47 ( int, int, int, (uminus_uminus int), bit0, pls ) 21.22/21.47 ( int, int, int, (uminus_uminus int), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, int, int, bit0, bit1, pls ) 21.22/21.47 ( int, int, int, bit0, bit1, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, bit0, bit1, min ) 21.22/21.47 ( int, int, int, bit0, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, int, int, bit0, bit0, pls ) 21.22/21.47 ( int, int, int, bit0, bit0, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, succ, bit1, min ) 21.22/21.47 ( int, int, int, succ, bit0, pls ) 21.22/21.47 ( int, int, int, (number_number_of int), bit1, pls ) 21.22/21.47 ( int, int, int, (number_number_of int), bit1, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, (number_number_of int), bit1, min ) 21.22/21.47 ( int, int, int, (number_number_of int), bit0, pls ) 21.22/21.47 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, int, int, (number_number_of int), bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( 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), (zero_zero int) ) 21.22/21.47 ( int, int, int, (abs_abs int), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (abs_abs int), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), (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) ) 21.22/21.47 ( int, int, int, pred, bit1, min ) 21.22/21.47 ( int, int, int, pred, bit0, pls ) 21.22/21.47 ( 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)))), (abs_abs int), v ) 21.22/21.47 ( 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)))), (abs_abs int), w ) 21.22/21.47 ( 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)))), (abs_abs int), skv_14 ) 21.22/21.47 ( 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)))), (abs_abs int), skv_20 ) 21.22/21.47 ( int, int, int, (fact_fact int), bit0, pls ) 21.22/21.47 ( int, int, int, (fact_fact int), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), bit0, pls ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int (fun int int) (times_times int) sa), v ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int (fun int int) (times_times int) sa), w ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int (fun int int) (times_times int) r), v ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int (fun int int) (times_times int) r), w ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (minus_minus int) y), (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (minus_minus int) y), (hAPP int (fun int int) (times_times int) skv_13), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP nat int (hAPP int _let_2 _let_3 x) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 y) _let_1))))))), (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) x), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) x), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( 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) x) v))), (hAPP int (fun int int) (times_times int) y), w ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) y), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) y), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) x) w))), (hAPP int (fun int int) (times_times int) y), v ) 21.22/21.47 ( int, 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))))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.22/21.47 ( int, 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))))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), w ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), v ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_2 r) v)))))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.22/21.47 ( int, int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w))))))), (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP nat int (hAPP int (fun nat int) 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(hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) skv_13), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, int, int, (hAPP int (fun int int) (times_times int) skv_19), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 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(minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus 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))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.22/21.47 ( int, (fun int int), int, legendre, (number_number_of int), min ) 21.22/21.47 ( 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), (zero_zero int) ) 21.22/21.47 ( int, (fun int int), nat, (hAPP (fun int (fun nat int)) (fun nat (fun int int)) (combc int nat int) (power_power int)), (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, nat, int, (number_number_of nat), bit1, pls ) 21.22/21.47 ( int, nat, int, (number_number_of nat), bit1, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, nat, int, (number_number_of nat), bit0, pls ) 21.22/21.47 ( int, nat, int, (number_number_of nat), bit0, (hAPP int int bit1 pls) ) 21.22/21.47 ( int, nat, int, nat_1, bit0, pls ) 21.22/21.47 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, nat, int, nat_1, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, nat, int, nat_1, (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, nat, nat, suc, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, nat, code_code_numeral, code_c271388182l_size, (number_number_of code_code_numeral), pls ) 21.22/21.47 ( int, nat, code_code_numeral, (size_size code_code_numeral), (number_number_of code_code_numeral), pls ) 21.22/21.47 ( 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) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( 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)) ) 21.22/21.47 ( 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)) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, bool, int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) 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(ord_less int) min), bit0, pls ) 21.22/21.47 ( int, bool, int, nat_neg, bit0, pls ) 21.22/21.47 ( int, bool, int, nat_neg, (number_number_of int), min ) 21.22/21.47 ( int, bool, int, nat_neg, (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, bool, int, nat_is_nat, bit0, pls ) 21.22/21.47 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, bool, int, nat_is_nat, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, bool, int, nat_is_nat, (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), bit1, min ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), bit0, pls ) 21.22/21.47 ( int, bool, int, (even_odd_even int), bit0, pls ) 21.22/21.47 ( int, bool, int, (even_odd_even int), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) pls), bit1, min ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) pls), bit0, pls ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, bool, int, twoSqu1091635170sum2sq, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.22/21.47 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.22/21.47 ( int, bool, int, twoSqu1091635170sum2sq, (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) ) 21.22/21.47 ( 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) ) 21.22/21.47 ( 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))), (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) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), bit1, min ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), bit0, pls ) 21.22/21.47 ( 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))), (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) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( 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)))), (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) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (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 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int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m))), (one_one int) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (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) ) 21.22/21.47 ( int, bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, bool, nat, prime, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( 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)) ) 21.22/21.47 ( int, bool, real, (hAPP real (fun real bool) (ord_less real) 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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)))))))) ) 21.22/21.47 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.22/21.47 ( int, real, real, sqrt, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.22/21.47 ( 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)) ) 21.22/21.47 ( 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)) ) 21.22/21.47 ( int, real, real, (hAPP real (fun real real) (inverse_divide real) (hAPP int real (number_number_of real) (hAPP 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int, (fun int bool), int, (ord_less_eq int), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( 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 ) 21.22/21.47 ( int, (fun int bool), int, (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), bit0, pls ) 21.22/21.47 ( 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) ) 21.22/21.47 ( 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 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) 21.22/21.47 ( 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))) ) 21.22/21.47 ( int, (product_prod int int), rat, quotient_of, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 21.22/21.47 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (zero_zero int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) (one_one int)), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, (product_prod int int), int, (hAPP int (fun int (product_prod int int)) (product_Pair int int) s), (fact_fact int), (zero_zero int) ) 21.22/21.47 ( int, (fun nat int), int, (power_power int), (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.22/21.47 ( int, (fun nat int), int, (power_power int), (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.22/21.47 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) x) v))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.22/21.47 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) x) w))), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.22/21.47 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 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w))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.22/21.48 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.22/21.48 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.22/21.48 ( int, (fun nat int), int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 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_let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))))))))), (fact_fact int), (zero_zero int) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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) ) 21.22/21.48 ( int, (fun int (fun int 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_0))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_4 _let_4) (combb _let_0 _let_0 int) (hAPP _let_2 _let_3 (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))))))))), (one_one int) ) 21.22/21.48 ( int, (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 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) 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21.22/21.48 ( nat, (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( nat, (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2))))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( nat, (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( nat, (fun int int), int, (plus_plus int), (hAPP int (fun nat int) (power_power int) skv_6), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( nat, (fun int int), int, (plus_plus int), (hAPP int (fun nat int) (power_power int) skv_23), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( nat, bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (one_one nat) ) 21.22/21.48 ( 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) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (hAPP _let_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( nat, (fun int (fun int bool)), int, zcong, (hAPP int (fun nat int) (power_power int) skv_16), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.22/21.48 ( 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) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 ) 21.22/21.48 ( real, int, nat, (semiring_1_of_nat int), natceiling, (one_one real) ) 21.22/21.48 ( real, nat, nat, suc, natceiling, (one_one real) ) 21.22/21.48 ( real, nat, nat, (fact_fact nat), natceiling, (one_one real) ) 21.22/21.48 ( real, nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), natceiling, (one_one real) ) 21.22/21.48 ( real, nat, nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), natceiling, (one_one real) ) 21.22/21.48 ( real, nat, real, natceiling, cos, skv_10 ) 21.22/21.48 ( real, nat, real, natfloor, cos, skv_10 ) 21.22/21.48 ( real, bool, nat, (even_odd_even nat), natceiling, (one_one real) ) 21.22/21.48 ( real, bool, nat, prime, natceiling, (one_one real) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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_10 ) 21.22/21.48 ( real, bool, real, (hAPP real (fun real bool) (ord_less real) pi), cos, skv_10 ) 21.22/21.48 ( 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_10 ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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_10 ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( real, real, nat, (real_1 nat), natceiling, (one_one real) ) 21.22/21.48 ( real, real, real, sin, cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( real, real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 21.22/21.48 ( real, real, real, cos, cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( real, real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( real, real, real, (sgn_sgn real), cos, skv_10 ) 21.22/21.48 ( real, real, real, sqrt, cos, skv_10 ) 21.22/21.48 ( real, real, real, tan, cos, skv_10 ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( real, real, real, (inverse_inverse real), cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( real, real, real, arctan, cos, skv_10 ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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))))))))) ) 21.22/21.48 ( real, real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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))))) ) 21.22/21.48 ( real, real, real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))), 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)))))))))) ) 21.22/21.48 ( real, real, complex, re, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.48 ( real, real, complex, re, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 21.22/21.48 ( real, real, complex, im, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.48 ( real, real, complex, im, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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)))))) ) 21.22/21.48 ( real, (fun nat nat), nat, (plus_plus nat), natceiling, (one_one real) ) 21.22/21.48 ( real, (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)))))))), natceiling, (one_one real) ) 21.22/21.48 ( real, (fun (filter nat) bool), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), cos, skv_10 ) 21.22/21.48 ( real, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), cos, skv_10 ) 21.22/21.48 ( real, complex, real, (of_real complex), (uminus_uminus real), (one_one real) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( real, complex, real, cis, cos, skv_10 ) 21.22/21.48 ( real, complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), cos, skv_10 ) 21.22/21.48 ( real, complex, complex, cnj, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.48 ( real, complex, complex, cnj, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 21.22/21.48 ( 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) ) 21.22/21.48 ( real, complex, complex, (uminus_uminus complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.48 ( real, complex, complex, expi, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 21.22/21.48 ( real, complex, complex, (inverse_inverse complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.48 ( 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 ) 21.22/21.48 ( 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) ) 21.22/21.48 ( real, (fun real complex), real, complex_1, cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( real, (fun real bool), real, (ord_less real), cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( 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)))) ) 21.22/21.48 ( 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) ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( real, (fun real bool), real, (ord_less_eq real), cos, skv_10 ) 21.22/21.48 ( 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))) ) 21.22/21.48 ( real, (fun real bool), real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 real) (fequal real)) cos))))), cos, skv_10 ) 21.22/21.48 ( 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 real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_1))) (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 real) (fequal real)) cos))))), (zero_zero real) ) 21.22/21.48 ( 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) ) 21.22/21.49 ( 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 nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), (one_one real) ) 21.22/21.49 ( 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)))) ) 21.22/21.49 ( real, (fun complex complex), complex, (times_times complex), (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.22/21.49 ( 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))) ) 21.22/21.49 ( 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_10 ) 21.22/21.49 ( real, 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(combb real _let_1 nat))) (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (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)))))) ) 21.22/21.49 ( (fun nat real), (fun real (fun (filter 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(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)) ) 21.22/21.49 ( (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_1))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_1) (fun _let_4 _let_3) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_4 (hAPP (fun real _let_0) (fun _let_2 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 21.22/21.49 ( (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 ) 21.22/21.49 ( (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 ) 21.22/21.49 ( (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 ) 21.22/21.49 ( (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 ) 21.22/21.49 ( (fun nat nat), (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (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)))) ) 21.22/21.49 ( (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 ) 21.22/21.49 ( (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))))) ) 21.22/21.49 ( (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 ) 21.22/21.49 ( complex, nat, real, natceiling, im, ii ) 21.22/21.49 ( complex, nat, real, natfloor, im, ii ) 21.22/21.49 ( complex, bool, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), im, ii ) 21.22/21.49 ( complex, real, real, (uminus_uminus real), im, ii ) 21.22/21.49 ( complex, real, real, sqrt, im, ii ) 21.22/21.49 ( complex, real, real, ln, im, ii ) 21.22/21.49 ( complex, real, real, arctan, im, ii ) 21.22/21.49 ( 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))) ) 21.22/21.49 ( 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))) ) 21.22/21.49 ( complex, (fun nat real), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), im, ii ) 21.22/21.49 ( complex, (fun real real), real, (inverse_divide real), im, ii ) 21.22/21.49 ( complex, complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), im, ii ) 21.22/21.49 ( 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))) ) 21.22/21.49 ( 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))) ) 21.22/21.49 ( 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 ) 21.22/21.49 ( complex, (fun real complex), real, complex_1, im, ii ) 21.22/21.49 ( complex, (fun real bool), real, (ord_less real), im, ii ) 21.22/21.49 ( 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) ) 21.22/21.49 ( (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP (fun _let_1 bool) (fun _let_2 _let_1) (combb _let_1 bool int) (fEx int)) (hAPP _let_0 _let_2 (hAPP _let_4 (fun _let_0 _let_2) (combc int _let_0 _let_1) (hAPP _let_2 _let_4 (hAPP (fun _let_1 _let_3) (fun _let_2 _let_4) (combb _let_1 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 21.22/21.49 ( (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)) ) 21.32/21.52 ( (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 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(let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun real _let_15))) (let ((_let_24 (fun _let_13 _let_13))) (let ((_let_25 (fun int _let_24))) (hAPP _let_17 (fun (fun int bool) _let_16) (combc real (fun int bool) (fun int (fun int bool))) (hAPP _let_18 _let_17 (hAPP (fun _let_8 _let_9) (fun _let_18 _let_17) (combb _let_8 _let_9 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_19 _let_18 (hAPP _let_11 (fun _let_19 _let_18) (combb _let_10 _let_8 real) (hAPP (fun _let_2 _let_3) _let_11 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_16 _let_19 (hAPP _let_12 (fun _let_16 _let_19) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_4 _let_12 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_20 _let_16 (hAPP _let_22 (fun _let_20 _let_16) (combc real _let_20 (fun int (fun int bool))) (hAPP _let_23 _let_22 (hAPP (fun _let_15 _let_21) (fun _let_23 _let_22) (combb _let_15 _let_21 real) (combb _let_13 (fun 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((_let_15 (fun _let_14 (fun int (fun int bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun _let_9 _let_9))) (let ((_let_19 (fun int _let_18))) (hAPP _let_12 _let_13 (hAPP _let_8 (fun _let_12 _let_13) (combb (fun int (fun int bool)) _let_7 real) (hAPP _let_3 _let_8 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj))) (hAPP _let_14 _let_12 (hAPP _let_16 (fun _let_14 _let_12) (combc real _let_14 (fun int (fun int bool))) (hAPP _let_17 _let_16 (hAPP (fun _let_11 _let_15) (fun _let_17 _let_16) (combb _let_11 _let_15 real) (combb _let_9 (fun int bool) int)) (hAPP _let_6 _let_17 (hAPP (fun _let_5 _let_11) (fun _let_6 _let_17) (combb _let_5 _let_11 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_14 (hAPP _let_19 (fun _let_9 _let_14) (combc int _let_9 _let_9) (hAPP _let_10 _let_19 (hAPP (fun _let_0 _let_18) (fun _let_10 _let_19) (combb _let_0 _let_18 int) (combb real real int)) (hAPP _let_9 _let_10 (hAPP (fun real _let_0) (fun _let_9 _let_10) (combb real _let_0 int) (inverse_divide real)) _let_4))) _let_4))))))))))))))))))))))) ) 21.41/21.61 ( (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 bool bool))) (let ((_let_2 (fun int _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 int) fconj)))))))))), (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 (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun real _let_2))) (hAPP _let_4 (fun (fun int (fun 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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 _let_1 _let_0))) (let ((_let_3 (fun (fun int _let_1) (fun int _let_0)))) (hAPP (fun _let_2 _let_3) (fun (fun real _let_2) (fun real _let_3)) (combb _let_2 _let_3 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)))))) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108584 $$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_108584) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_108584)))) ) 21.41/21.61 ( int, pls ) 21.41/21.61 ( int, (one_one int) ) 21.41/21.61 ( int, min ) 21.41/21.61 ( 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)))) ) 21.41/21.61 ( 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) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.41/21.61 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.61 ( nat, (one_one nat) ) 21.41/21.61 ( 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)))) ) 21.41/21.61 ( real, (one_one real) ) 21.41/21.61 ( 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) ) 21.41/21.61 ( complex, ii ) 21.41/21.61 ( complex, (one_one complex) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (zero_zero real)))) (= (zero_zero nat) (hAPP real nat natfloor X))) ) 21.41/21.61 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.61 ( (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)))) ) 21.41/21.61 ( (one_one real) ) 21.41/21.61 ( (zero_zero real) ) 21.41/21.61 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.61 ( skv_10 ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (times_times int) min) K_4) (hAPP int int (uminus_uminus int) K_4)) ) 21.41/21.61 ( pls ) 21.41/21.61 ( (one_one int) ) 21.41/21.61 ( min ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Q_3))) (not (= (one_one int) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) P_5) Q_3))) (= _let_1 (hAPP _let_0 _let_0 normalize _let_1))))) ) 21.41/21.61 ( (one_one int), (one_one int) ) 21.41/21.61 ( (zero_zero int), (one_one int) ) 21.41/21.61 ( s, (one_one int) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108611 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archim2085082626_floor X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_108611)) (hAPP int int (number_number_of int) BOUND_VARIABLE_108611))) ) 21.41/21.61 ( int, pls ) 21.41/21.61 ( int, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, min ) 21.41/21.61 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.61 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.61 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.61 ( nat, pls ) 21.41/21.61 ( nat, (hAPP int int bit1 pls) ) 21.41/21.61 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.61 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.61 ( real, min ) 21.41/21.61 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.61 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.61 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.61 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.61 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.61 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.41/21.61 ( complex, min ) 21.41/21.61 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.61 ( quickcheck_code_int, pls ) 21.41/21.61 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.41/21.61 ( quickcheck_code_int, (one_one int) ) 21.41/21.61 ( code_code_numeral, pls ) 21.41/21.61 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108640 $$unsorted) (BOUND_VARIABLE_108641 $$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_108640))) (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_108641)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_108641))))))) ) 21.41/21.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 21.41/21.61 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.61 ( 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 ) 21.41/21.61 ( 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))), m1 ) 21.41/21.61 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.41/21.61 ( 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_21 ) 21.41/21.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 21.41/21.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 21.41/21.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 21.41/21.61 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.41/21.61 ( int, y, v ) 21.41/21.61 ( int, y, w ) 21.41/21.61 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.61 ( int, sa, v ) 21.41/21.61 ( int, sa, w ) 21.41/21.61 ( int, x, v ) 21.41/21.61 ( int, x, w ) 21.41/21.61 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.41/21.61 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.61 ( int, r, v ) 21.41/21.61 ( int, r, w ) 21.41/21.61 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 21.41/21.61 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 21.41/21.61 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 21.41/21.61 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.41/21.61 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.41/21.61 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.61 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.61 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.41/21.61 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.41/21.61 ( 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)))))) ) 21.41/21.61 ( 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 ) 21.41/21.61 ( complex, ii, ii ) 21.41/21.61 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 21.41/21.61 ( 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 ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108662 $$unsorted) (BOUND_VARIABLE_108663 $$unsorted) (BOUND_VARIABLE_108664 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_108662))) (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_108664))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108663))) (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_108664) BOUND_VARIABLE_108663))))) ) 21.41/21.61 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.41/21.61 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.41/21.61 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.41/21.61 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_lessThan X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 21.41/21.61 ( rat ) 21.41/21.61 ( int ) 21.41/21.61 ( nat ) 21.41/21.61 ( bool ) 21.41/21.61 ( real ) 21.41/21.61 ( (filter nat) ) 21.41/21.61 ( (fun int bool) ) 21.41/21.61 ( (product_prod int int) ) 21.41/21.61 ( (fun nat bool) ) 21.41/21.61 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.41/21.61 ( quickcheck_code_int ) 21.41/21.61 ( code_code_numeral ) 21.41/21.61 ( (product_prod real real) ) 21.41/21.61 ( (filter real) ) 21.41/21.61 ( (product_prod nat nat) ) 21.41/21.61 ( (fun nat rat) ) 21.41/21.61 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Z_1))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) Z_1)) (hAPP nat nat suc (hAPP int nat nat_1 Z_1)))) ) 21.41/21.61 ( pls ) 21.41/21.61 ( (one_one int) ) 21.41/21.61 ( min ) 21.41/21.61 ( (zero_zero int) ) 21.41/21.61 ( s ) 21.41/21.61 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.61 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.41/21.61 ( (hAPP nat int (semiring_1_of_nat int) n) ) 21.41/21.61 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.61 ( skv_4 ) 21.41/21.61 ( skv_5 ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((Z_1 $$unsorted) (N $$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))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Z_1) (hAPP nat real (real_1 nat) N)))) ) 21.41/21.61 ( pi, (zero_zero nat) ) 21.41/21.61 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 21.41/21.61 ( (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) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108894 $$unsorted) (BOUND_VARIABLE_108895 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_108894))) (let ((_let_2 (hAPP nat X_a _let_1 (hAPP int nat _let_0 BOUND_VARIABLE_108895)))) (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_108895)))))))) ) 21.41/21.61 ( int, s, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, s1, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.61 ( int, v, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, w, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, y, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, x, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit1 pls) ) 21.41/21.61 ( int, skv_6, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, skv_7, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, skv_16, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, skv_23, (hAPP int int bit1 pls) ) 21.41/21.61 ( int, skv_24, (hAPP int int bit1 pls) ) 21.41/21.61 ( complex, ii, (hAPP int int bit1 pls) ) 21.41/21.61 ) 21.41/21.61 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) pls) (zero_zero X_a))) ) 21.41/21.61 ( rat ) 21.41/21.61 ( int ) 21.41/21.61 ( nat ) 21.41/21.61 ( real ) 21.41/21.62 ( complex ) 21.41/21.62 ( quickcheck_code_int ) 21.41/21.62 ( code_code_numeral ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_108926 $$unsorted) (BOUND_VARIABLE_108927 $$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_108927))))) (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_108926) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_108927)))) (or (and (not _let_1) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_108926))) _let_1))))) ) 21.41/21.62 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 Xa))) (not (hBOOL (hAPP real bool _let_0 Ya))) (= (= Ya Xa) (= (hAPP real real ln Xa) (hAPP real real ln Ya))))) ) 21.41/21.62 ( pi, pi ) 21.41/21.62 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_2 ) 21.41/21.62 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.41/21.62 ( skv_2, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( skv_9, skv_9 ) 21.41/21.62 ( skv_9, skv_12 ) 21.41/21.62 ( skv_12, skv_9 ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109088 $$unsorted) (BOUND_VARIABLE_109089 $$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_109089) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_109088) _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_109089) BOUND_VARIABLE_109088)) _let_3))))))) ) 21.41/21.62 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.41/21.62 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 21.41/21.62 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 21.41/21.62 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.41/21.62 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109112 $$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_109112) (zero_zero 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_109112)) (zero_zero int))))) ) 21.41/21.62 ( int, (one_one int) ) 21.41/21.62 ( int, min ) 21.41/21.62 ( int, (zero_zero int) ) 21.41/21.62 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.41/21.62 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.41/21.62 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.41/21.62 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.41/21.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( 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)))) ) 21.41/21.62 ( real, (zero_zero real) ) 21.41/21.62 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, skv_10 ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 21.41/21.62 ( rat ) 21.41/21.62 ( int ) 21.41/21.62 ( nat ) 21.41/21.62 ( bool ) 21.41/21.62 ( real ) 21.41/21.62 ( (filter nat) ) 21.41/21.62 ( complex ) 21.41/21.62 ( (fun int bool) ) 21.41/21.62 ( (product_prod int int) ) 21.41/21.62 ( (fun nat bool) ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.41/21.62 ( (product_prod real real) ) 21.41/21.62 ( (filter real) ) 21.41/21.62 ( (product_prod nat nat) ) 21.41/21.62 ( (fun nat rat) ) 21.41/21.62 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) min) K_4) (hAPP int int pred K_4)) ) 21.41/21.62 ( pls ) 21.41/21.62 ( min ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109213 $$unsorted) (BOUND_VARIABLE_109214 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_109213) BOUND_VARIABLE_109214)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_109213)) (hAPP int X_a _let_0 BOUND_VARIABLE_109214)))))) ) 21.41/21.62 ( int, pls, pls ) 21.41/21.62 ( int, pls, (hAPP int int bit1 pls) ) 21.41/21.62 ( nat, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109289 $$unsorted) (BOUND_VARIABLE_109290 $$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)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109289) BOUND_VARIABLE_109290)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_109289)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_109290))))))) ) 21.41/21.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.62 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( 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))))))))) ) 21.41/21.62 ( 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))) ) 21.41/21.62 ( 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))) ) 21.41/21.62 ( 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))) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_109313 $$unsorted) (BOUND_VARIABLE_109314 $$unsorted) (BOUND_VARIABLE_109315 $$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_109314) BOUND_VARIABLE_109315))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_109314 BOUND_VARIABLE_109313)) (hAPP X_a X_b BOUND_VARIABLE_109315 BOUND_VARIABLE_109313))))) ) 21.41/21.62 ( int, int, pls, bit0, bit0 ) 21.41/21.62 ( int, int, pls, pred, bit0 ) 21.41/21.62 ( int, int, min, bit1, bit1 ) 21.41/21.62 ( int, int, min, succ, bit1 ) 21.41/21.62 ( int, int, (zero_zero int), bit0, (fact_fact int) ) 21.41/21.62 ( nat, int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (semiring_1_of_nat int) ) 21.41/21.62 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), 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)))) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109346 $$unsorted) (BOUND_VARIABLE_109347 $$unsorted) (BOUND_VARIABLE_109348 $$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_109348))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109346) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_109347) BOUND_VARIABLE_109348)))) (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_109346) BOUND_VARIABLE_109348)) BOUND_VARIABLE_109347)))))) ) 21.41/21.62 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.41/21.62 ( int, (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.41/21.62 ( 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))) ) 21.41/21.62 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.41/21.62 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109376 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_109376) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_109376))) ) 21.41/21.62 ( int, pls ) 21.41/21.62 ( int, (one_one int) ) 21.41/21.62 ( int, min ) 21.41/21.62 ( int, s ) 21.41/21.62 ( 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)))) ) 21.41/21.62 ( int, s1 ) 21.41/21.62 ( int, m ) 21.41/21.62 ( 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) ) 21.41/21.62 ( int, t ) 21.41/21.62 ( int, v ) 21.41/21.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, w ) 21.41/21.62 ( int, y ) 21.41/21.62 ( int, sa ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.62 ( int, x ) 21.41/21.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.62 ( int, r ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.41/21.62 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.41/21.62 ( int, m1 ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.41/21.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, skv_14 ) 21.41/21.62 ( int, skv_20 ) 21.41/21.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( (fun int int), bit1 ) 21.41/21.62 ( (fun int int), bit0 ) 21.41/21.62 ( (fun int int), succ ) 21.41/21.62 ( (fun int int), pred ) 21.41/21.62 ( (fun int int), (fact_fact int) ) 21.41/21.62 ( (fun int int), zfact ) 21.41/21.62 ( nat, (one_one nat) ) 21.41/21.62 ( nat, n ) 21.41/21.62 ( nat, tn ) 21.41/21.62 ( bool, fTrue ) 21.41/21.62 ( bool, fFalse ) 21.41/21.62 ( real, pi ) 21.41/21.62 ( (fun nat real), (real_1 nat) ) 21.41/21.62 ( (fun nat real), cos_coeff ) 21.41/21.62 ( (fun nat real), sin_coeff ) 21.41/21.62 ( (fun real real), sin ) 21.41/21.62 ( (fun real real), cos ) 21.41/21.62 ( (fun real real), sqrt ) 21.41/21.62 ( (fun real real), tan ) 21.41/21.62 ( (fun real real), ln ) 21.41/21.62 ( (fun real real), arctan ) 21.41/21.62 ( (fun real real), arcsin ) 21.41/21.62 ( (fun real real), arccos ) 21.41/21.62 ( (fun nat nat), suc ) 21.41/21.62 ( (fun nat nat), (fact_fact nat) ) 21.41/21.62 ( (fun nat nat), nat_size ) 21.41/21.62 ( (fun nat nat), (size_size nat) ) 21.41/21.62 ( (fun nat nat), fact ) 21.41/21.62 ( (filter nat), sequentially ) 21.41/21.62 ( (fun int (fun int rat)), fract ) 21.41/21.62 ( complex, ii ) 21.41/21.62 ( (fun int bool), zOdd ) 21.41/21.62 ( (fun int bool), zprime ) 21.41/21.62 ( (fun int bool), zEven ) 21.41/21.62 ( (fun int bool), nat_neg ) 21.41/21.62 ( (fun int bool), nat_is_nat ) 21.41/21.62 ( (fun int bool), (even_odd_even int) ) 21.41/21.62 ( (fun int bool), twoSqu1091635170sum2sq ) 21.41/21.62 ( (fun int (fun int int)), legacy_zgcd ) 21.41/21.62 ( (fun int (fun int int)), (gcd_gcd int) ) 21.41/21.62 ( (fun int (fun int int)), inv ) 21.41/21.62 ( (fun int (fun int int)), multInv ) 21.41/21.62 ( (fun int (fun int int)), legendre ) 21.41/21.62 ( (fun int (fun int int)), standardRes ) 21.41/21.62 ( (fun int (fun int int)), nat_tsub ) 21.41/21.62 ( (fun int (fun int int)), z3div ) 21.41/21.62 ( (fun int (fun int int)), z3mod ) 21.41/21.62 ( (fun int (fun int int)), int_lcm ) 21.41/21.62 ( (fun int (fun int int)), int_gcd ) 21.41/21.62 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.41/21.62 ( (fun bool bool), fNot ) 21.41/21.62 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.41/21.62 ( (fun bool (fun bool bool)), fconj ) 21.41/21.62 ( (fun bool (fun bool bool)), fdisj ) 21.41/21.62 ( (fun bool (fun bool bool)), fimplies ) 21.41/21.62 ( (fun int (fun int bool)), quadRes ) 21.41/21.62 ( (fun int (fun int bool)), d22set ) 21.41/21.62 ( (fun int (fun int bool)), norRRset ) 21.41/21.62 ( (fun int (fun int bool)), sRStar ) 21.41/21.62 ( (fun int (fun int bool)), sr ) 21.41/21.62 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.41/21.62 ( (fun nat bool), (even_odd_even nat) ) 21.41/21.62 ( (fun nat bool), prime ) 21.41/21.62 ( (fun real complex), cis ) 21.41/21.62 ( (fun nat (fun nat bool)), coprime ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.41/21.62 ( (fun (product_prod int int) bool), frac_1 ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.41/21.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.41/21.62 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.41/21.62 ( (fun (fun int bool) bool), nat_nat_set ) 21.41/21.62 ( (fun nat (fun real real)), root ) 21.41/21.62 ( (fun real (fun real real)), log ) 21.41/21.62 ( (fun real (fun real real)), powr ) 21.41/21.62 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.41/21.62 ( (fun complex complex), cnj ) 21.41/21.62 ( (fun complex complex), expi ) 21.41/21.62 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.41/21.62 ( (fun nat (fun nat nat)), nat_gcd ) 21.41/21.62 ( (fun nat (fun nat nat)), nat_lcm ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.41/21.62 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.41/21.62 ( (fun int (fun (fun int bool) bool)), resSet ) 21.41/21.62 ( (fun int nat), nat_1 ) 21.41/21.62 ( (fun int nat), phi ) 21.41/21.62 ( (fun complex real), re ) 21.41/21.62 ( (fun complex real), im ) 21.41/21.62 ( (fun complex real), arg ) 21.41/21.62 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.41/21.62 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.41/21.62 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.41/21.62 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.41/21.62 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.41/21.62 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.41/21.62 ( (fun (product_prod nat nat) bool), pred_nat ) 21.41/21.62 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.41/21.62 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.41/21.62 ( (fun (fun int bool) int), (the int) ) 21.41/21.62 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.41/21.62 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.41/21.62 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.41/21.62 ( (fun real (fun real complex)), rcis ) 21.41/21.62 ( (fun real (fun real complex)), complex_1 ) 21.41/21.62 ( (fun int (fun int (fun int bool))), zcong ) 21.41/21.62 ( (fun int (fun int (fun int bool))), wset ) 21.41/21.62 ( (fun int (fun int (fun int bool))), noXRRset ) 21.41/21.62 ( (fun int (fun int (fun int bool))), bnorRset ) 21.41/21.62 ( (fun int (fun int (fun int bool))), zcongm ) 21.41/21.62 ( (fun real nat), natceiling ) 21.41/21.62 ( (fun real nat), natfloor ) 21.41/21.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.41/21.62 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.41/21.62 ( (fun int real), (real_1 int) ) 21.41/21.62 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.41/21.62 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.41/21.62 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.41/21.62 ( (fun complex nat), (size_size complex) ) 21.41/21.62 ( (fun complex nat), complex_size ) 21.41/21.62 ( (fun (fun nat rat) bool), vanishes ) 21.41/21.62 ( (fun (product_prod int int) rat), frct ) 21.41/21.62 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.41/21.62 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.41/21.62 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.41/21.62 ( (fun rat real), ratreal ) 21.41/21.62 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.41/21.62 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.41/21.62 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.41/21.62 ( (fun rat (product_prod int int)), quotient_of ) 21.41/21.62 ( (fun int (fun nat nat)), nat_aux ) 21.41/21.62 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.41/21.62 ( (fun int (list int)), quickc666637781d_zero ) 21.41/21.62 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.41/21.62 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.41/21.62 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.41/21.62 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.41/21.62 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.41/21.62 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.41/21.62 ( (fun code_code_numeral int), code_int_of ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109393 $$unsorted) (BOUND_VARIABLE_109394 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_109393))) (or (not (monoid_mult 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_109394)) BOUND_VARIABLE_109393) (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_109394))))) ) 21.41/21.62 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, v, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, w, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, y, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, x, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, skv_6, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, skv_7, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, skv_16, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, skv_23, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( int, skv_24, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109416 $$unsorted) (BOUND_VARIABLE_109417 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_109416) BOUND_VARIABLE_109417) sequentially))) (= (ti X_a BOUND_VARIABLE_109417) (hAPP _let_1 X_a (lim X_a) BOUND_VARIABLE_109416))))) ) 21.41/21.62 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109484 $$unsorted)) (or (not (preorder X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_109484) BOUND_VARIABLE_109484))) ) 21.41/21.62 ( int, (one_one int) ) 21.41/21.62 ( int, min ) 21.41/21.62 ( int, (zero_zero int) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.41/21.62 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.41/21.62 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, (zero_zero real) ) 21.41/21.62 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( real, skv_10 ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109589 $$unsorted) (BOUND_VARIABLE_109595 $$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)))) (or (not (number_ring X_a)) (and (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_109589)) (= (hAPP int X_a (number_number_of X_a) min) (hAPP nat X_a _let_1 BOUND_VARIABLE_109589))) (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_109595))) (= (one_one X_a) (hAPP nat X_a _let_1 BOUND_VARIABLE_109595))))))) ) 21.41/21.62 ( int, (one_one nat), (one_one nat) ) 21.41/21.62 ( real, (zero_zero nat), (zero_zero nat) ) 21.41/21.62 ) 21.41/21.62 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_109628 $$unsorted) (BOUND_VARIABLE_109629 $$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_n1866405975lgebra X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_109628) BOUND_VARIABLE_109629))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_109628 BOUND_VARIABLE_109629)) (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_109628)) BOUND_VARIABLE_109629)))))) ) 21.41/21.62 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 21.41/21.62 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 21.41/21.62 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 21.41/21.62 ( 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))) ) 21.41/21.62 ( int, int, bit1, pls ) 21.41/21.62 ( int, int, bit1, (hAPP int int bit1 pls) ) 21.41/21.62 ( int, int, bit1, min ) 21.41/21.62 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.41/21.62 ( 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)))))) ) 21.41/21.62 ( 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))))))) ) 21.41/21.62 ( int, int, (uminus_uminus int), pls ) 21.41/21.62 ( int, int, (uminus_uminus int), (one_one int) ) 21.41/21.62 ( int, int, (uminus_uminus int), min ) 21.41/21.62 ( int, int, bit0, pls ) 21.41/21.62 ( int, int, bit0, (hAPP int int bit1 pls) ) 21.41/21.62 ( int, int, bit0, min ) 21.41/21.62 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.62 ( int, int, succ, pls ) 21.41/21.62 ( int, int, succ, min ) 21.41/21.62 ( int, int, (number_number_of int), pls ) 21.41/21.62 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 21.41/21.62 ( int, int, (number_number_of int), min ) 21.41/21.62 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.62 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.62 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.62 ( 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 ) 21.41/21.62 ( 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) ) 21.41/21.62 ( int, int, (abs_abs int), v ) 21.41/21.62 ( int, int, (abs_abs int), w ) 21.41/21.62 ( int, int, (abs_abs int), skv_14 ) 21.41/21.62 ( int, int, (abs_abs int), skv_20 ) 21.41/21.62 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.62 ( int, int, pred, pls ) 21.41/21.62 ( int, int, pred, min ) 21.41/21.62 ( 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)))), (hAPP int int (abs_abs int) w) ) 21.41/21.62 ( 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)))), (hAPP int int (abs_abs int) v) ) 21.41/21.62 ( 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)))), (hAPP int int (abs_abs int) skv_14) ) 21.41/21.62 ( 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)))), (hAPP int int (abs_abs int) skv_20) ) 21.41/21.62 ( int, int, (fact_fact int), (one_one int) ) 21.41/21.62 ( int, int, (fact_fact int), (zero_zero int) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1 ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), skv_3 ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) sa), v ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) sa), w ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP nat int (hAPP int _let_2 _let_3 x) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 y) _let_1))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) x), v ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) x), w ) 21.41/21.62 ( 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) x) v))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) y), v ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) y), w ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 x) v)) (hAPP int int (hAPP int _let_0 _let_2 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.62 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) x) w))), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.41/21.62 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.62 ( 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 ) 21.41/21.62 ( 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))))), m1 ) 21.41/21.62 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.41/21.62 ( 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_21 ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.62 ( int, int, (hAPP int (fun int int) (times_times int) r), v ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (times_times int) r), w ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), v ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), v ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), w ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), w ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), v ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), w ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int 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int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP 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(hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus 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))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.63 ( 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) r) v))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w)))))), m1 ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (let ((_let_4 (minus_minus int))) (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) r) w))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.63 ( 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) ) 21.41/21.63 ( 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) ) 21.41/21.63 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun 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int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (times_times int) skv_13), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (times_times int) skv_19), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 21.41/21.63 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (semiring_1_of_nat int), (one_one nat) ) 21.41/21.63 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (semiring_1_of_nat int), n ) 21.41/21.63 ( int, nat, (hAPP int (fun nat int) (power_power int) v), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (hAPP int (fun nat int) (power_power int) w), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (hAPP int (fun nat int) (power_power int) x), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (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))) ) 21.41/21.63 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int 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(times_times int) r) w) ) 21.41/21.63 ( (fun int int), int, (minus_minus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.41/21.63 ( (fun int int), int, (minus_minus 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))) m1))) ) 21.41/21.63 ( (fun int int), int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.41/21.63 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min) ) 21.41/21.63 ( (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) ) 21.41/21.63 ( (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))) ) 21.41/21.63 ( nat, int, (number_number_of nat), pls ) 21.41/21.63 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 21.41/21.63 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.63 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.63 ( nat, int, nat_1, (one_one int) ) 21.41/21.63 ( nat, int, nat_1, (zero_zero int) ) 21.41/21.63 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( nat, int, nat_1, t ) 21.41/21.63 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.63 ( nat, nat, suc, (zero_zero nat) ) 21.41/21.63 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.63 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.41/21.63 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 21.41/21.63 ( nat, nat, (fact_fact nat), (one_one nat) ) 21.41/21.63 ( nat, nat, nat_size, (zero_zero nat) ) 21.41/21.63 ( nat, nat, (size_size nat), (zero_zero nat) ) 21.41/21.63 ( nat, nat, fact, (zero_zero nat) ) 21.41/21.63 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 21.41/21.63 ( nat, nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (one_one nat) ) 21.41/21.63 ( nat, real, natceiling, (one_one real) ) 21.41/21.63 ( nat, real, natceiling, (zero_zero real) ) 21.41/21.63 ( nat, real, natfloor, (one_one real) ) 21.41/21.63 ( nat, real, natfloor, (zero_zero real) ) 21.41/21.63 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 21.41/21.63 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 21.41/21.63 ( bool, int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( 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) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), min ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 21.41/21.63 ( bool, int, nat_neg, (one_one int) ) 21.41/21.63 ( bool, int, nat_neg, (zero_zero int) ) 21.41/21.63 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min) ) 21.41/21.63 ( bool, int, nat_is_nat, (one_one int) ) 21.41/21.63 ( bool, int, nat_is_nat, (zero_zero int) ) 21.41/21.63 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 21.41/21.63 ( bool, int, (even_odd_even int), (one_one int) ) 21.41/21.63 ( bool, int, (even_odd_even int), (zero_zero int) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 21.41/21.63 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( 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) (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)) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.41/21.63 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.63 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 21.41/21.63 ( bool, nat, (even_odd_even nat), (one_one nat) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.41/21.63 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.41/21.63 ( bool, nat, prime, (zero_zero nat) ) 21.41/21.63 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.63 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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) ) 21.41/21.63 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 21.41/21.63 ( 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)))) ) 21.41/21.63 ( 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))) ) 21.41/21.63 ( 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) ) 21.41/21.63 ( bool, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 21.41/21.63 ( 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 ) 21.41/21.63 ( 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 ) 21.41/21.64 ( 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) ) 21.41/21.64 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( bool, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 21.41/21.64 ( bool, (filter nat), (trivial_limit nat), sequentially ) 21.41/21.64 ( 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)) ) 21.41/21.64 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 21.41/21.64 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.41/21.64 ( 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) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( real, rat, ratreal, (one_one rat) ) 21.41/21.64 ( real, rat, ratreal, (zero_zero rat) ) 21.41/21.64 ( real, int, (number_number_of real), min ) 21.41/21.64 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.64 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.64 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.64 ( 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)))))))) ) 21.41/21.64 ( real, int, (real_1 int), (one_one int) ) 21.41/21.64 ( real, int, (real_1 int), (zero_zero int) ) 21.41/21.64 ( real, nat, (real_1 nat), (zero_zero nat) ) 21.41/21.64 ( real, nat, (real_1 nat), (one_one nat) ) 21.41/21.64 ( real, real, sin, pi ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, sin, (zero_zero real) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.41/21.64 ( real, real, cos, pi ) 21.41/21.64 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, cos, (zero_zero real) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.41/21.64 ( real, real, cos, skv_10 ) 21.41/21.64 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( real, 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)))) ) 21.41/21.64 ( real, real, (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)))) ) 21.41/21.64 ( 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))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, (uminus_uminus real), (one_one real) ) 21.41/21.64 ( 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) ) 21.41/21.64 ( 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))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( 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))))))))) ) 21.41/21.64 ( real, real, (sgn_sgn real), (zero_zero real) ) 21.41/21.64 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.64 ( real, real, sqrt, (one_one real) ) 21.41/21.64 ( real, real, sqrt, (zero_zero real) ) 21.41/21.64 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.64 ( 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))) ) 21.41/21.64 ( real, real, tan, pi ) 21.41/21.64 ( real, real, tan, (zero_zero real) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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)))) ) 21.41/21.64 ( real, real, ln, (one_one real) ) 21.41/21.64 ( real, real, (inverse_inverse real), (zero_zero real) ) 21.41/21.64 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.41/21.64 ( real, real, (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.41/21.64 ( real, real, arctan, (one_one real) ) 21.41/21.64 ( real, real, arctan, (zero_zero real) ) 21.41/21.64 ( 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))))) ) 21.41/21.64 ( 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)))))))))) ) 21.41/21.64 ( 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))) ) 21.41/21.64 ( 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))) ) 21.41/21.64 ( real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 21.41/21.64 ( 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)))))) ) 21.41/21.64 ( real, real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))), (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))))))))))) ) 21.41/21.64 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.41/21.64 ( real, complex, re, (zero_zero complex) ) 21.41/21.64 ( real, complex, re, ii ) 21.41/21.64 ( real, complex, re, (one_one complex) ) 21.41/21.64 ( real, complex, im, (zero_zero complex) ) 21.41/21.64 ( real, complex, im, ii ) 21.41/21.64 ( real, complex, im, (one_one complex) ) 21.41/21.64 ( real, (fun real bool), (the real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2)))))))))))))) ) 21.41/21.64 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min) ) 21.41/21.64 ( (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)))) ) 21.41/21.64 ( (fun nat real), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), (one_one real) ) 21.41/21.64 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 21.41/21.64 ( (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))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 21.41/21.64 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real 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_let_10 (fun _let_8 _let_7) (combc real _let_8 (fun int (fun int bool))) (hAPP _let_11 _let_10 (hAPP (fun _let_6 _let_9) (fun _let_11 _let_10) (combb _let_6 _let_9 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_2 _let_6) (fun _let_3 _let_11) (combb _let_2 _let_6 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_8 (hAPP _let_13 (fun _let_4 _let_8) (combc int _let_4 _let_4) (hAPP _let_5 _let_13 (hAPP (fun _let_0 _let_12) (fun _let_5 _let_13) (combb _let_0 _let_12 int) (combb real real int)) (hAPP _let_4 _let_5 (hAPP (fun real _let_0) (fun _let_4 _let_5) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))))))))))) ) 21.41/21.70 ( (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)))) ) 21.41/21.70 ( (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)))))) ) 21.41/21.70 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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))))))))), (real_1 int) ) 21.41/21.70 ( (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 _let_1 _let_0))) (let ((_let_3 (fun (fun int _let_1) (fun int _let_0)))) (hAPP (fun _let_2 _let_3) (fun (fun real _let_2) (fun real _let_3)) (combb _let_2 _let_3 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)))))) ) 21.41/21.70 ( (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 real) (fun int bool)))) (let ((_let_3 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun real _let_2))) (hAPP _let_5 _let_4 (hAPP (fun _let_2 _let_3) (fun _let_5 _let_4) (combb _let_2 _let_3 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_5) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real))))))))) ) 21.41/21.70 ( (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) ) 21.41/21.70 ( (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) ) 21.41/21.70 ( (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) ) 21.41/21.70 ( (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))))) ) 21.41/21.70 ( (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 int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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)))))))) ) 21.41/21.70 ( (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) ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N))) (= M N) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N)))) ) 21.41/21.70 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.70 ( (zero_zero nat), n ) 21.41/21.70 ( (zero_zero nat), tn ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((X $$unsorted)) (= (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X)) (hAPP real nat natfloor X)) ) 21.41/21.70 ( (one_one real) ) 21.41/21.70 ( (zero_zero real) ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109797 $$unsorted) (BOUND_VARIABLE_109798 $$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_109797) BOUND_VARIABLE_109798))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_109798) BOUND_VARIABLE_109797))) (= (ti X_a BOUND_VARIABLE_109797) (ti X_a BOUND_VARIABLE_109798))))) ) 21.41/21.70 ( int, pls, min ) 21.41/21.70 ( int, pls, (zero_zero int) ) 21.41/21.70 ( int, (one_one int), (zero_zero int) ) 21.41/21.70 ( int, (one_one int), t ) 21.41/21.70 ( int, min, pls ) 21.41/21.70 ( int, min, min ) 21.41/21.70 ( int, min, (zero_zero int) ) 21.41/21.70 ( int, (zero_zero int), pls ) 21.41/21.70 ( int, (zero_zero int), (one_one int) ) 21.41/21.70 ( int, (zero_zero int), min ) 21.41/21.70 ( int, (zero_zero int), s ) 21.41/21.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.41/21.70 ( int, (zero_zero int), skv_4 ) 21.41/21.70 ( int, (zero_zero int), skv_5 ) 21.41/21.70 ( int, s, (zero_zero int) ) 21.41/21.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.41/21.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 21.41/21.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 21.41/21.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.41/21.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.41/21.70 ( int, t, (one_one int) ) 21.41/21.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 21.41/21.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.70 ( int, skv_4, (zero_zero int) ) 21.41/21.70 ( int, skv_5, (zero_zero int) ) 21.41/21.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.41/21.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.70 ( real, pi, (zero_zero real) ) 21.41/21.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.41/21.70 ( 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)))) ) 21.41/21.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.41/21.70 ( 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))) ) 21.41/21.70 ( 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)))), (zero_zero real) ) 21.41/21.70 ( real, (zero_zero real), pi ) 21.41/21.70 ( 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)))) ) 21.41/21.70 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.70 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.70 ( real, (zero_zero real), skv_10 ) 21.41/21.70 ( real, (zero_zero real), skv_11 ) 21.41/21.70 ( real, (zero_zero real), skv_15 ) 21.41/21.70 ( real, (zero_zero real), skv_18 ) 21.41/21.70 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.41/21.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.41/21.70 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.70 ( real, skv_10, (zero_zero real) ) 21.41/21.70 ( real, skv_11, (zero_zero real) ) 21.41/21.70 ( real, skv_15, (zero_zero real) ) 21.41/21.70 ( real, skv_18, (zero_zero real) ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B))) (not (forall ((D_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) D_2))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) Y_1))) D_2))) (and (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) B)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_1) Y_1)))) ))) ))))) ) 21.41/21.70 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 21.41/21.70 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.70 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 21.41/21.70 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 21.41/21.70 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.41/21.70 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109926 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_109926)) (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_109926)) _let_0))))) ) 21.41/21.70 ( int, pls ) 21.41/21.70 ( int, min ) 21.41/21.70 ( int, s ) 21.41/21.70 ( int, s1 ) 21.41/21.70 ( int, m ) 21.41/21.70 ( int, t ) 21.41/21.70 ( int, v ) 21.41/21.70 ( int, w ) 21.41/21.70 ( int, y ) 21.41/21.70 ( int, sa ) 21.41/21.70 ( int, x ) 21.41/21.70 ( int, r ) 21.41/21.70 ( int, m1 ) 21.41/21.70 ( int, skv_14 ) 21.41/21.70 ( int, skv_20 ) 21.41/21.70 ( (fun int int), bit1 ) 21.41/21.70 ( (fun int int), bit0 ) 21.41/21.70 ( (fun int int), succ ) 21.41/21.70 ( (fun int int), pred ) 21.41/21.70 ( (fun int int), (fact_fact int) ) 21.41/21.70 ( (fun int int), zfact ) 21.41/21.70 ( nat, n ) 21.41/21.70 ( nat, tn ) 21.41/21.70 ( bool, fTrue ) 21.41/21.70 ( bool, fFalse ) 21.41/21.70 ( real, pi ) 21.41/21.70 ( (fun nat real), (real_1 nat) ) 21.41/21.70 ( (fun nat real), cos_coeff ) 21.41/21.70 ( (fun nat real), sin_coeff ) 21.41/21.70 ( (fun real real), sin ) 21.41/21.70 ( (fun real real), cos ) 21.41/21.70 ( (fun real real), sqrt ) 21.41/21.70 ( (fun real real), tan ) 21.41/21.70 ( (fun real real), ln ) 21.41/21.70 ( (fun real real), arctan ) 21.41/21.70 ( (fun real real), arcsin ) 21.41/21.70 ( (fun real real), arccos ) 21.41/21.70 ( (fun nat nat), suc ) 21.41/21.70 ( (fun nat nat), (fact_fact nat) ) 21.41/21.70 ( (fun nat nat), nat_size ) 21.41/21.70 ( (fun nat nat), (size_size nat) ) 21.41/21.70 ( (fun nat nat), fact ) 21.41/21.70 ( (filter nat), sequentially ) 21.41/21.70 ( (fun int (fun int rat)), fract ) 21.41/21.70 ( complex, ii ) 21.41/21.70 ( (fun int bool), zOdd ) 21.41/21.70 ( (fun int bool), zprime ) 21.41/21.70 ( (fun int bool), zEven ) 21.41/21.70 ( (fun int bool), nat_neg ) 21.41/21.70 ( (fun int bool), nat_is_nat ) 21.41/21.70 ( (fun int bool), (even_odd_even int) ) 21.41/21.70 ( (fun int bool), twoSqu1091635170sum2sq ) 21.41/21.70 ( (fun int (fun int int)), legacy_zgcd ) 21.41/21.70 ( (fun int (fun int int)), (gcd_gcd int) ) 21.41/21.70 ( (fun int (fun int int)), inv ) 21.41/21.70 ( (fun int (fun int int)), multInv ) 21.41/21.70 ( (fun int (fun int int)), legendre ) 21.41/21.70 ( (fun int (fun int int)), standardRes ) 21.41/21.70 ( (fun int (fun int int)), nat_tsub ) 21.41/21.70 ( (fun int (fun int int)), z3div ) 21.41/21.70 ( (fun int (fun int int)), z3mod ) 21.41/21.70 ( (fun int (fun int int)), int_lcm ) 21.41/21.70 ( (fun int (fun int int)), int_gcd ) 21.41/21.70 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.41/21.70 ( (fun bool bool), fNot ) 21.41/21.70 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.41/21.70 ( (fun bool (fun bool bool)), fconj ) 21.41/21.70 ( (fun bool (fun bool bool)), fdisj ) 21.41/21.70 ( (fun bool (fun bool bool)), fimplies ) 21.41/21.70 ( (fun int (fun int bool)), quadRes ) 21.41/21.70 ( (fun int (fun int bool)), d22set ) 21.41/21.70 ( (fun int (fun int bool)), norRRset ) 21.41/21.70 ( (fun int (fun int bool)), sRStar ) 21.41/21.70 ( (fun int (fun int bool)), sr ) 21.41/21.70 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.41/21.70 ( (fun nat bool), (even_odd_even nat) ) 21.41/21.70 ( (fun nat bool), prime ) 21.41/21.70 ( (fun real complex), cis ) 21.41/21.70 ( (fun nat (fun nat bool)), coprime ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.41/21.70 ( (fun (product_prod int int) bool), frac_1 ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.41/21.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.41/21.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.41/21.70 ( (fun (fun int bool) bool), nat_nat_set ) 21.41/21.70 ( (fun nat (fun real real)), root ) 21.41/21.70 ( (fun real (fun real real)), log ) 21.41/21.70 ( (fun real (fun real real)), powr ) 21.41/21.70 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.41/21.70 ( (fun complex complex), cnj ) 21.41/21.70 ( (fun complex complex), expi ) 21.41/21.70 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.41/21.70 ( (fun nat (fun nat nat)), nat_gcd ) 21.41/21.70 ( (fun nat (fun nat nat)), nat_lcm ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.41/21.70 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.41/21.70 ( (fun int (fun (fun int bool) bool)), resSet ) 21.41/21.70 ( (fun int nat), nat_1 ) 21.41/21.70 ( (fun int nat), phi ) 21.41/21.70 ( (fun complex real), re ) 21.41/21.70 ( (fun complex real), im ) 21.41/21.70 ( (fun complex real), arg ) 21.41/21.70 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.41/21.70 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.41/21.70 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.41/21.70 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.41/21.70 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.41/21.70 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.41/21.70 ( (fun (product_prod nat nat) bool), pred_nat ) 21.41/21.70 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.41/21.70 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.41/21.70 ( (fun (fun int bool) int), (the int) ) 21.41/21.70 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.41/21.70 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.41/21.70 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.41/21.70 ( (fun real (fun real complex)), rcis ) 21.41/21.70 ( (fun real (fun real complex)), complex_1 ) 21.41/21.70 ( (fun int (fun int (fun int bool))), zcong ) 21.41/21.70 ( (fun int (fun int (fun int bool))), wset ) 21.41/21.70 ( (fun int (fun int (fun int bool))), noXRRset ) 21.41/21.70 ( (fun int (fun int (fun int bool))), bnorRset ) 21.41/21.70 ( (fun int (fun int (fun int bool))), zcongm ) 21.41/21.70 ( (fun real nat), natceiling ) 21.41/21.70 ( (fun real nat), natfloor ) 21.41/21.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.41/21.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.41/21.70 ( (fun int real), (real_1 int) ) 21.41/21.70 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.41/21.70 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.41/21.70 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.41/21.70 ( (fun complex nat), (size_size complex) ) 21.41/21.70 ( (fun complex nat), complex_size ) 21.41/21.70 ( (fun (fun nat rat) bool), vanishes ) 21.41/21.70 ( (fun (product_prod int int) rat), frct ) 21.41/21.70 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.41/21.70 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.41/21.70 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.41/21.70 ( (fun rat real), ratreal ) 21.41/21.70 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.41/21.70 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.41/21.70 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.41/21.70 ( (fun rat (product_prod int int)), quotient_of ) 21.41/21.70 ( (fun int (fun nat nat)), nat_aux ) 21.41/21.70 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.41/21.70 ( (fun int (list int)), quickc666637781d_zero ) 21.41/21.70 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.41/21.70 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.41/21.70 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.41/21.70 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.41/21.70 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.41/21.70 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.41/21.70 ( (fun code_code_numeral int), code_int_of ) 21.41/21.70 ) 21.41/21.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109948 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_109948) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_109948))) ) 21.41/21.70 ( int, pls ) 21.41/21.70 ( int, (one_one int) ) 21.41/21.70 ( int, min ) 21.41/21.70 ( int, s ) 21.41/21.71 ( 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)))) ) 21.41/21.71 ( int, s1 ) 21.41/21.71 ( int, m ) 21.41/21.71 ( 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) ) 21.41/21.71 ( int, t ) 21.41/21.71 ( int, v ) 21.41/21.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.71 ( int, w ) 21.41/21.71 ( int, y ) 21.41/21.71 ( int, sa ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.71 ( int, x ) 21.41/21.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.41/21.71 ( int, r ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.41/21.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.41/21.71 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.41/21.71 ( int, m1 ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.41/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.41/21.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.71 ( int, skv_14 ) 21.41/21.71 ( int, skv_20 ) 21.41/21.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.41/21.71 ( (fun int int), bit1 ) 21.41/21.71 ( (fun int int), bit0 ) 21.41/21.71 ( (fun int int), succ ) 21.41/21.71 ( (fun int int), pred ) 21.41/21.71 ( (fun int int), (fact_fact int) ) 21.41/21.71 ( (fun int int), zfact ) 21.41/21.71 ( nat, (one_one nat) ) 21.41/21.71 ( nat, n ) 21.41/21.71 ( nat, tn ) 21.41/21.71 ( bool, fTrue ) 21.41/21.71 ( bool, fFalse ) 21.41/21.71 ( real, pi ) 21.41/21.71 ( (fun nat real), (real_1 nat) ) 21.41/21.71 ( (fun nat real), cos_coeff ) 21.41/21.71 ( (fun nat real), sin_coeff ) 21.41/21.71 ( (fun real real), sin ) 21.41/21.71 ( (fun real real), cos ) 21.41/21.71 ( (fun real real), sqrt ) 21.41/21.71 ( (fun real real), tan ) 21.41/21.71 ( (fun real real), ln ) 21.41/21.71 ( (fun real real), arctan ) 21.41/21.71 ( (fun real real), arcsin ) 21.41/21.71 ( (fun real real), arccos ) 21.41/21.71 ( (fun nat nat), suc ) 21.41/21.71 ( (fun nat nat), (fact_fact nat) ) 21.41/21.71 ( (fun nat nat), nat_size ) 21.41/21.71 ( (fun nat nat), (size_size nat) ) 21.41/21.71 ( (fun nat nat), fact ) 21.41/21.71 ( (filter nat), sequentially ) 21.41/21.71 ( (fun int (fun int rat)), fract ) 21.41/21.71 ( complex, ii ) 21.41/21.71 ( (fun int bool), zOdd ) 21.41/21.71 ( (fun int bool), zprime ) 21.41/21.71 ( (fun int bool), zEven ) 21.41/21.71 ( (fun int bool), nat_neg ) 21.41/21.71 ( (fun int bool), nat_is_nat ) 21.41/21.71 ( (fun int bool), (even_odd_even int) ) 21.41/21.71 ( (fun int bool), twoSqu1091635170sum2sq ) 21.41/21.71 ( (fun int (fun int int)), legacy_zgcd ) 21.41/21.71 ( (fun int (fun int int)), (gcd_gcd int) ) 21.41/21.71 ( (fun int (fun int int)), inv ) 21.41/21.71 ( (fun int (fun int int)), multInv ) 21.41/21.71 ( (fun int (fun int int)), legendre ) 21.41/21.71 ( (fun int (fun int int)), standardRes ) 21.41/21.71 ( (fun int (fun int int)), nat_tsub ) 21.41/21.71 ( (fun int (fun int int)), z3div ) 21.41/21.71 ( (fun int (fun int int)), z3mod ) 21.41/21.71 ( (fun int (fun int int)), int_lcm ) 21.41/21.71 ( (fun int (fun int int)), int_gcd ) 21.41/21.71 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.41/21.71 ( (fun bool bool), fNot ) 21.41/21.71 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.41/21.71 ( (fun bool (fun bool bool)), fconj ) 21.41/21.71 ( (fun bool (fun bool bool)), fdisj ) 21.41/21.71 ( (fun bool (fun bool bool)), fimplies ) 21.41/21.71 ( (fun int (fun int bool)), quadRes ) 21.41/21.71 ( (fun int (fun int bool)), d22set ) 21.41/21.71 ( (fun int (fun int bool)), norRRset ) 21.41/21.71 ( (fun int (fun int bool)), sRStar ) 21.41/21.71 ( (fun int (fun int bool)), sr ) 21.41/21.71 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.41/21.71 ( (fun nat bool), (even_odd_even nat) ) 21.41/21.71 ( (fun nat bool), prime ) 21.41/21.71 ( (fun real complex), cis ) 21.41/21.71 ( (fun nat (fun nat bool)), coprime ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.41/21.71 ( (fun (product_prod int int) bool), frac_1 ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.41/21.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.41/21.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.41/21.71 ( (fun (fun int bool) bool), nat_nat_set ) 21.41/21.71 ( (fun nat (fun real real)), root ) 21.41/21.71 ( (fun real (fun real real)), log ) 21.41/21.71 ( (fun real (fun real real)), powr ) 21.41/21.71 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.41/21.71 ( (fun complex complex), cnj ) 21.41/21.71 ( (fun complex complex), expi ) 21.41/21.71 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.41/21.71 ( (fun nat (fun nat nat)), nat_gcd ) 21.41/21.71 ( (fun nat (fun nat nat)), nat_lcm ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.41/21.71 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.41/21.71 ( (fun int (fun (fun int bool) bool)), resSet ) 21.41/21.71 ( (fun int nat), nat_1 ) 21.41/21.71 ( (fun int nat), phi ) 21.41/21.71 ( (fun complex real), re ) 21.41/21.71 ( (fun complex real), im ) 21.41/21.71 ( (fun complex real), arg ) 21.41/21.71 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.41/21.71 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.41/21.71 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.41/21.71 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.41/21.71 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.41/21.71 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.41/21.71 ( (fun (product_prod nat nat) bool), pred_nat ) 21.41/21.71 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.41/21.71 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.41/21.71 ( (fun (fun int bool) int), (the int) ) 21.41/21.71 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.41/21.71 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.41/21.71 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.41/21.71 ( (fun real (fun real complex)), rcis ) 21.41/21.71 ( (fun real (fun real complex)), complex_1 ) 21.41/21.71 ( (fun int (fun int (fun int bool))), zcong ) 21.41/21.71 ( (fun int (fun int (fun int bool))), wset ) 21.41/21.71 ( (fun int (fun int (fun int bool))), noXRRset ) 21.41/21.71 ( (fun int (fun int (fun int bool))), bnorRset ) 21.41/21.71 ( (fun int (fun int (fun int bool))), zcongm ) 21.41/21.71 ( (fun real nat), natceiling ) 21.41/21.71 ( (fun real nat), natfloor ) 21.41/21.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.41/21.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.41/21.71 ( (fun int real), (real_1 int) ) 21.41/21.71 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.41/21.71 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.41/21.71 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.41/21.71 ( (fun complex nat), (size_size complex) ) 21.41/21.71 ( (fun complex nat), complex_size ) 21.41/21.71 ( (fun (fun nat rat) bool), vanishes ) 21.41/21.71 ( (fun (product_prod int int) rat), frct ) 21.41/21.71 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.41/21.71 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.41/21.71 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.41/21.71 ( (fun rat real), ratreal ) 21.41/21.71 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.41/21.71 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.41/21.71 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.41/21.71 ( (fun rat (product_prod int int)), quotient_of ) 21.41/21.71 ( (fun int (fun nat nat)), nat_aux ) 21.41/21.71 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.41/21.71 ( (fun int (list int)), quickc666637781d_zero ) 21.41/21.71 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.41/21.71 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.41/21.71 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.41/21.71 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.41/21.71 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.41/21.71 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.41/21.71 ( (fun code_code_numeral int), code_int_of ) 21.41/21.71 ) 21.41/21.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_109977 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (fun X_a bool))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= (hAPP _let_1 X_a (the X_a) (hAPP _let_0 _let_1 (sums X_a) BOUND_VARIABLE_109977)) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_109977))))) ) 21.41/21.71 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))) ) 21.41/21.71 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.41/21.71 ) 21.41/21.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110027 $$unsorted) (BOUND_VARIABLE_110028 $$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_110028))) (let ((_let_3 (hAPP int X_a _let_1 BOUND_VARIABLE_110027))) (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)))))))) ) 21.41/21.71 ( int, pls, pls ) 21.41/21.71 ( int, pls, (hAPP int int bit1 pls) ) 21.41/21.71 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.41/21.71 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.41/21.71 ( int, (hAPP int int bit1 pls), pls ) 21.41/21.71 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), pls ) 21.41/21.71 ) 21.41/21.71 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (even_odd_even int))) (= (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) Xa) Na))) (and (hBOOL (hAPP int bool _let_0 Xa)) (not (= (zero_zero nat) Na))))) ) 21.41/21.71 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.41/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 Z1))) (= (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 Z2) Z3)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 Z2)) Z3))))) ) 21.59/21.71 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, v ) 21.59/21.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, w ) 21.59/21.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, v ) 21.59/21.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, w ) 21.59/21.71 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), m1 ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))) ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (= (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_1 V)) (hAPP int int _let_1 W)) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) V) (hAPP int int (uminus_uminus int) W)))))) ) 21.59/21.71 ( (one_one int), pls ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) Ya) Xa))) (= Xa (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastAtMost real) Ya) Xa))))) ) 21.59/21.71 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.59/21.71 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (zero_zero real), pi ) 21.59/21.71 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.71 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.71 ( (zero_zero real), skv_10 ) 21.59/21.71 ( (zero_zero real), skv_11 ) 21.59/21.71 ( (zero_zero real), skv_15 ) 21.59/21.71 ( (zero_zero real), skv_18 ) 21.59/21.71 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.59/21.71 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (X $$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_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) B))) (not (forall ((D_2 $$unsorted)) (or (not (forall ((Y_1 $$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) Y_1))) D_2))) (and (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 Y_1) B)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_1) Y_1))))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) D_2)))) ))))) ) 21.59/21.71 ( 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) ) 21.59/21.71 ( (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)))) ) 21.59/21.71 ( (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)))), pi, (zero_zero real) ) 21.59/21.71 ( (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 ) 21.59/21.71 ( (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) ) 21.59/21.71 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (fun nat nat))) (let ((_let_4 (fun nat bool))) (let ((_let_5 (zero_zero real))) (let ((_let_6 (fun nat _let_2))) (let ((_let_7 (fun _let_0 _let_0))) (let ((_let_8 (combs nat real real))) (let ((_let_9 (fun real _let_2))) (let ((_let_10 (fun _let_0 _let_6))) (let ((_let_11 (combb real _let_2 nat))) (let ((_let_12 (fun _let_3 _let_0))) (let ((_let_13 (combb nat real nat))) (let ((_let_14 (fun nat _let_3))) (let ((_let_15 (fun nat _let_9))) (= (one_one real) (hAPP _let_4 real (hAPP _let_0 (fun _let_4 real) (big_co1399186613setsum nat real) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 (hAPP _let_9 _let_10 _let_11 (times_times real)) (hAPP real _let_0 (hAPP _let_6 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_6 (hAPP _let_15 _let_10 (combs nat real _let_2) (hAPP _let_4 _let_15 (hAPP (fun bool _let_9) (fun _let_4 _let_15) (combb bool _let_9 nat) (if real)) (even_odd_even nat))) (hAPP _let_0 _let_0 (hAPP _let_6 _let_7 _let_8 (hAPP _let_0 _let_6 (hAPP _let_9 _let_10 _let_11 (inverse_divide real)) (hAPP _let_3 _let_0 (hAPP _let_0 _let_12 _let_13 (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min))) (hAPP nat _let_3 (hAPP _let_14 _let_14 (combc nat nat nat) (div_div nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_3 _let_0 (hAPP _let_0 _let_12 _let_13 (real_1 nat)) (fact_fact nat))))) _let_5))) (hAPP real _let_0 _let_1 _let_5))) (hAPP nat _let_4 (hAPP nat (fun nat _let_4) (ord_atLeastLessThan nat) (zero_zero nat)) (hAPP nat nat suc Na)))))))))))))))))))) ) 21.59/21.71 ( (zero_zero nat) ) 21.59/21.71 ( (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.71 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((M $$unsorted)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) (zero_zero nat)))) ) 21.59/21.71 ( (zero_zero nat) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110132 $$unsorted) (BOUND_VARIABLE_110133 $$unsorted) (BOUND_VARIABLE_110134 $$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)) (= (and (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_110133) BOUND_VARIABLE_110134)) BOUND_VARIABLE_110132)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_110132) (hAPP X_a X_a (hAPP X_a _let_2 (plus_plus X_a) BOUND_VARIABLE_110133) BOUND_VARIABLE_110134)))) (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_110132) BOUND_VARIABLE_110133))) BOUND_VARIABLE_110134)))))))) ) 21.59/21.71 ( int, (zero_zero int), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.71 ( int, (zero_zero 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) ) 21.59/21.71 ( 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) ) 21.59/21.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 21.59/21.71 ( 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) ) 21.59/21.71 ( int, m1, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.71 ( 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) ) 21.59/21.71 ( int, skv_5, (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) ) 21.59/21.71 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110163 $$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 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_110163)) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_110163) _let_0)))))) ) 21.59/21.71 ( int, s ) 21.59/21.71 ( int, s1 ) 21.59/21.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.71 ( int, v ) 21.59/21.71 ( int, w ) 21.59/21.71 ( int, y ) 21.59/21.71 ( int, x ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.59/21.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.59/21.71 ( int, skv_6 ) 21.59/21.71 ( int, skv_7 ) 21.59/21.71 ( int, skv_14 ) 21.59/21.71 ( int, skv_16 ) 21.59/21.71 ( int, skv_20 ) 21.59/21.71 ( int, skv_23 ) 21.59/21.71 ( int, skv_24 ) 21.59/21.71 ( complex, ii ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (uminus_uminus int))) (let ((_let_2 (times_times int))) (= (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 _let_2 Z_1) W)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int _let_1 Z_1)) W))))) ) 21.59/21.71 ( pls, (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))) m1))) ) 21.59/21.71 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.71 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.71 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.71 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.59/21.71 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.71 ) 21.59/21.71 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP rat real ratreal (hAPP int rat (number_number_of rat) K_4)) (hAPP int real (number_number_of real) K_4)) ) 21.59/21.71 ( min ) 21.59/21.71 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.71 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.71 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.71 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.59/21.71 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110180 $$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_110180)) (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_110180) BOUND_VARIABLE_110180)))))) ) 21.59/21.72 ( int, (one_one int) ) 21.59/21.72 ( 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)))) ) 21.59/21.72 ( 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) ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.59/21.72 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.59/21.72 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( nat, (one_one nat) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((P_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (= (and (forall ((D_2 $$unsorted)) (or (not (= A_3 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) B_2) D_2))) (hBOOL (hAPP nat bool P_1 D_2))) ) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) A_3) B_2))) (hBOOL (hAPP nat bool P_1 (zero_zero nat))))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) A_3) B_2)))) ) 21.59/21.72 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat nat_1 t), (one_one nat) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 (zero_zero nat)))) (or (not (hBOOL (hAPP nat bool _let_2 N))) (not (hBOOL (hAPP nat bool _let_2 M))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N)) M)))))) ) 21.59/21.72 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (N $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X)) (hAPP real real _let_2 Y))))))) ) 21.59/21.72 ( (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))) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110248 $$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) _let_0) BOUND_VARIABLE_110248)))) ) 21.59/21.72 ( 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))) m1))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.59/21.72 ) 21.59/21.72 (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)) ) 21.59/21.72 ( pls ) 21.59/21.72 ( (hAPP int int bit1 pls) ) 21.59/21.72 ( (one_one int) ) 21.59/21.72 ( min ) 21.59/21.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.72 ( (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)))) ) 21.59/21.72 ( (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) ) 21.59/21.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.59/21.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.59/21.72 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.72 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.59/21.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110311 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_110311) (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_110311))) ) 21.59/21.72 ( int, pls ) 21.59/21.72 ( int, min ) 21.59/21.72 ( int, s ) 21.59/21.72 ( int, s1 ) 21.59/21.72 ( int, m ) 21.59/21.72 ( int, t ) 21.59/21.72 ( int, v ) 21.59/21.72 ( int, w ) 21.59/21.72 ( int, y ) 21.59/21.72 ( int, sa ) 21.59/21.72 ( int, x ) 21.59/21.72 ( int, r ) 21.59/21.72 ( int, m1 ) 21.59/21.72 ( int, skv_14 ) 21.59/21.72 ( int, skv_20 ) 21.59/21.72 ( (fun int int), bit1 ) 21.59/21.72 ( (fun int int), bit0 ) 21.59/21.72 ( (fun int int), succ ) 21.59/21.72 ( (fun int int), pred ) 21.59/21.72 ( (fun int int), (fact_fact int) ) 21.59/21.72 ( (fun int int), zfact ) 21.59/21.72 ( nat, n ) 21.59/21.72 ( nat, tn ) 21.59/21.72 ( bool, fTrue ) 21.59/21.72 ( bool, fFalse ) 21.59/21.72 ( real, pi ) 21.59/21.72 ( (fun nat real), (real_1 nat) ) 21.59/21.72 ( (fun nat real), cos_coeff ) 21.59/21.72 ( (fun nat real), sin_coeff ) 21.59/21.72 ( (fun real real), sin ) 21.59/21.72 ( (fun real real), cos ) 21.59/21.72 ( (fun real real), sqrt ) 21.59/21.72 ( (fun real real), tan ) 21.59/21.72 ( (fun real real), ln ) 21.59/21.72 ( (fun real real), arctan ) 21.59/21.72 ( (fun real real), arcsin ) 21.59/21.72 ( (fun real real), arccos ) 21.59/21.72 ( (fun nat nat), suc ) 21.59/21.72 ( (fun nat nat), (fact_fact nat) ) 21.59/21.72 ( (fun nat nat), nat_size ) 21.59/21.72 ( (fun nat nat), (size_size nat) ) 21.59/21.72 ( (fun nat nat), fact ) 21.59/21.72 ( (filter nat), sequentially ) 21.59/21.72 ( (fun int (fun int rat)), fract ) 21.59/21.72 ( complex, ii ) 21.59/21.72 ( (fun int bool), zOdd ) 21.59/21.72 ( (fun int bool), zprime ) 21.59/21.72 ( (fun int bool), zEven ) 21.59/21.72 ( (fun int bool), nat_neg ) 21.59/21.72 ( (fun int bool), nat_is_nat ) 21.59/21.72 ( (fun int bool), (even_odd_even int) ) 21.59/21.72 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.72 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.72 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.72 ( (fun int (fun int int)), inv ) 21.59/21.72 ( (fun int (fun int int)), multInv ) 21.59/21.72 ( (fun int (fun int int)), legendre ) 21.59/21.72 ( (fun int (fun int int)), standardRes ) 21.59/21.72 ( (fun int (fun int int)), nat_tsub ) 21.59/21.72 ( (fun int (fun int int)), z3div ) 21.59/21.72 ( (fun int (fun int int)), z3mod ) 21.59/21.72 ( (fun int (fun int int)), int_lcm ) 21.59/21.72 ( (fun int (fun int int)), int_gcd ) 21.59/21.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.72 ( (fun bool bool), fNot ) 21.59/21.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.72 ( (fun bool (fun bool bool)), fconj ) 21.59/21.72 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.72 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.72 ( (fun int (fun int bool)), quadRes ) 21.59/21.72 ( (fun int (fun int bool)), d22set ) 21.59/21.72 ( (fun int (fun int bool)), norRRset ) 21.59/21.72 ( (fun int (fun int bool)), sRStar ) 21.59/21.72 ( (fun int (fun int bool)), sr ) 21.59/21.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.72 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.72 ( (fun nat bool), prime ) 21.59/21.72 ( (fun real complex), cis ) 21.59/21.72 ( (fun nat (fun nat bool)), coprime ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.72 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.72 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.72 ( (fun nat (fun real real)), root ) 21.59/21.72 ( (fun real (fun real real)), log ) 21.59/21.72 ( (fun real (fun real real)), powr ) 21.59/21.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.72 ( (fun complex complex), cnj ) 21.59/21.72 ( (fun complex complex), expi ) 21.59/21.72 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.72 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.72 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.72 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.72 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.72 ( (fun int nat), nat_1 ) 21.59/21.72 ( (fun int nat), phi ) 21.59/21.72 ( (fun complex real), re ) 21.59/21.72 ( (fun complex real), im ) 21.59/21.72 ( (fun complex real), arg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.72 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.72 ( (fun (fun int bool) int), (the int) ) 21.59/21.72 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.72 ( (fun real (fun real complex)), rcis ) 21.59/21.72 ( (fun real (fun real complex)), complex_1 ) 21.59/21.72 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.72 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.72 ( (fun real nat), natceiling ) 21.59/21.72 ( (fun real nat), natfloor ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.72 ( (fun int real), (real_1 int) ) 21.59/21.72 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.72 ( (fun complex nat), (size_size complex) ) 21.59/21.72 ( (fun complex nat), complex_size ) 21.59/21.72 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.72 ( (fun (product_prod int int) rat), frct ) 21.59/21.72 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.72 ( (fun rat real), ratreal ) 21.59/21.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.72 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.72 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.72 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.72 ( (fun code_code_numeral int), code_int_of ) 21.59/21.72 ) 21.59/21.72 (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 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ))) ) 21.59/21.72 ( real ) 21.59/21.72 ( complex ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$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)))) ) 21.59/21.72 ( rat ) 21.59/21.72 ( int ) 21.59/21.72 ( nat ) 21.59/21.72 ( real ) 21.59/21.72 ( complex ) 21.59/21.72 ( quickcheck_code_int ) 21.59/21.72 ( code_code_numeral ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((R_3 $$unsorted)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_3) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) R_3)) ii)) ) 21.59/21.72 ( (hAPP int real (number_number_of real) min) ) 21.59/21.72 ( pi ) 21.59/21.72 ( (one_one real) ) 21.59/21.72 ( (zero_zero real) ) 21.59/21.72 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) Xa))) (= (= (one_one real) Xa) (= _let_0 (hAPP real real ln Xa))))) ) 21.59/21.72 ( pi ) 21.59/21.72 ( (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)))) ) 21.59/21.72 ( (one_one real) ) 21.59/21.72 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( skv_2 ) 21.59/21.72 ( skv_9 ) 21.59/21.72 ( skv_12 ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) Xa)) (hBOOL (hAPP real bool _let_2 (hAPP real real ln Xa)))))))) ) 21.59/21.72 ( (one_one real) ) 21.59/21.72 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((N $$unsorted)) (= (hAPP real int (archimedean_ceiling real) (hAPP int real (real_1 int) N)) (ti int N)) ) 21.59/21.72 ( pls ) 21.59/21.72 ( (one_one int) ) 21.59/21.72 ( min ) 21.59/21.72 ( (zero_zero int) ) 21.59/21.72 ( s ) 21.59/21.72 ( s1 ) 21.59/21.72 ( m ) 21.59/21.72 ( t ) 21.59/21.72 ( v ) 21.59/21.72 ( w ) 21.59/21.72 ( y ) 21.59/21.72 ( sa ) 21.59/21.72 ( x ) 21.59/21.72 ( r ) 21.59/21.72 ( m1 ) 21.59/21.72 ( skv_14 ) 21.59/21.72 ( skv_20 ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110516 $$unsorted) (BOUND_VARIABLE_110517 $$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_110516)) (hAPP X_a int _let_0 BOUND_VARIABLE_110517)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_110516) BOUND_VARIABLE_110517)))) ) 21.59/21.72 ( int, (one_one int), t ) 21.59/21.72 ( int, min, min ) 21.59/21.72 ( int, min, (zero_zero int) ) 21.59/21.72 ( int, (zero_zero int), pls ) 21.59/21.72 ( int, (zero_zero int), (one_one int) ) 21.59/21.72 ( int, (zero_zero int), min ) 21.59/21.72 ( 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))) ) 21.59/21.72 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.72 ( 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))) ) 21.59/21.72 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.72 ( 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))) ) 21.59/21.72 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.72 ( 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))) ) 21.59/21.72 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.72 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.72 ( nat, (zero_zero nat), n ) 21.59/21.72 ( nat, (zero_zero nat), tn ) 21.59/21.72 ( real, pi, (zero_zero real) ) 21.59/21.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( 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))) ) 21.59/21.72 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( real, (zero_zero real), pi ) 21.59/21.72 ( 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)))) ) 21.59/21.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( real, (zero_zero real), skv_2 ) 21.59/21.72 ( real, (zero_zero real), skv_9 ) 21.59/21.72 ( real, (zero_zero real), skv_12 ) 21.59/21.72 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.59/21.72 ( 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) ) 21.59/21.72 ( 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 ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (plus_plus real) X) (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)))) ) 21.59/21.72 ( pi ) 21.59/21.72 ( (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)))) ) 21.59/21.72 ( (zero_zero real) ) 21.59/21.72 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.59/21.72 ( (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) ) 21.59/21.72 ( (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 (hAPP int int bit1 pls))))) ) 21.59/21.72 ( (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)))) ) 21.59/21.72 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (product_prod nat nat))) (let ((_let_3 (fun nat _let_2))) (let ((_let_4 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_1 (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP nat bool (hAPP nat _let_1 (ord_less_eq nat) N) M))) (= (hAPP nat _let_2 (hAPP nat _let_3 (product_Pair nat nat) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 (div_div nat) _let_4) N))) (hAPP nat nat (hAPP nat _let_0 (div_mod nat) _let_4) N)) (hAPP nat _let_2 (hAPP nat _let_3 divmod_nat M) N)))))))) ) 21.59/21.72 ( (hAPP int nat nat_1 t), (one_one nat) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110555 $$unsorted) (BOUND_VARIABLE_110556 $$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 BOUND_VARIABLE_110555) (hAPP X_a X_a _let_2 BOUND_VARIABLE_110556)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_110555)) BOUND_VARIABLE_110556)))))) ) 21.59/21.72 ( int, pls, (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))) m1))) ) 21.59/21.72 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.72 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.72 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.72 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110576 $$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_110576)) (= _let_0 (ti X_a BOUND_VARIABLE_110576))))) ) 21.59/21.72 ( int, pls ) 21.59/21.72 ( int, min ) 21.59/21.72 ( int, s ) 21.59/21.72 ( int, s1 ) 21.59/21.72 ( int, m ) 21.59/21.72 ( int, t ) 21.59/21.72 ( int, v ) 21.59/21.72 ( int, w ) 21.59/21.72 ( int, y ) 21.59/21.72 ( int, sa ) 21.59/21.72 ( int, x ) 21.59/21.72 ( int, r ) 21.59/21.72 ( int, m1 ) 21.59/21.72 ( int, skv_14 ) 21.59/21.72 ( int, skv_20 ) 21.59/21.72 ( (fun int int), bit1 ) 21.59/21.72 ( (fun int int), bit0 ) 21.59/21.72 ( (fun int int), succ ) 21.59/21.72 ( (fun int int), pred ) 21.59/21.72 ( (fun int int), (fact_fact int) ) 21.59/21.72 ( (fun int int), zfact ) 21.59/21.72 ( nat, n ) 21.59/21.72 ( nat, tn ) 21.59/21.72 ( bool, fTrue ) 21.59/21.72 ( bool, fFalse ) 21.59/21.72 ( real, pi ) 21.59/21.72 ( real, (zero_zero real) ) 21.59/21.72 ( (fun nat real), (real_1 nat) ) 21.59/21.72 ( (fun nat real), cos_coeff ) 21.59/21.72 ( (fun nat real), sin_coeff ) 21.59/21.72 ( (fun real real), sin ) 21.59/21.72 ( (fun real real), cos ) 21.59/21.72 ( (fun real real), sqrt ) 21.59/21.72 ( (fun real real), tan ) 21.59/21.72 ( (fun real real), ln ) 21.59/21.72 ( (fun real real), arctan ) 21.59/21.72 ( (fun real real), arcsin ) 21.59/21.72 ( (fun real real), arccos ) 21.59/21.72 ( (fun nat nat), suc ) 21.59/21.72 ( (fun nat nat), (fact_fact nat) ) 21.59/21.72 ( (fun nat nat), nat_size ) 21.59/21.72 ( (fun nat nat), (size_size nat) ) 21.59/21.72 ( (fun nat nat), fact ) 21.59/21.72 ( (filter nat), sequentially ) 21.59/21.72 ( (fun int (fun int rat)), fract ) 21.59/21.72 ( complex, ii ) 21.59/21.72 ( (fun int bool), zOdd ) 21.59/21.72 ( (fun int bool), zprime ) 21.59/21.72 ( (fun int bool), zEven ) 21.59/21.72 ( (fun int bool), nat_neg ) 21.59/21.72 ( (fun int bool), nat_is_nat ) 21.59/21.72 ( (fun int bool), (even_odd_even int) ) 21.59/21.72 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.72 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.72 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.72 ( (fun int (fun int int)), inv ) 21.59/21.72 ( (fun int (fun int int)), multInv ) 21.59/21.72 ( (fun int (fun int int)), legendre ) 21.59/21.72 ( (fun int (fun int int)), standardRes ) 21.59/21.72 ( (fun int (fun int int)), nat_tsub ) 21.59/21.72 ( (fun int (fun int int)), z3div ) 21.59/21.72 ( (fun int (fun int int)), z3mod ) 21.59/21.72 ( (fun int (fun int int)), int_lcm ) 21.59/21.72 ( (fun int (fun int int)), int_gcd ) 21.59/21.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.72 ( (fun bool bool), fNot ) 21.59/21.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.72 ( (fun bool (fun bool bool)), fconj ) 21.59/21.72 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.72 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.72 ( (fun int (fun int bool)), quadRes ) 21.59/21.72 ( (fun int (fun int bool)), d22set ) 21.59/21.72 ( (fun int (fun int bool)), norRRset ) 21.59/21.72 ( (fun int (fun int bool)), sRStar ) 21.59/21.72 ( (fun int (fun int bool)), sr ) 21.59/21.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.72 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.72 ( (fun nat bool), prime ) 21.59/21.72 ( (fun real complex), cis ) 21.59/21.72 ( (fun nat (fun nat bool)), coprime ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.72 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.72 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.72 ( (fun nat (fun real real)), root ) 21.59/21.72 ( (fun real (fun real real)), log ) 21.59/21.72 ( (fun real (fun real real)), powr ) 21.59/21.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.72 ( (fun complex complex), cnj ) 21.59/21.72 ( (fun complex complex), expi ) 21.59/21.72 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.72 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.72 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.72 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.72 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.72 ( (fun int nat), nat_1 ) 21.59/21.72 ( (fun int nat), phi ) 21.59/21.72 ( (fun complex real), re ) 21.59/21.72 ( (fun complex real), im ) 21.59/21.72 ( (fun complex real), arg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.72 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.72 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.72 ( (fun (fun int bool) int), (the int) ) 21.59/21.72 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.72 ( (fun real (fun real complex)), rcis ) 21.59/21.72 ( (fun real (fun real complex)), complex_1 ) 21.59/21.72 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.72 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.72 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.72 ( (fun real nat), natceiling ) 21.59/21.72 ( (fun real nat), natfloor ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.72 ( (fun int real), (real_1 int) ) 21.59/21.72 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.72 ( (fun complex nat), (size_size complex) ) 21.59/21.72 ( (fun complex nat), complex_size ) 21.59/21.72 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.72 ( (fun (product_prod int int) rat), frct ) 21.59/21.72 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.72 ( (fun rat real), ratreal ) 21.59/21.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.72 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.72 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.72 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.72 ( (fun code_code_numeral int), code_int_of ) 21.59/21.72 ) 21.59/21.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110607 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linord219039673up_add X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_110607)) (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_110607) BOUND_VARIABLE_110607))))) ) 21.59/21.72 ( int, pls ) 21.59/21.72 ( int, (one_one int) ) 21.59/21.72 ( int, min ) 21.59/21.72 ( int, s ) 21.59/21.72 ( 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)))) ) 21.59/21.72 ( int, s1 ) 21.59/21.72 ( int, m ) 21.59/21.72 ( 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) ) 21.59/21.72 ( int, t ) 21.59/21.72 ( int, v ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, w ) 21.59/21.72 ( int, y ) 21.59/21.72 ( int, sa ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( int, x ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.72 ( int, r ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.59/21.72 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.59/21.72 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.59/21.72 ( int, m1 ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.72 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( int, skv_14 ) 21.59/21.72 ( int, skv_20 ) 21.59/21.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.72 ( (fun int int), bit1 ) 21.59/21.72 ( (fun int int), bit0 ) 21.59/21.72 ( (fun int int), succ ) 21.59/21.72 ( (fun int int), pred ) 21.59/21.72 ( (fun int int), (fact_fact int) ) 21.59/21.72 ( (fun int int), zfact ) 21.59/21.72 ( nat, (one_one nat) ) 21.59/21.72 ( nat, n ) 21.59/21.72 ( nat, tn ) 21.59/21.72 ( bool, fTrue ) 21.59/21.72 ( bool, fFalse ) 21.59/21.72 ( real, pi ) 21.59/21.72 ( (fun nat real), (real_1 nat) ) 21.59/21.72 ( (fun nat real), cos_coeff ) 21.59/21.72 ( (fun nat real), sin_coeff ) 21.59/21.72 ( (fun real real), sin ) 21.59/21.72 ( (fun real real), cos ) 21.59/21.72 ( (fun real real), sqrt ) 21.59/21.72 ( (fun real real), tan ) 21.59/21.72 ( (fun real real), ln ) 21.59/21.72 ( (fun real real), arctan ) 21.59/21.72 ( (fun real real), arcsin ) 21.59/21.72 ( (fun real real), arccos ) 21.59/21.72 ( (fun nat nat), suc ) 21.59/21.72 ( (fun nat nat), (fact_fact nat) ) 21.59/21.72 ( (fun nat nat), nat_size ) 21.59/21.72 ( (fun nat nat), (size_size nat) ) 21.59/21.72 ( (fun nat nat), fact ) 21.59/21.72 ( (filter nat), sequentially ) 21.59/21.72 ( (fun int (fun int rat)), fract ) 21.59/21.72 ( complex, ii ) 21.59/21.72 ( (fun int bool), zOdd ) 21.59/21.72 ( (fun int bool), zprime ) 21.59/21.72 ( (fun int bool), zEven ) 21.59/21.72 ( (fun int bool), nat_neg ) 21.59/21.72 ( (fun int bool), nat_is_nat ) 21.59/21.72 ( (fun int bool), (even_odd_even int) ) 21.59/21.72 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.72 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.72 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.72 ( (fun int (fun int int)), inv ) 21.59/21.72 ( (fun int (fun int int)), multInv ) 21.59/21.72 ( (fun int (fun int int)), legendre ) 21.59/21.72 ( (fun int (fun int int)), standardRes ) 21.59/21.72 ( (fun int (fun int int)), nat_tsub ) 21.59/21.72 ( (fun int (fun int int)), z3div ) 21.59/21.72 ( (fun int (fun int int)), z3mod ) 21.59/21.72 ( (fun int (fun int int)), int_lcm ) 21.59/21.72 ( (fun int (fun int int)), int_gcd ) 21.59/21.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.72 ( (fun bool bool), fNot ) 21.59/21.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.72 ( (fun bool (fun bool bool)), fconj ) 21.59/21.72 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.72 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.72 ( (fun int (fun int bool)), quadRes ) 21.59/21.72 ( (fun int (fun int bool)), d22set ) 21.59/21.72 ( (fun int (fun int bool)), norRRset ) 21.59/21.72 ( (fun int (fun int bool)), sRStar ) 21.59/21.72 ( (fun int (fun int bool)), sr ) 21.59/21.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.72 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.72 ( (fun nat bool), prime ) 21.59/21.72 ( (fun real complex), cis ) 21.59/21.72 ( (fun nat (fun nat bool)), coprime ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.72 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.73 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.73 ( (fun nat (fun real real)), root ) 21.59/21.73 ( (fun real (fun real real)), log ) 21.59/21.73 ( (fun real (fun real real)), powr ) 21.59/21.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.73 ( (fun complex complex), cnj ) 21.59/21.73 ( (fun complex complex), expi ) 21.59/21.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.73 ( (fun int nat), nat_1 ) 21.59/21.73 ( (fun int nat), phi ) 21.59/21.73 ( (fun complex real), re ) 21.59/21.73 ( (fun complex real), im ) 21.59/21.73 ( (fun complex real), arg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.73 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.73 ( (fun (fun int bool) int), (the int) ) 21.59/21.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.73 ( (fun real (fun real complex)), rcis ) 21.59/21.73 ( (fun real (fun real complex)), complex_1 ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.73 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.73 ( (fun real nat), natceiling ) 21.59/21.73 ( (fun real nat), natfloor ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.73 ( (fun int real), (real_1 int) ) 21.59/21.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.73 ( (fun complex nat), (size_size complex) ) 21.59/21.73 ( (fun complex nat), complex_size ) 21.59/21.73 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.73 ( (fun (product_prod int int) rat), frct ) 21.59/21.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.73 ( (fun rat real), ratreal ) 21.59/21.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.73 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.73 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.73 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.73 ( (fun code_code_numeral int), code_int_of ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X))) (not (hBOOL (hAPP int bool _let_0 Y))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 X)) (hAPP int nat nat_1 Y)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) nat_tsub X) Y))))) ) 21.59/21.73 ( (one_one int), t ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110639 $$unsorted)) (or (not (real_normed_vector X_a)) (= (not (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_110639))) (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_110639))))) ) 21.59/21.73 ( int, pls ) 21.59/21.73 ( int, min ) 21.59/21.73 ( int, s ) 21.59/21.73 ( int, s1 ) 21.59/21.73 ( int, m ) 21.59/21.73 ( int, t ) 21.59/21.73 ( int, v ) 21.59/21.73 ( int, w ) 21.59/21.73 ( int, y ) 21.59/21.73 ( int, sa ) 21.59/21.73 ( int, x ) 21.59/21.73 ( int, r ) 21.59/21.73 ( int, m1 ) 21.59/21.73 ( int, skv_14 ) 21.59/21.73 ( int, skv_20 ) 21.59/21.73 ( (fun int int), bit1 ) 21.59/21.73 ( (fun int int), bit0 ) 21.59/21.73 ( (fun int int), succ ) 21.59/21.73 ( (fun int int), pred ) 21.59/21.73 ( (fun int int), (fact_fact int) ) 21.59/21.73 ( (fun int int), zfact ) 21.59/21.73 ( nat, n ) 21.59/21.73 ( nat, tn ) 21.59/21.73 ( bool, fTrue ) 21.59/21.73 ( bool, fFalse ) 21.59/21.73 ( real, pi ) 21.59/21.73 ( (fun nat real), (real_1 nat) ) 21.59/21.73 ( (fun nat real), cos_coeff ) 21.59/21.73 ( (fun nat real), sin_coeff ) 21.59/21.73 ( (fun real real), sin ) 21.59/21.73 ( (fun real real), cos ) 21.59/21.73 ( (fun real real), sqrt ) 21.59/21.73 ( (fun real real), tan ) 21.59/21.73 ( (fun real real), ln ) 21.59/21.73 ( (fun real real), arctan ) 21.59/21.73 ( (fun real real), arcsin ) 21.59/21.73 ( (fun real real), arccos ) 21.59/21.73 ( (fun nat nat), suc ) 21.59/21.73 ( (fun nat nat), (fact_fact nat) ) 21.59/21.73 ( (fun nat nat), nat_size ) 21.59/21.73 ( (fun nat nat), (size_size nat) ) 21.59/21.73 ( (fun nat nat), fact ) 21.59/21.73 ( (filter nat), sequentially ) 21.59/21.73 ( (fun int (fun int rat)), fract ) 21.59/21.73 ( complex, ii ) 21.59/21.73 ( (fun int bool), zOdd ) 21.59/21.73 ( (fun int bool), zprime ) 21.59/21.73 ( (fun int bool), zEven ) 21.59/21.73 ( (fun int bool), nat_neg ) 21.59/21.73 ( (fun int bool), nat_is_nat ) 21.59/21.73 ( (fun int bool), (even_odd_even int) ) 21.59/21.73 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.73 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.73 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.73 ( (fun int (fun int int)), inv ) 21.59/21.73 ( (fun int (fun int int)), multInv ) 21.59/21.73 ( (fun int (fun int int)), legendre ) 21.59/21.73 ( (fun int (fun int int)), standardRes ) 21.59/21.73 ( (fun int (fun int int)), nat_tsub ) 21.59/21.73 ( (fun int (fun int int)), z3div ) 21.59/21.73 ( (fun int (fun int int)), z3mod ) 21.59/21.73 ( (fun int (fun int int)), int_lcm ) 21.59/21.73 ( (fun int (fun int int)), int_gcd ) 21.59/21.73 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.73 ( (fun bool bool), fNot ) 21.59/21.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.73 ( (fun bool (fun bool bool)), fconj ) 21.59/21.73 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.73 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.73 ( (fun int (fun int bool)), quadRes ) 21.59/21.73 ( (fun int (fun int bool)), d22set ) 21.59/21.73 ( (fun int (fun int bool)), norRRset ) 21.59/21.73 ( (fun int (fun int bool)), sRStar ) 21.59/21.73 ( (fun int (fun int bool)), sr ) 21.59/21.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.73 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.73 ( (fun nat bool), prime ) 21.59/21.73 ( (fun real complex), cis ) 21.59/21.73 ( (fun nat (fun nat bool)), coprime ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.73 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.73 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.73 ( (fun nat (fun real real)), root ) 21.59/21.73 ( (fun real (fun real real)), log ) 21.59/21.73 ( (fun real (fun real real)), powr ) 21.59/21.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.73 ( (fun complex complex), cnj ) 21.59/21.73 ( (fun complex complex), expi ) 21.59/21.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.73 ( (fun int nat), nat_1 ) 21.59/21.73 ( (fun int nat), phi ) 21.59/21.73 ( (fun complex real), re ) 21.59/21.73 ( (fun complex real), im ) 21.59/21.73 ( (fun complex real), arg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.73 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.73 ( (fun (fun int bool) int), (the int) ) 21.59/21.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.73 ( (fun real (fun real complex)), rcis ) 21.59/21.73 ( (fun real (fun real complex)), complex_1 ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.73 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.73 ( (fun real nat), natceiling ) 21.59/21.73 ( (fun real nat), natfloor ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.73 ( (fun int real), (real_1 int) ) 21.59/21.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.73 ( (fun complex nat), (size_size complex) ) 21.59/21.73 ( (fun complex nat), complex_size ) 21.59/21.73 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.73 ( (fun (product_prod int int) rat), frct ) 21.59/21.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.73 ( (fun rat real), ratreal ) 21.59/21.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.73 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.73 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.73 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.73 ( (fun code_code_numeral int), code_int_of ) 21.59/21.73 ) 21.59/21.73 (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))) ) 21.59/21.73 ( nat ) 21.59/21.73 ( bool ) 21.59/21.73 ( real ) 21.59/21.73 ( complex ) 21.59/21.73 ( (fun nat (product_prod real real)) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110682 $$unsorted) (BOUND_VARIABLE_110683 $$unsorted) (BOUND_VARIABLE_110684 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (= _let_1 (ti X_a BOUND_VARIABLE_110684)))) (let ((_let_3 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_110682))) (or (not (field_inverse_zero X_a)) (not (number X_a)) (= (and (or _let_2 (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) _let_3) BOUND_VARIABLE_110684) (ti X_a BOUND_VARIABLE_110683))) (or (not _let_2) (= _let_1 _let_3))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_110683) BOUND_VARIABLE_110684)))))))) ) 21.59/21.73 ( int, pls, s, s ) 21.59/21.73 ( int, (hAPP int int bit1 pls), m, m ) 21.59/21.73 ( int, min, v, v ) 21.59/21.73 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), r, r ) 21.59/21.73 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), s1, s1 ) 21.59/21.73 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), min, min ) 21.59/21.73 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), n, n ) 21.59/21.73 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), tn, tn ) 21.59/21.73 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), pi, pi ) 21.59/21.73 ( complex, min, ii, ii ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X $$unsorted) (Y $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos X)) (hAPP real real cos Y)))))) ) 21.59/21.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 21.59/21.73 ) 21.59/21.73 (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)))) ) 21.59/21.73 ( bool, (ord_less real), pi, (zero_zero real) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( bool, (ord_less real), (zero_zero real), pi ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( bool, (ord_less real), (zero_zero real), skv_2 ) 21.59/21.73 ( bool, (ord_less real), (zero_zero real), skv_9 ) 21.59/21.73 ( bool, (ord_less real), (zero_zero real), skv_12 ) 21.59/21.73 ( 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) ) 21.59/21.73 ( 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) ) 21.59/21.73 ( 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 ) 21.59/21.73 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( bool, (ord_less_eq real), (zero_zero real), pi ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( bool, (ord_less_eq real), (zero_zero real), skv_10 ) 21.59/21.73 ( bool, (ord_less_eq real), (zero_zero real), skv_11 ) 21.59/21.73 ( bool, (ord_less_eq real), (zero_zero real), skv_15 ) 21.59/21.73 ( bool, (ord_less_eq real), (zero_zero real), skv_18 ) 21.59/21.73 ( 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) ) 21.59/21.73 ( bool, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.73 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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))))))))) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.59/21.73 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.59/21.73 ( 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)))))) ) 21.59/21.73 ( 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 ) 21.59/21.73 ( real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.59/21.73 ( complex, complex_1, (one_one real), (zero_zero real) ) 21.59/21.73 ( complex, complex_1, (zero_zero real), (one_one real) ) 21.59/21.73 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 21.59/21.73 ) 21.59/21.73 (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))) ) 21.59/21.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( (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))) ) 21.59/21.73 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( y ) 21.59/21.73 ( x ) 21.59/21.73 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.59/21.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.59/21.73 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.59/21.73 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.59/21.73 ( (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))) m1))) ) 21.59/21.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110909 $$unsorted) (BOUND_VARIABLE_110910 $$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_110910) BOUND_VARIABLE_110909)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_110909)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_110910)))))))) ) 21.59/21.73 ( int, pls, pls ) 21.59/21.73 ( int, pls, (one_one int) ) 21.59/21.73 ( int, pls, (zero_zero int) ) 21.59/21.73 ( int, (one_one int), pls ) 21.59/21.73 ( int, (one_one int), (one_one int) ) 21.59/21.73 ( int, (one_one int), (zero_zero int) ) 21.59/21.73 ( int, min, min ) 21.59/21.73 ( int, min, (zero_zero int) ) 21.59/21.73 ( int, (zero_zero int), min ) 21.59/21.73 ( 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))), (zero_zero int) ) 21.59/21.73 ( 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 ) 21.59/21.73 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( 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 ) 21.59/21.73 ( 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 ) 21.59/21.73 ( 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_5 ) 21.59/21.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.59/21.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.59/21.73 ( int, t, (one_one int) ) 21.59/21.73 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.59/21.73 ( nat, n, (zero_zero nat) ) 21.59/21.73 ( nat, tn, (zero_zero nat) ) 21.59/21.73 ( real, pi, (zero_zero real) ) 21.59/21.73 ( 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)) ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( 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) ) 21.59/21.73 ( real, (zero_zero real), pi ) 21.59/21.73 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( 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))))) ) 21.59/21.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.59/21.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.59/21.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.59/21.73 ( real, skv_2, (zero_zero real) ) 21.59/21.73 ( real, skv_9, (zero_zero real) ) 21.59/21.73 ( real, skv_12, (zero_zero real) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (div_div int))) (let ((_let_2 (abs_abs int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y) X))) (= (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 X) Y)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 X)) (hAPP int int _let_2 Y))))))) ) 21.59/21.73 ( (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))), (hAPP 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)) ) 21.59/21.73 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((V $$unsorted)) (= (hAPP int real (number_number_of real) V) (hAPP complex real re (hAPP int complex (number_number_of complex) V))) ) 21.59/21.73 ( min ) 21.59/21.73 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.73 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.73 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.73 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$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)))) ) 21.59/21.73 ( rat ) 21.59/21.73 ( int ) 21.59/21.73 ( nat ) 21.59/21.73 ( bool ) 21.59/21.73 ( real ) 21.59/21.73 ( (filter nat) ) 21.59/21.73 ( (fun int bool) ) 21.59/21.73 ( (product_prod int int) ) 21.59/21.73 ( (fun nat bool) ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.59/21.73 ( quickcheck_code_int ) 21.59/21.73 ( code_code_numeral ) 21.59/21.73 ( (product_prod real real) ) 21.59/21.73 ( (filter real) ) 21.59/21.73 ( (product_prod nat nat) ) 21.59/21.73 ( (fun nat rat) ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110945 $$unsorted) (BOUND_VARIABLE_110946 $$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_110945) BOUND_VARIABLE_110946))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_110945) BOUND_VARIABLE_110946)))) ) 21.59/21.73 ( int, (one_one int), t ) 21.59/21.73 ( int, min, pls ) 21.59/21.73 ( int, min, min ) 21.59/21.73 ( int, min, (zero_zero int) ) 21.59/21.73 ( int, (zero_zero int), pls ) 21.59/21.73 ( int, (zero_zero int), (one_one int) ) 21.59/21.73 ( int, (zero_zero int), min ) 21.59/21.73 ( int, (zero_zero int), s ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.73 ( int, (zero_zero int), skv_4 ) 21.59/21.73 ( int, (zero_zero int), skv_5 ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.73 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( nat, (zero_zero nat), n ) 21.59/21.73 ( nat, (zero_zero nat), tn ) 21.59/21.73 ( real, pi, (zero_zero real) ) 21.59/21.73 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( real, (zero_zero real), pi ) 21.59/21.73 ( 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)))) ) 21.59/21.73 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( real, (zero_zero real), skv_2 ) 21.59/21.73 ( real, (zero_zero real), skv_9 ) 21.59/21.73 ( real, (zero_zero real), skv_10 ) 21.59/21.73 ( real, (zero_zero real), skv_11 ) 21.59/21.73 ( real, (zero_zero real), skv_12 ) 21.59/21.73 ( real, (zero_zero real), skv_15 ) 21.59/21.73 ( real, (zero_zero real), skv_18 ) 21.59/21.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.59/21.73 ( 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) ) 21.59/21.73 ( 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 ) 21.59/21.73 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ) 21.59/21.73 (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 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) P_6) A_1))) (not (hBOOL (hAPP int bool zprime P_6)))) ))) ) 21.59/21.73 ( t ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_110992 $$unsorted)) (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_110992))) (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_110992) BOUND_VARIABLE_110992)))))) ) 21.59/21.73 ( int, pls ) 21.59/21.73 ( int, min ) 21.59/21.73 ( int, s ) 21.59/21.73 ( int, s1 ) 21.59/21.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( int, m ) 21.59/21.73 ( 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))) ) 21.59/21.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.73 ( int, t ) 21.59/21.73 ( int, v ) 21.59/21.73 ( int, w ) 21.59/21.73 ( int, y ) 21.59/21.73 ( int, sa ) 21.59/21.73 ( int, x ) 21.59/21.73 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.73 ( int, r ) 21.59/21.73 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.73 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.73 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( int, m1 ) 21.59/21.73 ( int, skv_13 ) 21.59/21.73 ( int, skv_14 ) 21.59/21.73 ( int, skv_19 ) 21.59/21.73 ( int, skv_20 ) 21.59/21.73 ( (fun int int), bit1 ) 21.59/21.73 ( (fun int int), bit0 ) 21.59/21.73 ( (fun int int), succ ) 21.59/21.73 ( (fun int int), pred ) 21.59/21.73 ( (fun int int), (fact_fact int) ) 21.59/21.73 ( (fun int int), zfact ) 21.59/21.73 ( nat, n ) 21.59/21.73 ( nat, tn ) 21.59/21.73 ( bool, fTrue ) 21.59/21.73 ( bool, fFalse ) 21.59/21.73 ( real, pi ) 21.59/21.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( 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))))) ) 21.59/21.73 ( (fun nat real), (real_1 nat) ) 21.59/21.73 ( (fun nat real), cos_coeff ) 21.59/21.73 ( (fun nat real), sin_coeff ) 21.59/21.73 ( (fun real real), sin ) 21.59/21.73 ( (fun real real), cos ) 21.59/21.73 ( (fun real real), sqrt ) 21.59/21.73 ( (fun real real), tan ) 21.59/21.73 ( (fun real real), ln ) 21.59/21.73 ( (fun real real), arctan ) 21.59/21.73 ( (fun real real), arcsin ) 21.59/21.73 ( (fun real real), arccos ) 21.59/21.73 ( (fun nat nat), suc ) 21.59/21.73 ( (fun nat nat), (fact_fact nat) ) 21.59/21.73 ( (fun nat nat), nat_size ) 21.59/21.73 ( (fun nat nat), (size_size nat) ) 21.59/21.73 ( (fun nat nat), fact ) 21.59/21.73 ( (filter nat), sequentially ) 21.59/21.73 ( (fun int (fun int rat)), fract ) 21.59/21.73 ( complex, ii ) 21.59/21.73 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( 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)) ) 21.59/21.73 ( (fun int bool), zOdd ) 21.59/21.73 ( (fun int bool), zprime ) 21.59/21.73 ( (fun int bool), zEven ) 21.59/21.73 ( (fun int bool), nat_neg ) 21.59/21.73 ( (fun int bool), nat_is_nat ) 21.59/21.73 ( (fun int bool), (even_odd_even int) ) 21.59/21.73 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.73 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.73 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.73 ( (fun int (fun int int)), inv ) 21.59/21.73 ( (fun int (fun int int)), multInv ) 21.59/21.73 ( (fun int (fun int int)), legendre ) 21.59/21.73 ( (fun int (fun int int)), standardRes ) 21.59/21.73 ( (fun int (fun int int)), nat_tsub ) 21.59/21.73 ( (fun int (fun int int)), z3div ) 21.59/21.73 ( (fun int (fun int int)), z3mod ) 21.59/21.73 ( (fun int (fun int int)), int_lcm ) 21.59/21.73 ( (fun int (fun int int)), int_gcd ) 21.59/21.73 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.73 ( (fun bool bool), fNot ) 21.59/21.73 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.73 ( (fun bool (fun bool bool)), fconj ) 21.59/21.73 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.73 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.73 ( (fun int (fun int bool)), quadRes ) 21.59/21.73 ( (fun int (fun int bool)), d22set ) 21.59/21.73 ( (fun int (fun int bool)), norRRset ) 21.59/21.73 ( (fun int (fun int bool)), sRStar ) 21.59/21.73 ( (fun int (fun int bool)), sr ) 21.59/21.73 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.73 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.73 ( (fun nat bool), prime ) 21.59/21.73 ( (fun real complex), cis ) 21.59/21.73 ( (fun nat (fun nat bool)), coprime ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.73 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.73 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.73 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.73 ( (fun nat (fun real real)), root ) 21.59/21.73 ( (fun real (fun real real)), log ) 21.59/21.73 ( (fun real (fun real real)), powr ) 21.59/21.73 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.73 ( (fun complex complex), cnj ) 21.59/21.73 ( (fun complex complex), expi ) 21.59/21.73 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.73 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.73 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.73 ( (fun int nat), nat_1 ) 21.59/21.73 ( (fun int nat), phi ) 21.59/21.73 ( (fun complex real), re ) 21.59/21.73 ( (fun complex real), im ) 21.59/21.73 ( (fun complex real), arg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.73 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.73 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.73 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.73 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.73 ( (fun (fun int bool) int), (the int) ) 21.59/21.73 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.73 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.73 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.73 ( (fun real (fun real complex)), rcis ) 21.59/21.73 ( (fun real (fun real complex)), complex_1 ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.73 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.73 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.73 ( (fun real nat), natceiling ) 21.59/21.73 ( (fun real nat), natfloor ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.73 ( (fun int real), (real_1 int) ) 21.59/21.73 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.73 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.73 ( (fun complex nat), (size_size complex) ) 21.59/21.73 ( (fun complex nat), complex_size ) 21.59/21.73 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.73 ( (fun (product_prod int int) rat), frct ) 21.59/21.73 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.73 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.73 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.73 ( (fun rat real), ratreal ) 21.59/21.73 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.73 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.73 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.73 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.73 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.73 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.73 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.73 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.73 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.73 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.73 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.73 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.73 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.73 ( (fun code_code_numeral int), code_int_of ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (real_1 nat))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP nat real _let_0 N)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) X) (hAPP nat real _let_0 (hAPP nat nat suc N))))) (= N (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X)))))) ) 21.59/21.73 ( (zero_zero nat), pi ) 21.59/21.73 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ( (zero_zero nat), skv_10 ) 21.59/21.73 ( (zero_zero nat), skv_11 ) 21.59/21.73 ( (zero_zero nat), skv_15 ) 21.59/21.73 ( (zero_zero nat), skv_18 ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$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)))) ) 21.59/21.73 ( int ) 21.59/21.73 ( nat ) 21.59/21.73 ( bool ) 21.59/21.73 ( real ) 21.59/21.73 ( (filter nat) ) 21.59/21.73 ( (fun int bool) ) 21.59/21.73 ( (product_prod int int) ) 21.59/21.73 ( (fun nat bool) ) 21.59/21.73 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.59/21.73 ( (product_prod real real) ) 21.59/21.73 ( (filter real) ) 21.59/21.73 ( (product_prod nat nat) ) 21.59/21.73 ( (fun nat rat) ) 21.59/21.73 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 N) _let_1) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (one_one nat))) _let_1)))))) ) 21.59/21.73 ( (zero_zero nat) ) 21.59/21.73 ( (one_one nat) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$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)))) ) 21.59/21.73 ( int ) 21.59/21.73 ( nat ) 21.59/21.73 ( real ) 21.59/21.73 ( complex ) 21.59/21.73 ( (product_prod int int) ) 21.59/21.73 ( quickcheck_code_int ) 21.59/21.73 ( code_code_numeral ) 21.59/21.73 ( (product_prod nat nat) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111069 $$unsorted) (BOUND_VARIABLE_111070 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int (number_number_of int) BOUND_VARIABLE_111069)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_111070))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_111069)) BOUND_VARIABLE_111070)))) ) 21.59/21.73 ( int, pls, pls ) 21.59/21.73 ( int, pls, (one_one int) ) 21.59/21.73 ( int, pls, min ) 21.59/21.73 ( int, pls, s ) 21.59/21.73 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.73 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.73 ( int, pls, skv_4 ) 21.59/21.73 ( int, pls, skv_5 ) 21.59/21.73 ( int, (hAPP int int bit1 pls), t ) 21.59/21.73 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), pi ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111119 $$unsorted) (BOUND_VARIABLE_111120 $$unsorted) (BOUND_VARIABLE_111121 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_111121))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_111121))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111119) BOUND_VARIABLE_111120)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_111119)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_111120)))))))) ) 21.59/21.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111144 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_111144)) (field_char_0_Rats X_a))))) ) 21.59/21.73 ( real, (one_one int) ) 21.59/21.73 ( real, (zero_zero int) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_111193 $$unsorted) (BOUND_VARIABLE_111194 $$unsorted) (BOUND_VARIABLE_111195 $$unsorted) (BOUND_VARIABLE_111196 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_111194) BOUND_VARIABLE_111195) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_111196)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_111193))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_1) BOUND_VARIABLE_111196)) S_1))) (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_111196)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_111194 X_1)) BOUND_VARIABLE_111195)) BOUND_VARIABLE_111193))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1)))) ))))) ) 21.59/21.73 ( real, real, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X $$unsorted)) (or (= (zero_zero real) X) (= (one_one real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (inverse_inverse real) X)) X))) ) 21.59/21.73 ( (zero_zero real) ) 21.59/21.73 ) 21.59/21.73 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (minus_minus real))) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_2 X) Y)) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin X)) (hAPP real real cos Y))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos X)) (hAPP real real sin Y))))))) ) 21.59/21.73 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.59/21.73 ) 21.59/21.74 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (real_1 nat))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fact_fact nat))) (let ((_let_4 (inverse_inverse real))) (= (hAPP nat real (hAPP _let_0 _let_0 (diffs real) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) _let_4) (hAPP _let_2 _let_0 (hAPP _let_0 (fun _let_2 _let_0) (combb nat real nat) _let_1) _let_3))) X_1) (hAPP real real _let_4 (hAPP nat real _let_1 (hAPP nat nat _let_3 X_1))))))))) ) 21.59/21.74 ( (zero_zero nat) ) 21.59/21.74 ( (one_one nat) ) 21.59/21.74 ) 21.59/21.74 (instantiation (forall ((N $$unsorted)) (= (ti int N) (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int quickcheck_of_int N))) ) 21.59/21.74 ( pls ) 21.59/21.74 ( (hAPP int int bit1 pls) ) 21.59/21.74 ( (one_one int) ) 21.59/21.74 ( min ) 21.59/21.74 ( s ) 21.59/21.74 ( s1 ) 21.59/21.74 ( m ) 21.59/21.74 ( t ) 21.59/21.74 ( v ) 21.59/21.74 ( w ) 21.59/21.74 ( y ) 21.59/21.74 ( sa ) 21.59/21.74 ( x ) 21.59/21.74 ( r ) 21.59/21.74 ( m1 ) 21.59/21.74 ( skv_14 ) 21.59/21.74 ( skv_20 ) 21.59/21.74 ) 21.59/21.74 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln X)) X))))) ) 21.59/21.74 ( pi ) 21.59/21.74 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.74 ( (one_one real) ) 21.59/21.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.74 ( skv_2 ) 21.59/21.74 ( skv_9 ) 21.59/21.74 ( skv_12 ) 21.59/21.74 ) 21.59/21.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111292 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (ti X_a BOUND_VARIABLE_111292) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_111292) (one_one X_a)))) ) 21.59/21.74 ( int, pls ) 21.59/21.74 ( int, min ) 21.59/21.74 ( int, s ) 21.59/21.74 ( int, s1 ) 21.59/21.74 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.74 ( int, m ) 21.59/21.74 ( 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))) ) 21.59/21.74 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.74 ( int, t ) 21.59/21.74 ( int, v ) 21.59/21.74 ( int, w ) 21.59/21.74 ( int, y ) 21.59/21.74 ( int, sa ) 21.59/21.74 ( int, x ) 21.59/21.74 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.74 ( int, r ) 21.59/21.74 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.77 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.77 ( int, m1 ) 21.59/21.77 ( int, skv_13 ) 21.59/21.77 ( int, skv_14 ) 21.59/21.77 ( int, skv_19 ) 21.59/21.77 ( int, skv_20 ) 21.59/21.77 ( (fun int int), bit1 ) 21.59/21.77 ( (fun int int), bit0 ) 21.59/21.77 ( (fun int int), succ ) 21.59/21.77 ( (fun int int), pred ) 21.59/21.77 ( (fun int int), (fact_fact int) ) 21.59/21.77 ( (fun int int), zfact ) 21.59/21.77 ( nat, n ) 21.59/21.77 ( nat, tn ) 21.59/21.77 ( bool, fTrue ) 21.59/21.77 ( bool, fFalse ) 21.59/21.77 ( real, pi ) 21.59/21.77 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.77 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.77 ( 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))))) ) 21.59/21.77 ( (fun nat real), (real_1 nat) ) 21.59/21.77 ( (fun nat real), cos_coeff ) 21.59/21.77 ( (fun nat real), sin_coeff ) 21.59/21.77 ( (fun real real), sin ) 21.59/21.77 ( (fun real real), cos ) 21.59/21.77 ( (fun real real), sqrt ) 21.59/21.77 ( (fun real real), tan ) 21.59/21.77 ( (fun real real), ln ) 21.59/21.77 ( (fun real real), arctan ) 21.59/21.77 ( (fun real real), arcsin ) 21.59/21.77 ( (fun real real), arccos ) 21.59/21.77 ( (fun nat nat), suc ) 21.59/21.77 ( (fun nat nat), (fact_fact nat) ) 21.59/21.77 ( (fun nat nat), nat_size ) 21.59/21.77 ( (fun nat nat), (size_size nat) ) 21.59/21.77 ( (fun nat nat), fact ) 21.59/21.77 ( (filter nat), sequentially ) 21.59/21.77 ( (fun int (fun int rat)), fract ) 21.59/21.77 ( complex, ii ) 21.59/21.77 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.77 ( 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)) ) 21.59/21.77 ( (fun int bool), zOdd ) 21.59/21.77 ( (fun int bool), zprime ) 21.59/21.77 ( (fun int bool), zEven ) 21.59/21.77 ( (fun int bool), nat_neg ) 21.59/21.77 ( (fun int bool), nat_is_nat ) 21.59/21.77 ( (fun int bool), (even_odd_even int) ) 21.59/21.77 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.77 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.77 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.77 ( (fun int (fun int int)), inv ) 21.59/21.77 ( (fun int (fun int int)), multInv ) 21.59/21.77 ( (fun int (fun int int)), legendre ) 21.59/21.77 ( (fun int (fun int int)), standardRes ) 21.59/21.77 ( (fun int (fun int int)), nat_tsub ) 21.59/21.77 ( (fun int (fun int int)), z3div ) 21.59/21.77 ( (fun int (fun int int)), z3mod ) 21.59/21.77 ( (fun int (fun int int)), int_lcm ) 21.59/21.77 ( (fun int (fun int int)), int_gcd ) 21.59/21.77 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.77 ( (fun bool bool), fNot ) 21.59/21.77 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.77 ( (fun bool (fun bool bool)), fconj ) 21.59/21.77 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.77 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.77 ( (fun int (fun int bool)), quadRes ) 21.59/21.77 ( (fun int (fun int bool)), d22set ) 21.59/21.77 ( (fun int (fun int bool)), norRRset ) 21.59/21.77 ( (fun int (fun int bool)), sRStar ) 21.59/21.77 ( (fun int (fun int bool)), sr ) 21.59/21.77 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.77 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.77 ( (fun nat bool), prime ) 21.59/21.77 ( (fun real complex), cis ) 21.59/21.77 ( (fun nat (fun nat bool)), coprime ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.77 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.77 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.77 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.77 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.77 ( (fun nat (fun real real)), root ) 21.59/21.77 ( (fun real (fun real real)), log ) 21.59/21.77 ( (fun real (fun real real)), powr ) 21.59/21.77 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.77 ( (fun complex complex), cnj ) 21.59/21.77 ( (fun complex complex), expi ) 21.59/21.77 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.77 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.77 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.77 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.77 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.77 ( (fun int nat), nat_1 ) 21.59/21.77 ( (fun int nat), phi ) 21.59/21.77 ( (fun complex real), re ) 21.59/21.77 ( (fun complex real), im ) 21.59/21.77 ( (fun complex real), arg ) 21.59/21.77 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.77 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.77 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.77 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.77 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.77 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.77 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.77 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.77 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.77 ( (fun (fun int bool) int), (the int) ) 21.59/21.77 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.77 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.77 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.77 ( (fun real (fun real complex)), rcis ) 21.59/21.77 ( (fun real (fun real complex)), complex_1 ) 21.59/21.77 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.77 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.77 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.77 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.77 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.77 ( (fun real nat), natceiling ) 21.59/21.77 ( (fun real nat), natfloor ) 21.59/21.77 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.77 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.77 ( (fun int real), (real_1 int) ) 21.59/21.77 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.77 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.77 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.77 ( (fun complex nat), (size_size complex) ) 21.59/21.77 ( (fun complex nat), complex_size ) 21.59/21.77 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.77 ( (fun (product_prod int int) rat), frct ) 21.59/21.77 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.77 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.77 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.77 ( (fun rat real), ratreal ) 21.59/21.77 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.77 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.77 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.77 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.77 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.77 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.77 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.77 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.77 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.77 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.77 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.77 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.77 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.77 ( (fun code_code_numeral int), code_int_of ) 21.59/21.77 ) 21.59/21.77 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP real real (uminus_uminus real) (hAPP int real _let_0 X)) (hAPP int real _let_0 (hAPP int int (uminus_uminus int) X)))) ) 21.59/21.77 ( pls ) 21.59/21.77 ( (one_one int) ) 21.59/21.77 ( min ) 21.59/21.77 ) 21.59/21.77 (instantiation (forall ((A_1 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int rat))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (times_times int))) (or (= _let_2 (ti int B)) (= _let_2 (ti int D_3)) (= (hAPP rat rat (hAPP rat (fun rat rat) (plus_plus rat) (hAPP int rat (hAPP int _let_1 fract A_1) B)) (hAPP int rat (hAPP int _let_1 fract C_1) D_3)) (hAPP int rat (hAPP int _let_1 fract (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_3 A_1) D_3)) (hAPP int int (hAPP int _let_0 _let_3 C_1) B))) (hAPP int int (hAPP int _let_0 _let_3 B) D_3)))))))) ) 21.59/21.77 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.77 ( x, y, v, w ) 21.59/21.77 ( r, sa, v, w ) 21.59/21.77 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v, w ) 21.59/21.77 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.77 ) 21.59/21.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111366 $$unsorted) (BOUND_VARIABLE_111367 $$unsorted) (BOUND_VARIABLE_111368 $$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_111368))) (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_111366) BOUND_VARIABLE_111368)) BOUND_VARIABLE_111367))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_111366) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_111367) BOUND_VARIABLE_111368))))))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.77 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.59/21.77 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.59/21.77 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.77 ) 21.59/21.77 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= (hAPP quickcheck_code_int int quickcheck_int_of Xa) (hAPP quickcheck_code_int int quickcheck_int_of Ya)) (= Xa Ya)) ) 21.59/21.77 ( (zero_zero quickcheck_code_int), (zero_zero quickcheck_code_int) ) 21.59/21.77 ) 21.59/21.78 (instantiation (forall ((U $$unsorted)) (let ((_let_0 (fun int bool))) (= (hAPP int nat nat_1 U) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) (zero_zero int)) U)))) ) 21.59/21.78 ( (one_one int) ) 21.59/21.78 ( (zero_zero int) ) 21.59/21.78 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( t ) 21.59/21.78 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111441 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_111441)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_111441))))) ) 21.59/21.78 ( real, pi ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Xa)) (= Xa (hAPP real real (hAPP real (fun real real) powr Xa) (one_one real)))) ) 21.59/21.78 ( pi ) 21.59/21.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( skv_2 ) 21.59/21.78 ( skv_9 ) 21.59/21.78 ( skv_12 ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111492 $$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_111492)) (field_char_0_Rats X_a))))) ) 21.59/21.78 ( int, (zero_zero nat) ) 21.59/21.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, (one_one nat) ) 21.59/21.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, n ) 21.59/21.78 ( real, (zero_zero nat) ) 21.59/21.78 ( real, (one_one nat) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 Z1) Z2)) W) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 Z1) W)) (hAPP int int (hAPP int _let_0 _let_2 Z2) W)))))) ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), m1 ) 21.59/21.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n), skv_3 ) 21.59/21.78 ( (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) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( (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 ) 21.59/21.78 ( (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), m1 ) 21.59/21.78 ( (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) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.59/21.78 ( (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_21 ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, v ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 21.59/21.78 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, w ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root Na) Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0))))))) ) 21.59/21.78 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$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)))) ) 21.59/21.78 ( rat ) 21.59/21.78 ( int ) 21.59/21.78 ( (fun int int) ) 21.59/21.78 ( nat ) 21.59/21.78 ( bool ) 21.59/21.78 ( real ) 21.59/21.78 ( (fun nat real) ) 21.59/21.78 ( (fun real real) ) 21.59/21.78 ( complex ) 21.59/21.78 ( (fun int bool) ) 21.59/21.78 ( (product_prod int int) ) 21.59/21.78 ( (fun (product_prod int int) int) ) 21.59/21.78 ( (fun int (fun int bool)) ) 21.59/21.78 ( (fun nat bool) ) 21.59/21.78 ( (fun (product_prod int int) bool) ) 21.59/21.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.59/21.78 ( (fun real bool) ) 21.59/21.78 ( quickcheck_code_int ) 21.59/21.78 ( code_code_numeral ) 21.59/21.78 ( (fun int (fun int (fun int bool))) ) 21.59/21.78 ( (fun int real) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (tendsto real real) F) L) (hAPP real _let_0 (at real) C)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) L) (zero_zero real)))) (not (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= C X_1) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) C) X_1))) R_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F X_1)) (zero_zero real)))))) ))) ))))) ) 21.59/21.78 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((Xa $$unsorted)) (= (or (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (not (= Xa (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_1)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) )) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N_1)) (not (= Xa (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_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)))))))))) ))) (= (zero_zero real) (hAPP real real cos Xa))) ) 21.59/21.78 ( pi ) 21.59/21.78 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (zero_zero real) ) 21.59/21.78 ( (hAPP real 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))))) ) 21.59/21.78 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.59/21.78 ( (hAPP real real (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))))) ) 21.59/21.78 ( (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)))) ) 21.59/21.78 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.59/21.78 ( skv_10 ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111630 $$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_111630)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_111630))) ) 21.59/21.78 ( real, (one_one int) ) 21.59/21.78 ( real, (zero_zero int) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111657 $$unsorted) (BOUND_VARIABLE_111658 $$unsorted) (BOUND_VARIABLE_111659 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_111657))) (or (not (cancel_semigroup_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_111658) (hAPP X_a X_a _let_0 BOUND_VARIABLE_111659))) (= (ti X_a BOUND_VARIABLE_111659) (ti X_a BOUND_VARIABLE_111658)))) ) 21.59/21.78 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.78 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.59/21.78 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.78 ( 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) ) 21.59/21.78 ( 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) ) 21.59/21.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 21.59/21.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.78 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, m1 ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.59/21.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111704 $$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 (archimedean_ceiling X_a) BOUND_VARIABLE_111704))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_111704)))) ) 21.59/21.78 ( int, pls ) 21.59/21.78 ( int, (one_one int) ) 21.59/21.78 ( int, min ) 21.59/21.78 ( 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))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( nat, n ) 21.59/21.78 ( nat, tn ) 21.59/21.78 ( real, pi ) 21.59/21.78 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( real, skv_2 ) 21.59/21.78 ( real, skv_9 ) 21.59/21.78 ( real, skv_12 ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real sqrt X))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) _let_0) X) (hAPP real real (inverse_inverse real) _let_0)))) ) 21.59/21.78 ( pi ) 21.59/21.78 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (one_one real) ) 21.59/21.78 ( (zero_zero real) ) 21.59/21.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.78 ( skv_10 ) 21.59/21.78 ( skv_11 ) 21.59/21.78 ( skv_15 ) 21.59/21.78 ( skv_18 ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111819 $$unsorted) (BOUND_VARIABLE_111820 $$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_111819)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_111820) BOUND_VARIABLE_111819)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_111820))))))))) ) 21.59/21.78 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.59/21.78 ( 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))) ) 21.59/21.78 ( int, v, y ) 21.59/21.78 ( int, v, sa ) 21.59/21.78 ( int, v, x ) 21.59/21.78 ( int, v, r ) 21.59/21.78 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.78 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.78 ( int, w, y ) 21.59/21.78 ( int, w, sa ) 21.59/21.78 ( int, w, x ) 21.59/21.78 ( int, w, r ) 21.59/21.78 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.78 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.78 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.78 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.78 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( int, skv_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))) ) 21.59/21.78 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( 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))))) ) 21.59/21.78 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( 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)))) ) 21.59/21.78 ( complex, ii, ii ) 21.59/21.78 ( 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)) ) 21.59/21.78 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111839 $$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_111839) (zero_zero nat)))) ) 21.59/21.78 ( int, s ) 21.59/21.78 ( int, s1 ) 21.59/21.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( int, v ) 21.59/21.78 ( int, w ) 21.59/21.78 ( int, y ) 21.59/21.78 ( int, x ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.59/21.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.59/21.78 ( int, skv_6 ) 21.59/21.78 ( int, skv_7 ) 21.59/21.78 ( int, skv_16 ) 21.59/21.78 ( int, skv_23 ) 21.59/21.78 ( int, skv_24 ) 21.59/21.78 ( real, (hAPP int real (number_number_of real) min) ) 21.59/21.78 ( 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)))) ) 21.59/21.78 ( complex, ii ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) (zero_zero int)))) (= (one_one int) (hAPP int int zfact N))) ) 21.59/21.78 ( (one_one int) ) 21.59/21.78 ( min ) 21.59/21.78 ( (zero_zero int) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int int))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) (zero_zero int))) (= (hAPP int int zfact N) (hAPP int int (hAPP int _let_0 (times_times int) N) (hAPP int int zfact (hAPP int int (hAPP int _let_0 (minus_minus int) N) (one_one int))))))) ) 21.59/21.78 ( (one_one int) ) 21.59/21.78 ( min ) 21.59/21.78 ( (zero_zero int) ) 21.59/21.78 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.78 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( y ) 21.59/21.78 ( sa ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) w)) ) 21.59/21.78 ( x ) 21.59/21.78 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.59/21.78 ( r ) 21.59/21.78 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.78 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.59/21.78 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.59/21.78 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.78 ( (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))) m1))) ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) v)) ) 21.59/21.78 ( skv_13 ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.59/21.78 ( skv_19 ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_4))) (= (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) P_4) zOdd)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_4))))) ) 21.59/21.78 ( (one_one int) ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.78 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= X (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_1) (hAPP nat nat (hAPP nat _let_0 (div_div nat) X) _let_1)))))) ) 21.59/21.78 ( (zero_zero nat) ) 21.59/21.78 ( (one_one nat) ) 21.59/21.78 ) 21.59/21.78 (instantiation (forall ((Z_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Z_1) N))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) N))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z_1) N)))) ) 21.59/21.78 ( (one_one int), t ) 21.59/21.78 ( min, pls ) 21.59/21.78 ( min, min ) 21.59/21.78 ( (zero_zero int), pls ) 21.59/21.78 ( (zero_zero int), (one_one int) ) 21.59/21.78 ( (zero_zero int), min ) 21.59/21.78 ( (zero_zero int), s ) 21.59/21.78 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.78 ( (zero_zero int), skv_4 ) 21.59/21.78 ( (zero_zero int), skv_5 ) 21.59/21.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 21.59/21.78 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.78 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (one_one X_a))))) ) 21.59/21.79 ( rat ) 21.59/21.79 ( int ) 21.59/21.79 ( nat ) 21.59/21.79 ( real ) 21.59/21.79 ( complex ) 21.59/21.79 ( quickcheck_code_int ) 21.59/21.79 ( code_code_numeral ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_111977 $$unsorted) (BOUND_VARIABLE_111978 $$unsorted) (BOUND_VARIABLE_111979 $$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 (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_111977) BOUND_VARIABLE_111978)) BOUND_VARIABLE_111979) (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_111977) BOUND_VARIABLE_111979)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_111978) BOUND_VARIABLE_111979))))))) ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), m1 ) 21.59/21.79 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), skv_3 ) 21.59/21.79 ( 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), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( 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), t ) 21.59/21.79 ( 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), m1 ) 21.59/21.79 ( 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), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.59/21.79 ( 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), skv_21 ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, v ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 21.59/21.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, w ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112025 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archim2085082626_floor X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_112025)) (hAPP int int (uminus_uminus int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_112025)))) ) 21.59/21.79 ( int, pls ) 21.59/21.79 ( int, (one_one int) ) 21.59/21.79 ( int, min ) 21.59/21.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ( real, (one_one real) ) 21.59/21.79 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.59/21.79 ( complex, ii ) 21.59/21.79 ( complex, (one_one complex) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (= (hAPP int int _let_1 N) (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))))) ) 21.59/21.79 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one int) ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, w ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, v ) 21.59/21.79 ( v, x, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.59/21.79 ( v, r, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.79 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (iszero X_a))) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 21.59/21.79 ( rat ) 21.59/21.79 ( int ) 21.59/21.79 ( nat ) 21.59/21.79 ( bool ) 21.59/21.79 ( real ) 21.59/21.79 ( (filter nat) ) 21.59/21.79 ( complex ) 21.59/21.79 ( (fun int bool) ) 21.59/21.79 ( (product_prod int int) ) 21.59/21.79 ( (fun nat bool) ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.59/21.79 ( quickcheck_code_int ) 21.59/21.79 ( code_code_numeral ) 21.59/21.79 ( (product_prod real real) ) 21.59/21.79 ( (filter real) ) 21.59/21.79 ( (product_prod nat nat) ) 21.59/21.79 ( (fun nat rat) ) 21.59/21.79 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod X_b X_a))) (= (ti X_a B) (hAPP _let_0 X_a (product_snd X_b X_a) (hAPP X_a _let_0 (hAPP X_b (fun X_a _let_0) (product_Pair X_b X_a) A_1) B)))) ) 21.59/21.79 ( int, int, (one_one int), (one_one int) ) 21.59/21.79 ( int, int, (zero_zero int), (one_one int) ) 21.59/21.79 ( int, int, s, (one_one int) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N))) (= (zero_zero nat) N)) ) 21.59/21.79 ( (one_one nat), (one_one nat) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112080 $$unsorted) (BOUND_VARIABLE_112081 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (hAPP nat nat suc BOUND_VARIABLE_112081))) (or (not (ring_1 X_a)) (= (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_112080 _let_1)) (hAPP nat X_a (hAPP _let_0 _let_0 (diffs X_a) BOUND_VARIABLE_112080) BOUND_VARIABLE_112081))))) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 21.59/21.79 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) v), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) w), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) x), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) y), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2))))))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v))))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))))), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) skv_6), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) skv_7), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) skv_16), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) skv_23), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( int, (hAPP int (fun nat int) (power_power int) skv_24), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( (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)) ) 21.59/21.79 ( nat, suc, (zero_zero nat) ) 21.59/21.79 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( nat, (fact_fact nat), (zero_zero nat) ) 21.59/21.79 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (zero_zero nat) ) 21.59/21.79 ( nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (zero_zero nat) ) 21.59/21.79 ( bool, (even_odd_even nat), (zero_zero nat) ) 21.59/21.79 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( bool, prime, (zero_zero nat) ) 21.59/21.79 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( real, (real_1 nat), (zero_zero nat) ) 21.59/21.79 ( (fun real real), root, (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ( (fun nat nat), (plus_plus nat), (zero_zero nat) ) 21.59/21.79 ( (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)) ) 21.59/21.79 ( (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) ) 21.59/21.79 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112198 $$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_112198) (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls))) (ti X_a BOUND_VARIABLE_112198))) ) 21.59/21.79 ( int, pls ) 21.59/21.79 ( int, min ) 21.59/21.79 ( int, s ) 21.59/21.79 ( int, s1 ) 21.59/21.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ( int, m ) 21.59/21.79 ( 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))) ) 21.59/21.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( int, t ) 21.59/21.79 ( int, v ) 21.59/21.79 ( int, w ) 21.59/21.79 ( int, y ) 21.59/21.79 ( int, sa ) 21.59/21.79 ( int, x ) 21.59/21.79 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.79 ( int, r ) 21.59/21.79 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.79 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ( int, m1 ) 21.59/21.79 ( int, skv_13 ) 21.59/21.79 ( int, skv_14 ) 21.59/21.79 ( int, skv_19 ) 21.59/21.79 ( int, skv_20 ) 21.59/21.79 ( (fun int int), bit1 ) 21.59/21.79 ( (fun int int), bit0 ) 21.59/21.79 ( (fun int int), succ ) 21.59/21.79 ( (fun int int), pred ) 21.59/21.79 ( (fun int int), (fact_fact int) ) 21.59/21.79 ( (fun int int), zfact ) 21.59/21.79 ( nat, n ) 21.59/21.79 ( nat, tn ) 21.59/21.79 ( bool, fTrue ) 21.59/21.79 ( bool, fFalse ) 21.59/21.79 ( real, pi ) 21.59/21.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ( 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))))) ) 21.59/21.79 ( (fun nat real), (real_1 nat) ) 21.59/21.79 ( (fun nat real), cos_coeff ) 21.59/21.79 ( (fun nat real), sin_coeff ) 21.59/21.79 ( (fun real real), sin ) 21.59/21.79 ( (fun real real), cos ) 21.59/21.79 ( (fun real real), sqrt ) 21.59/21.79 ( (fun real real), tan ) 21.59/21.79 ( (fun real real), ln ) 21.59/21.79 ( (fun real real), arctan ) 21.59/21.79 ( (fun real real), arcsin ) 21.59/21.79 ( (fun real real), arccos ) 21.59/21.79 ( (fun nat nat), suc ) 21.59/21.79 ( (fun nat nat), (fact_fact nat) ) 21.59/21.79 ( (fun nat nat), nat_size ) 21.59/21.79 ( (fun nat nat), (size_size nat) ) 21.59/21.79 ( (fun nat nat), fact ) 21.59/21.79 ( (filter nat), sequentially ) 21.59/21.79 ( (fun int (fun int rat)), fract ) 21.59/21.79 ( complex, ii ) 21.59/21.79 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( 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)) ) 21.59/21.79 ( (fun int bool), zOdd ) 21.59/21.79 ( (fun int bool), zprime ) 21.59/21.79 ( (fun int bool), zEven ) 21.59/21.79 ( (fun int bool), nat_neg ) 21.59/21.79 ( (fun int bool), nat_is_nat ) 21.59/21.79 ( (fun int bool), (even_odd_even int) ) 21.59/21.79 ( (fun int bool), twoSqu1091635170sum2sq ) 21.59/21.79 ( (fun int (fun int int)), legacy_zgcd ) 21.59/21.79 ( (fun int (fun int int)), (gcd_gcd int) ) 21.59/21.79 ( (fun int (fun int int)), inv ) 21.59/21.79 ( (fun int (fun int int)), multInv ) 21.59/21.79 ( (fun int (fun int int)), legendre ) 21.59/21.79 ( (fun int (fun int int)), standardRes ) 21.59/21.79 ( (fun int (fun int int)), nat_tsub ) 21.59/21.79 ( (fun int (fun int int)), z3div ) 21.59/21.79 ( (fun int (fun int int)), z3mod ) 21.59/21.79 ( (fun int (fun int int)), int_lcm ) 21.59/21.79 ( (fun int (fun int int)), int_gcd ) 21.59/21.79 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.59/21.79 ( (fun bool bool), fNot ) 21.59/21.79 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.59/21.79 ( (fun bool (fun bool bool)), fconj ) 21.59/21.79 ( (fun bool (fun bool bool)), fdisj ) 21.59/21.79 ( (fun bool (fun bool bool)), fimplies ) 21.59/21.79 ( (fun int (fun int bool)), quadRes ) 21.59/21.79 ( (fun int (fun int bool)), d22set ) 21.59/21.79 ( (fun int (fun int bool)), norRRset ) 21.59/21.79 ( (fun int (fun int bool)), sRStar ) 21.59/21.79 ( (fun int (fun int bool)), sr ) 21.59/21.79 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.59/21.79 ( (fun nat bool), (even_odd_even nat) ) 21.59/21.79 ( (fun nat bool), prime ) 21.59/21.79 ( (fun real complex), cis ) 21.59/21.79 ( (fun nat (fun nat bool)), coprime ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.59/21.79 ( (fun (product_prod int int) bool), frac_1 ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.59/21.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.59/21.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.59/21.79 ( (fun (fun int bool) bool), nat_nat_set ) 21.59/21.79 ( (fun nat (fun real real)), root ) 21.59/21.79 ( (fun real (fun real real)), log ) 21.59/21.79 ( (fun real (fun real real)), powr ) 21.59/21.79 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.59/21.79 ( (fun complex complex), cnj ) 21.59/21.79 ( (fun complex complex), expi ) 21.59/21.79 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.59/21.79 ( (fun nat (fun nat nat)), nat_gcd ) 21.59/21.79 ( (fun nat (fun nat nat)), nat_lcm ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.59/21.79 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.59/21.79 ( (fun int (fun (fun int bool) bool)), resSet ) 21.59/21.79 ( (fun int nat), nat_1 ) 21.59/21.79 ( (fun int nat), phi ) 21.59/21.79 ( (fun complex real), re ) 21.59/21.79 ( (fun complex real), im ) 21.59/21.79 ( (fun complex real), arg ) 21.59/21.79 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.59/21.79 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.59/21.79 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.59/21.79 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.59/21.79 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.59/21.79 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.59/21.79 ( (fun (product_prod nat nat) bool), pred_nat ) 21.59/21.79 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.59/21.79 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.59/21.79 ( (fun (fun int bool) int), (the int) ) 21.59/21.79 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.59/21.79 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.59/21.79 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.59/21.79 ( (fun real (fun real complex)), rcis ) 21.59/21.79 ( (fun real (fun real complex)), complex_1 ) 21.59/21.79 ( (fun int (fun int (fun int bool))), zcong ) 21.59/21.79 ( (fun int (fun int (fun int bool))), wset ) 21.59/21.79 ( (fun int (fun int (fun int bool))), noXRRset ) 21.59/21.79 ( (fun int (fun int (fun int bool))), bnorRset ) 21.59/21.79 ( (fun int (fun int (fun int bool))), zcongm ) 21.59/21.79 ( (fun real nat), natceiling ) 21.59/21.79 ( (fun real nat), natfloor ) 21.59/21.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.59/21.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.59/21.79 ( (fun int real), (real_1 int) ) 21.59/21.79 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.59/21.79 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.59/21.79 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.59/21.79 ( (fun complex nat), (size_size complex) ) 21.59/21.79 ( (fun complex nat), complex_size ) 21.59/21.79 ( (fun (fun nat rat) bool), vanishes ) 21.59/21.79 ( (fun (product_prod int int) rat), frct ) 21.59/21.79 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.59/21.79 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.59/21.79 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.59/21.79 ( (fun rat real), ratreal ) 21.59/21.79 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.59/21.79 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.59/21.79 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.59/21.79 ( (fun rat (product_prod int int)), quotient_of ) 21.59/21.79 ( (fun int (fun nat nat)), nat_aux ) 21.59/21.79 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.59/21.79 ( (fun int (list int)), quickc666637781d_zero ) 21.59/21.79 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.59/21.79 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.59/21.79 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.59/21.79 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.59/21.79 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.59/21.79 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.59/21.79 ( (fun code_code_numeral int), code_int_of ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112209 $$unsorted) (BOUND_VARIABLE_112210 $$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_112209)) (hAPP X_a real _let_0 BOUND_VARIABLE_112210)))) (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_112209) BOUND_VARIABLE_112210)))))) ) 21.59/21.79 ( 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)))), (hAPP int int (number_number_of int) min) ) 21.59/21.79 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.79 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.79 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.79 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.59/21.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.59/21.79 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.59/21.79 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.79 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.59/21.79 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.59/21.79 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (minus_minus real))) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 _let_2 X) Y)) (hAPP real real (hAPP real _let_0 _let_2 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos Y)) (hAPP real real sin X))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin Y)) (hAPP real real cos X))))))) ) 21.59/21.79 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112242 $$unsorted) (BOUND_VARIABLE_112243 $$unsorted) (BOUND_VARIABLE_112244 $$unsorted) (BOUND_VARIABLE_112245 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_112244) BOUND_VARIABLE_112245))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_112242) BOUND_VARIABLE_112243))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_112244))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_112242))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_112244) BOUND_VARIABLE_112242)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_112245) BOUND_VARIABLE_112243))))))))) ) 21.59/21.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((Z $$unsorted) (Wa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Wa))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Wa) Z)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 Wa)) (hAPP int nat nat_1 Z)))))) ) 21.59/21.79 ( pls, (zero_zero int) ) 21.59/21.79 ( (one_one int), (zero_zero int) ) 21.59/21.79 ( min, min ) 21.59/21.79 ( min, (zero_zero int) ) 21.59/21.79 ( (zero_zero int), min ) 21.59/21.79 ( (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))), (zero_zero int) ) 21.59/21.79 ( (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))), s ) 21.59/21.79 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( (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))), t ) 21.59/21.79 ( (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))), skv_4 ) 21.59/21.79 ( (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))), skv_5 ) 21.59/21.79 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.59/21.79 ( t, (one_one int) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((Z $$unsorted) (Wa $$unsorted)) (let ((_let_0 (fun int bool))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Z) Wa)) (and (not (= (ti int Wa) (ti int Z))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) Z) Wa))))) ) 21.59/21.79 ( (one_one int), t ) 21.59/21.79 ( min, pls ) 21.59/21.79 ( min, min ) 21.59/21.79 ( min, (zero_zero int) ) 21.59/21.79 ( (zero_zero int), pls ) 21.59/21.79 ( (zero_zero int), (one_one int) ) 21.59/21.79 ( (zero_zero int), min ) 21.59/21.79 ( (zero_zero int), s ) 21.59/21.79 ( (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))) ) 21.59/21.79 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.79 ( (zero_zero int), skv_4 ) 21.59/21.79 ( (zero_zero int), skv_5 ) 21.59/21.79 ( 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))) ) 21.59/21.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.79 ( 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))) ) 21.59/21.79 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( 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))) ) 21.59/21.79 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.79 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112288 $$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_112288) (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_112288)) sequentially)))))))) ) 21.59/21.79 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C $$unsorted)) (let ((_let_0 (hAPP real (fun real real) (times_times real) C))) (or (= (zero_zero real) C) (= (= A_3 B_2) (= (hAPP real real _let_0 A_3) (hAPP real real _let_0 B_2))))) ) 21.59/21.79 ( pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( 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))))) ) 21.59/21.79 ( pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.79 ( (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)))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112327 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_112327))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_112327)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_112327))))) ) 21.59/21.79 ( int, pls ) 21.59/21.79 ( int, (hAPP int int bit1 pls) ) 21.59/21.79 ( int, min ) 21.59/21.79 ( nat, pls ) 21.59/21.79 ( nat, (hAPP int int bit1 pls) ) 21.59/21.79 ( nat, min ) 21.59/21.79 ( quickcheck_code_int, pls ) 21.59/21.79 ( quickcheck_code_int, min ) 21.59/21.79 ( code_code_numeral, pls ) 21.59/21.79 ( code_code_numeral, min ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_112365 $$unsorted) (BOUND_VARIABLE_112366 $$unsorted) (BOUND_VARIABLE_112367 $$unsorted) (BOUND_VARIABLE_112368 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_112366) (hAPP X_b X_a BOUND_VARIABLE_112367 BOUND_VARIABLE_112368)))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_112368) BOUND_VARIABLE_112365))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less X_b) X_1) Y_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (hAPP X_b X_a BOUND_VARIABLE_112367 X_1)) (hAPP X_b X_a BOUND_VARIABLE_112367 Y_1)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_112366) (hAPP X_b X_a BOUND_VARIABLE_112367 BOUND_VARIABLE_112365))))) ) 21.59/21.79 ( int, int, min, (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)))) (hAPP int int (abs_abs int) w)), (uminus_uminus int), min ) 21.59/21.79 ( int, int, (zero_zero int), min, (number_number_of int), min ) 21.59/21.79 ( int, int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), bit1, pls ) 21.59/21.79 ( int, int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.79 ( int, int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)), pred, pls ) 21.59/21.79 ( 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) ) 21.59/21.79 ( int, nat, n, (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)))) (hAPP int int (abs_abs int) v)), (semiring_1_of_nat int), (zero_zero nat) ) 21.59/21.79 ( real, 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)))), sin, (zero_zero real) ) 21.59/21.79 ( 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))), (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.59/21.79 ( real, real, (zero_zero real), skv_10, tan, pi ) 21.59/21.79 ( 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)))), arctan, (one_one real) ) 21.59/21.79 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (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)))), pi ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (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)) (hAPP rat _let_0 quotient_of (hAPP rat rat (sgn_sgn rat) P_5)))) ) 21.59/21.79 ( (zero_zero rat) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_112483 $$unsorted) (BOUND_VARIABLE_112484 $$unsorted) (BOUND_VARIABLE_112485 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_a real))) (let ((_let_4 (norm_norm X_b))) (let ((_let_5 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_112485))) (or (not (topological_space X_a)) (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_112483) BOUND_VARIABLE_112484) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (tendsto X_a real) (hAPP _let_2 _let_3 (hAPP (fun X_b real) (fun _let_2 _let_3) (combb X_b real X_a) _let_4) BOUND_VARIABLE_112483)) (hAPP X_b real _let_4 BOUND_VARIABLE_112484)) _let_5))))))))) ) 21.59/21.79 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.79 ) 21.59/21.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112515 $$unsorted) (BOUND_VARIABLE_112516 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (linordered_idom X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_112516) (hAPP X_a X_a _let_0 BOUND_VARIABLE_112515))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_112515) BOUND_VARIABLE_112516)))) ) 21.59/21.79 ( 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))), (hAPP 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)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((Ma $$unsorted) (Wa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Wa))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 Wa)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Wa) (hAPP nat int (semiring_1_of_nat int) Ma)))))) ) 21.59/21.80 ( (zero_zero nat), min ) 21.59/21.80 ( (zero_zero nat), (zero_zero int) ) 21.59/21.80 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 21.59/21.80 ( (one_one nat), (zero_zero int) ) 21.59/21.80 ( n, (zero_zero int) ) 21.59/21.80 ( tn, (zero_zero int) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) Y) X))) (= (hAPP int int (abs_abs int) Y) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) Y))) ) 21.59/21.80 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 21.59/21.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112635 $$unsorted) (BOUND_VARIABLE_112636 $$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_112636))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_112635)))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112636) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112635) _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_112636) BOUND_VARIABLE_112635)))))))) ) 21.59/21.80 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.59/21.80 ( 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))) ) 21.59/21.80 ( int, v, y ) 21.59/21.80 ( int, v, sa ) 21.59/21.80 ( int, v, x ) 21.59/21.80 ( int, v, r ) 21.59/21.80 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.80 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.80 ( int, w, y ) 21.59/21.80 ( int, w, sa ) 21.59/21.80 ( int, w, x ) 21.59/21.80 ( int, w, r ) 21.59/21.80 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.80 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.80 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.80 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, skv_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))) ) 21.59/21.80 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( 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))))) ) 21.59/21.80 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( 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)))) ) 21.59/21.80 ( complex, ii, ii ) 21.59/21.80 ( 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)) ) 21.59/21.80 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112674 $$unsorted) (BOUND_VARIABLE_112675 $$unsorted) (BOUND_VARIABLE_112676 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_112674))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112675) BOUND_VARIABLE_112676))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112674) (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_112676)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_112675))))))) ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112716 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linord1117847801e_zero X_a)) (not (number_ring X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_112716) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_112716))))) ) 21.59/21.80 ( real, pi ) 21.59/21.80 ( real, (one_one real) ) 21.59/21.80 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.80 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112837 $$unsorted) (BOUND_VARIABLE_112838 $$unsorted) (BOUND_VARIABLE_112839 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_112837))) (or (not (ordere216010020id_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_112839))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_112838))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_112838) BOUND_VARIABLE_112839))))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112864 $$unsorted) (BOUND_VARIABLE_112865 $$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_112864) BOUND_VARIABLE_112865)) BOUND_VARIABLE_112865) (ti X_a BOUND_VARIABLE_112864)))) ) 21.59/21.80 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.59/21.80 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.59/21.80 ( 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) ) 21.59/21.80 ( 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) ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.59/21.80 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( nat, (one_one nat), (one_one nat) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112921 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (number_number_of int) BOUND_VARIABLE_112921) (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_112921)))) ) 21.59/21.80 ( int, pls ) 21.59/21.80 ( int, (hAPP int int bit1 pls) ) 21.59/21.80 ( int, min ) 21.59/21.80 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.80 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.80 ( nat, pls ) 21.59/21.80 ( nat, (hAPP int int bit1 pls) ) 21.59/21.80 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.80 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.80 ( real, min ) 21.59/21.80 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.80 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.59/21.80 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.80 ( 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)))))))) ) 21.59/21.80 ( complex, min ) 21.59/21.80 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.59/21.80 ( quickcheck_code_int, pls ) 21.59/21.80 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.59/21.80 ( quickcheck_code_int, (one_one int) ) 21.59/21.80 ( code_code_numeral, pls ) 21.59/21.80 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112956 $$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_112956) BOUND_VARIABLE_112956) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_112956) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.80 ( int, s ) 21.59/21.80 ( int, s1 ) 21.59/21.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( 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))) ) 21.59/21.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, v ) 21.59/21.80 ( int, w ) 21.59/21.80 ( int, y ) 21.59/21.80 ( int, sa ) 21.59/21.80 ( int, x ) 21.59/21.80 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.59/21.80 ( int, r ) 21.59/21.80 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.59/21.80 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.59/21.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.59/21.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.59/21.80 ( int, skv_6 ) 21.59/21.80 ( int, skv_7 ) 21.59/21.80 ( int, skv_13 ) 21.59/21.80 ( int, skv_16 ) 21.59/21.80 ( int, skv_19 ) 21.59/21.80 ( int, skv_23 ) 21.59/21.80 ( int, skv_24 ) 21.59/21.80 ( real, (hAPP int real (number_number_of real) min) ) 21.59/21.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.80 ( 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)))) ) 21.59/21.80 ( 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))))) ) 21.59/21.80 ( complex, ii ) 21.59/21.80 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ( 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)) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (A_2 $$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_2)) (ti _let_0 A_2)))) ) 21.59/21.80 ( int, zOdd ) 21.59/21.80 ( int, zprime ) 21.59/21.80 ( int, zEven ) 21.59/21.80 ( int, nat_neg ) 21.59/21.80 ( int, nat_is_nat ) 21.59/21.80 ( int, (even_odd_even int) ) 21.59/21.80 ( int, twoSqu1091635170sum2sq ) 21.59/21.80 ( nat, (even_odd_even nat) ) 21.59/21.80 ( nat, prime ) 21.59/21.80 ( bool, fNot ) 21.59/21.80 ( (fun int bool), nat_nat_set ) 21.59/21.80 ( (product_prod int int), frac_1 ) 21.59/21.80 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 21.59/21.80 ( (product_prod nat nat), pred_nat ) 21.59/21.80 ( (fun nat rat), vanishes ) 21.59/21.80 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 21.59/21.80 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_112976 $$unsorted) (BOUND_VARIABLE_112977 $$unsorted) (BOUND_VARIABLE_112978 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (linordered_idom X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_112978)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_112976) BOUND_VARIABLE_112977))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_112976) BOUND_VARIABLE_112978)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_112977) BOUND_VARIABLE_112978)))))))) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.80 ) 21.59/21.80 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_113022 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_3))) (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) (ti X_a A_3)) (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_113022))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Y_1))) (= (ti X_a Y_1) (ti X_a BOUND_VARIABLE_113022))) ))) ) 21.59/21.80 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 21.59/21.80 ( int, pls, (hAPP int (fun int bool) (ord_less int) pls), pls ) 21.59/21.80 ( int, pls, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 21.59/21.80 ( int, (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 21.59/21.80 ( int, (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 21.59/21.80 ( int, (one_one int), nat_neg, (one_one int) ) 21.59/21.80 ( int, (one_one int), nat_is_nat, (one_one int) ) 21.59/21.80 ( int, (one_one int), (even_odd_even int), (one_one int) ) 21.59/21.80 ( int, min, (hAPP int (fun int bool) (ord_less int) min), min ) 21.59/21.80 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 21.59/21.80 ( int, min, (hAPP int (fun int bool) (ord_less int) pls), min ) 21.59/21.80 ( int, min, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 21.59/21.80 ( int, (zero_zero int), (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 21.59/21.80 ( int, (zero_zero int), nat_neg, (zero_zero int) ) 21.59/21.80 ( int, (zero_zero int), nat_is_nat, (zero_zero int) ) 21.59/21.80 ( int, (zero_zero int), (even_odd_even int), (zero_zero int) ) 21.59/21.80 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), 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))) ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (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))) ) 21.59/21.80 ( 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))), (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))), (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.59/21.80 ( 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))) ) 21.59/21.80 ( 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))) ) 21.59/21.80 ( 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))) ) 21.59/21.80 ( int, (hAPP int int (number_number_of int) min), (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) ) 21.59/21.80 ( int, (hAPP int int (number_number_of int) min), nat_neg, (hAPP int int (number_number_of int) min) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.59/21.81 ( int, t, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 21.59/21.81 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 21.59/21.81 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 21.59/21.81 ( int, (hAPP 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)), (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) (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)) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 21.59/21.81 ( int, skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 21.59/21.81 ( int, skv_5, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 21.59/21.81 ( nat, (zero_zero nat), (even_odd_even nat), (zero_zero nat) ) 21.59/21.81 ( nat, (zero_zero nat), prime, (zero_zero nat) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( nat, (one_one nat), (even_odd_even nat), (one_one nat) ) 21.59/21.81 ( nat, (hAPP nat nat suc (zero_zero nat)), prime, (hAPP nat nat suc (zero_zero nat)) ) 21.59/21.81 ( nat, n, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.59/21.81 ( nat, tn, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.59/21.81 ( real, pi, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 21.59/21.81 ( real, pi, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 21.59/21.81 ( 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 ) 21.59/21.81 ( 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 ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( 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))) ) 21.59/21.81 ( 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_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.81 ( real, (hAPP real real (hAPP 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)))) ) 21.59/21.81 ( real, (hAPP real real (hAPP 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)))) ) 21.59/21.81 ( real, (one_one real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 21.59/21.81 ( 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) ) 21.59/21.81 ( real, (zero_zero real), (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 21.59/21.81 ( 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) ) 21.59/21.81 ( 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) ) 21.59/21.81 ( 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)))) ) 21.59/21.81 ( 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)))) ) 21.59/21.81 ( 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)))) ) 21.59/21.81 ( 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)))) ) 21.59/21.81 ( real, skv_2, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 21.59/21.81 ( real, skv_9, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 21.59/21.81 ( real, skv_10, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 21.59/21.81 ( real, skv_11, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 21.59/21.81 ( real, skv_12, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 21.59/21.81 ( real, skv_15, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 21.59/21.81 ( real, skv_18, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 21.59/21.81 ( (filter nat), sequentially, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 21.59/21.81 ( (filter nat), sequentially, (trivial_limit nat), sequentially ) 21.59/21.81 ( (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)) ) 21.59/21.81 ( (fun int bool), zEven, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 21.59/21.81 ( (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) ) 21.59/21.81 ( (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)) ) 21.59/21.81 ( (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))))) ) 21.59/21.81 ) 21.59/21.81 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP nat real (real_1 nat) N)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP real nat natfloor X)) N)))) ) 21.59/21.81 ( (zero_zero nat), pi ) 21.59/21.81 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.81 ( (zero_zero nat), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.59/21.81 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 21.59/21.81 ( n, (zero_zero real) ) 21.59/21.81 ( tn, (zero_zero real) ) 21.59/21.81 ) 21.59/21.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113049 $$unsorted) (BOUND_VARIABLE_113050 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_113049) (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_113049) BOUND_VARIABLE_113050)) BOUND_VARIABLE_113050)))) ) 21.59/21.81 ( 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) ) 21.59/21.81 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.81 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.81 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.81 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.59/21.81 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.59/21.81 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.59/21.81 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.59/21.81 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.81 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.59/21.81 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.59/21.81 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.59/21.81 ) 21.59/21.81 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= X (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.59/21.81 ( pi ) 21.59/21.81 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.59/21.81 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.81 ( (one_one real) ) 21.59/21.81 ( (zero_zero real) ) 21.59/21.81 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.59/21.81 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.59/21.81 ( skv_10 ) 21.59/21.81 ( skv_11 ) 21.59/21.81 ( skv_15 ) 21.59/21.81 ( skv_18 ) 21.59/21.81 ) 21.59/21.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113078 $$unsorted) (BOUND_VARIABLE_113079 $$unsorted) (BOUND_VARIABLE_113080 $$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_113078))) (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_113079)) BOUND_VARIABLE_113080) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113079) BOUND_VARIABLE_113080))))))) ) 21.59/21.81 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, v ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, w ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, v ) 21.59/21.81 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, w ) 21.59/21.81 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.59/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), m1 ) 21.70/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))) ) 21.70/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.70/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.70/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.70/21.81 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.70/21.81 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.70/21.81 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.70/21.81 ( 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 ) 21.70/21.81 ) 21.70/21.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113102 $$unsorted) (BOUND_VARIABLE_113103 $$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_113103) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (hBOOL (hAPP X_a bool BOUND_VARIABLE_113102 (hAPP int X_a (ring_1_of_int X_a) Z_2))) )) (hBOOL (hAPP X_a bool BOUND_VARIABLE_113102 BOUND_VARIABLE_113103)))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 21.70/21.81 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.70/21.81 ( 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) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) min), min ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 21.70/21.81 ( int, nat_neg, (one_one int) ) 21.70/21.81 ( int, nat_neg, (zero_zero int) ) 21.70/21.81 ( int, nat_neg, (hAPP int int (number_number_of int) min) ) 21.70/21.81 ( int, nat_is_nat, (one_one int) ) 21.70/21.81 ( int, nat_is_nat, (zero_zero int) ) 21.70/21.81 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.70/21.81 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 21.70/21.81 ( int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 21.70/21.81 ( int, (even_odd_even int), (one_one int) ) 21.70/21.81 ( int, (even_odd_even int), (zero_zero int) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) pls), min ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 21.70/21.81 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( 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) (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)) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.70/21.81 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.70/21.81 ( nat, (even_odd_even nat), (zero_zero nat) ) 21.70/21.81 ( nat, (even_odd_even nat), (one_one nat) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.70/21.81 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.70/21.81 ( nat, prime, (zero_zero nat) ) 21.70/21.81 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.70/21.81 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 21.70/21.81 ( 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)))) ) 21.70/21.81 ( 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)))) ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 21.70/21.81 ( 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)))) ) 21.70/21.81 ( 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)))) ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 21.70/21.81 ( 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)))) ) 21.70/21.81 ( 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))) ) 21.70/21.81 ( 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) ) 21.70/21.81 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 21.70/21.81 ( 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)))) ) 21.71/21.81 ( 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))) ) 21.71/21.81 ( 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) ) 21.71/21.81 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 21.71/21.81 ( 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 ) 21.71/21.81 ( 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 ) 21.71/21.81 ( 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) ) 21.71/21.81 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.81 ( (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 21.71/21.81 ( (filter nat), (trivial_limit nat), sequentially ) 21.71/21.81 ( (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)) ) 21.71/21.81 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 21.71/21.81 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.71/21.81 ( (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) ) 21.71/21.81 ( (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))))) ) 21.71/21.81 ) 21.71/21.81 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113127 $$unsorted) (BOUND_VARIABLE_113128 $$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_113127) BOUND_VARIABLE_113128)) _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_113127) _let_1)) (hAPP nat X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_113128) _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_113127)) BOUND_VARIABLE_113128))))))))))) ) 21.71/21.81 ( 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) ) 21.71/21.81 ( int, v, w ) 21.71/21.81 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.81 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.81 ( int, x, y ) 21.71/21.81 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.81 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.81 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.71/21.82 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.82 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.82 ( int, skv_6, skv_7 ) 21.71/21.82 ( int, skv_23, skv_24 ) 21.71/21.82 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.71/21.82 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.71/21.82 ( complex, (hAPP real complex (of_real complex) pi), ii ) 21.71/21.82 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= _let_0 (ti (fun real X_a) _let_0)))) ) 21.71/21.82 ( nat ) 21.71/21.82 ( bool ) 21.71/21.82 ( real ) 21.71/21.82 ( (fun nat real) ) 21.71/21.82 ( (fun real real) ) 21.71/21.82 ( (fun (filter nat) bool) ) 21.71/21.82 ( complex ) 21.71/21.82 ( (fun int bool) ) 21.71/21.82 ( (fun bool bool) ) 21.71/21.82 ( (fun int (fun int bool)) ) 21.71/21.82 ( (fun real complex) ) 21.71/21.82 ( (fun real bool) ) 21.71/21.82 ( (fun nat (product_prod real real)) ) 21.71/21.82 ( (fun real (fun nat (product_prod real real))) ) 21.71/21.82 ( (fun (filter real) bool) ) 21.71/21.82 ( (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 21.71/21.82 ( (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 21.71/21.82 ( (fun int (fun int (fun bool bool))) ) 21.71/21.82 ( (fun int (fun nat bool)) ) 21.71/21.82 ( (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 21.71/21.82 ( (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 21.71/21.82 ( (fun int (fun nat (fun bool bool))) ) 21.71/21.82 ( (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 21.71/21.82 ( (fun (fun nat real) (fun nat bool)) ) 21.71/21.82 ( (fun (fun int real) (fun int bool)) ) 21.71/21.82 ( (fun (fun int (fun int real)) (fun int (fun int bool))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113240 $$unsorted)) (or (not (linordered_idom X_a)) (= (= (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a)) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_113240)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_113240) (zero_zero X_a))))) ) 21.71/21.82 ( rat, (zero_zero rat) ) 21.71/21.82 ( int, (one_one int) ) 21.71/21.82 ( int, min ) 21.71/21.82 ( int, (zero_zero int) ) 21.71/21.82 ( int, s ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.82 ( int, t ) 21.71/21.82 ( int, m1 ) 21.71/21.82 ( int, skv_4 ) 21.71/21.82 ( int, skv_5 ) 21.71/21.82 ( nat, (zero_zero nat) ) 21.71/21.82 ( real, pi ) 21.71/21.82 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( real, (one_one real) ) 21.71/21.82 ( real, (zero_zero real) ) 21.71/21.82 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.71/21.82 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113258 $$unsorted) (BOUND_VARIABLE_113259 $$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_113259))) (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_113259)) BOUND_VARIABLE_113258)))))))) ) 21.71/21.82 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_113285 $$unsorted) (BOUND_VARIABLE_113286 $$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_113285 BOUND_VARIABLE_113286)) (hAPP X_b X_a (hAPP _let_0 _let_0 (uminus_uminus _let_0) BOUND_VARIABLE_113285) BOUND_VARIABLE_113286)))) ) 21.71/21.82 ( int, int, bit1, min ) 21.71/21.82 ( int, int, bit0, pls ) 21.71/21.82 ( int, int, (fact_fact int), (zero_zero int) ) 21.71/21.82 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.71/21.82 ( real, complex, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.71/21.82 ( complex, real, im, ii ) 21.71/21.82 ( 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))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113306 $$unsorted)) (let ((_let_0 (one_one X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_113306))) (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_113306) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (= (hAPP X_a X_a (uminus_uminus X_a) _let_0) _let_1) (= _let_0 _let_1)))))) ) 21.71/21.82 ( int, pls ) 21.71/21.82 ( int, min ) 21.71/21.82 ( int, s ) 21.71/21.82 ( int, s1 ) 21.71/21.82 ( int, m ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.82 ( int, t ) 21.71/21.82 ( int, v ) 21.71/21.82 ( int, w ) 21.71/21.82 ( int, y ) 21.71/21.82 ( int, sa ) 21.71/21.82 ( int, x ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.71/21.82 ( int, r ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.71/21.82 ( int, m1 ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.82 ( int, skv_6 ) 21.71/21.82 ( int, skv_7 ) 21.71/21.82 ( int, skv_14 ) 21.71/21.82 ( int, skv_16 ) 21.71/21.82 ( int, skv_20 ) 21.71/21.82 ( int, skv_23 ) 21.71/21.82 ( int, skv_24 ) 21.71/21.82 ( (fun int int), bit1 ) 21.71/21.82 ( (fun int int), bit0 ) 21.71/21.82 ( (fun int int), succ ) 21.71/21.82 ( (fun int int), pred ) 21.71/21.82 ( (fun int int), (fact_fact int) ) 21.71/21.82 ( (fun int int), zfact ) 21.71/21.82 ( nat, n ) 21.71/21.82 ( nat, tn ) 21.71/21.82 ( bool, fTrue ) 21.71/21.82 ( bool, fFalse ) 21.71/21.82 ( real, (hAPP int real (number_number_of real) min) ) 21.71/21.82 ( real, pi ) 21.71/21.82 ( 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)))) ) 21.71/21.82 ( (fun nat real), (real_1 nat) ) 21.71/21.82 ( (fun nat real), cos_coeff ) 21.71/21.82 ( (fun nat real), sin_coeff ) 21.71/21.82 ( (fun real real), sin ) 21.71/21.82 ( (fun real real), cos ) 21.71/21.82 ( (fun real real), sqrt ) 21.71/21.82 ( (fun real real), tan ) 21.71/21.82 ( (fun real real), ln ) 21.71/21.82 ( (fun real real), arctan ) 21.71/21.82 ( (fun real real), arcsin ) 21.71/21.82 ( (fun real real), arccos ) 21.71/21.82 ( (fun nat nat), suc ) 21.71/21.82 ( (fun nat nat), (fact_fact nat) ) 21.71/21.82 ( (fun nat nat), nat_size ) 21.71/21.82 ( (fun nat nat), (size_size nat) ) 21.71/21.82 ( (fun nat nat), fact ) 21.71/21.82 ( (filter nat), sequentially ) 21.71/21.82 ( (fun int (fun int rat)), fract ) 21.71/21.82 ( complex, ii ) 21.71/21.82 ( (fun int bool), zOdd ) 21.71/21.82 ( (fun int bool), zprime ) 21.71/21.82 ( (fun int bool), zEven ) 21.71/21.82 ( (fun int bool), nat_neg ) 21.71/21.82 ( (fun int bool), nat_is_nat ) 21.71/21.82 ( (fun int bool), (even_odd_even int) ) 21.71/21.82 ( (fun int bool), twoSqu1091635170sum2sq ) 21.71/21.82 ( (fun int (fun int int)), legacy_zgcd ) 21.71/21.82 ( (fun int (fun int int)), (gcd_gcd int) ) 21.71/21.82 ( (fun int (fun int int)), inv ) 21.71/21.82 ( (fun int (fun int int)), multInv ) 21.71/21.82 ( (fun int (fun int int)), legendre ) 21.71/21.82 ( (fun int (fun int int)), standardRes ) 21.71/21.82 ( (fun int (fun int int)), nat_tsub ) 21.71/21.82 ( (fun int (fun int int)), z3div ) 21.71/21.82 ( (fun int (fun int int)), z3mod ) 21.71/21.82 ( (fun int (fun int int)), int_lcm ) 21.71/21.82 ( (fun int (fun int int)), int_gcd ) 21.71/21.82 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.71/21.82 ( (fun bool bool), fNot ) 21.71/21.82 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.71/21.82 ( (fun bool (fun bool bool)), fconj ) 21.71/21.82 ( (fun bool (fun bool bool)), fdisj ) 21.71/21.82 ( (fun bool (fun bool bool)), fimplies ) 21.71/21.82 ( (fun int (fun int bool)), quadRes ) 21.71/21.82 ( (fun int (fun int bool)), d22set ) 21.71/21.82 ( (fun int (fun int bool)), norRRset ) 21.71/21.82 ( (fun int (fun int bool)), sRStar ) 21.71/21.82 ( (fun int (fun int bool)), sr ) 21.71/21.82 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.71/21.82 ( (fun nat bool), (even_odd_even nat) ) 21.71/21.82 ( (fun nat bool), prime ) 21.71/21.82 ( (fun real complex), cis ) 21.71/21.82 ( (fun nat (fun nat bool)), coprime ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.71/21.82 ( (fun (product_prod int int) bool), frac_1 ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.71/21.82 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.71/21.82 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.71/21.82 ( (fun (fun int bool) bool), nat_nat_set ) 21.71/21.82 ( (fun nat (fun real real)), root ) 21.71/21.82 ( (fun real (fun real real)), log ) 21.71/21.82 ( (fun real (fun real real)), powr ) 21.71/21.82 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.71/21.82 ( (fun complex complex), cnj ) 21.71/21.82 ( (fun complex complex), expi ) 21.71/21.82 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.71/21.82 ( (fun nat (fun nat nat)), nat_gcd ) 21.71/21.82 ( (fun nat (fun nat nat)), nat_lcm ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.71/21.82 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.71/21.82 ( (fun int (fun (fun int bool) bool)), resSet ) 21.71/21.82 ( (fun int nat), nat_1 ) 21.71/21.82 ( (fun int nat), phi ) 21.71/21.82 ( (fun complex real), re ) 21.71/21.82 ( (fun complex real), im ) 21.71/21.82 ( (fun complex real), arg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.71/21.82 ( (fun (product_prod nat nat) bool), pred_nat ) 21.71/21.82 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.71/21.82 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.71/21.82 ( (fun (fun int bool) int), (the int) ) 21.71/21.82 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.71/21.82 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.71/21.82 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.71/21.82 ( (fun real (fun real complex)), rcis ) 21.71/21.82 ( (fun real (fun real complex)), complex_1 ) 21.71/21.82 ( (fun int (fun int (fun int bool))), zcong ) 21.71/21.82 ( (fun int (fun int (fun int bool))), wset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), noXRRset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), bnorRset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), zcongm ) 21.71/21.82 ( (fun real nat), natceiling ) 21.71/21.82 ( (fun real nat), natfloor ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.71/21.82 ( (fun int real), (real_1 int) ) 21.71/21.82 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.71/21.82 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.71/21.82 ( (fun complex nat), (size_size complex) ) 21.71/21.82 ( (fun complex nat), complex_size ) 21.71/21.82 ( (fun (fun nat rat) bool), vanishes ) 21.71/21.82 ( (fun (product_prod int int) rat), frct ) 21.71/21.82 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.71/21.82 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.71/21.82 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.71/21.82 ( (fun rat real), ratreal ) 21.71/21.82 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.71/21.82 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.71/21.82 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.71/21.82 ( (fun rat (product_prod int int)), quotient_of ) 21.71/21.82 ( (fun int (fun nat nat)), nat_aux ) 21.71/21.82 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.71/21.82 ( (fun int (list int)), quickc666637781d_zero ) 21.71/21.82 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.71/21.82 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.71/21.82 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.71/21.82 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.71/21.82 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.71/21.82 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.71/21.82 ( (fun code_code_numeral int), code_int_of ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) min)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (= (hAPP real real cos (hAPP real real arcsin X)) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (minus_minus real) _let_0) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 21.71/21.82 ( (hAPP int real (number_number_of real) min) ) 21.71/21.82 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( (zero_zero real) ) 21.71/21.82 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( skv_10 ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113379 $$unsorted) (BOUND_VARIABLE_113380 $$unsorted) (BOUND_VARIABLE_113381 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_113381)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_113381) BOUND_VARIABLE_113379)) BOUND_VARIABLE_113380)) BOUND_VARIABLE_113381) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113379) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_113380) BOUND_VARIABLE_113381))))))) ) 21.71/21.82 ( 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)))) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v, r ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w, sa ) 21.71/21.82 ( int, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), x ) 21.71/21.82 ( int, v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.82 ( int, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), r ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X $$unsorted) (N $$unsorted) (M $$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 M))) (let ((_let_3 (hAPP nat _let_0 root N))) (or (not (hBOOL (hAPP nat bool _let_1 M))) (not (hBOOL (hAPP nat bool _let_1 N))) (= (hAPP real real _let_3 (hAPP real real _let_2 X)) (hAPP real real _let_2 (hAPP real real _let_3 X)))))))) ) 21.71/21.82 ( (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))) ) 21.71/21.82 ( (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))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat _let_1))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto nat real) A_3) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_0 bool (monoseq real) A_3))) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_3 (hAPP (fun real _let_1) (fun _let_0 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3)))))))) ) 21.71/21.82 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= X (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real (hAPP nat (fun real real) root N) X)) N))) ) 21.71/21.82 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113512 $$unsorted) (BOUND_VARIABLE_113513 $$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 (ord_less_eq X_a) BOUND_VARIABLE_113513) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113512) _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_113513) BOUND_VARIABLE_113512)) _let_2)))))) ) 21.71/21.82 ( 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)))) ) 21.71/21.82 ( 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) ) 21.71/21.82 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.71/21.82 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.71/21.82 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.82 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.82 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.71/21.82 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.71/21.82 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.71/21.82 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.82 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.71/21.82 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.82 ( nat, (one_one nat), (one_one nat) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113618 $$unsorted) (BOUND_VARIABLE_113619 $$unsorted) (BOUND_VARIABLE_113620 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_113620)) (= (= (ti X_a BOUND_VARIABLE_113618) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_113619) BOUND_VARIABLE_113620)) (= (ti X_a BOUND_VARIABLE_113619) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_113618) BOUND_VARIABLE_113620))))) ) 21.71/21.82 ( real, pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113652 $$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_113652))) (= _let_0 (ti X_a BOUND_VARIABLE_113652)))) ) 21.71/21.82 ( int, pls ) 21.71/21.82 ( int, min ) 21.71/21.82 ( int, s ) 21.71/21.82 ( int, s1 ) 21.71/21.82 ( int, m ) 21.71/21.82 ( int, t ) 21.71/21.82 ( int, v ) 21.71/21.82 ( int, w ) 21.71/21.82 ( int, y ) 21.71/21.82 ( int, sa ) 21.71/21.82 ( int, x ) 21.71/21.82 ( int, r ) 21.71/21.82 ( int, m1 ) 21.71/21.82 ( int, skv_14 ) 21.71/21.82 ( int, skv_20 ) 21.71/21.82 ( (fun int int), bit1 ) 21.71/21.82 ( (fun int int), bit0 ) 21.71/21.82 ( (fun int int), succ ) 21.71/21.82 ( (fun int int), pred ) 21.71/21.82 ( (fun int int), (fact_fact int) ) 21.71/21.82 ( (fun int int), zfact ) 21.71/21.82 ( nat, n ) 21.71/21.82 ( nat, tn ) 21.71/21.82 ( bool, fTrue ) 21.71/21.82 ( bool, fFalse ) 21.71/21.82 ( real, pi ) 21.71/21.82 ( real, (zero_zero real) ) 21.71/21.82 ( (fun nat real), (real_1 nat) ) 21.71/21.82 ( (fun nat real), cos_coeff ) 21.71/21.82 ( (fun nat real), sin_coeff ) 21.71/21.82 ( (fun real real), sin ) 21.71/21.82 ( (fun real real), cos ) 21.71/21.82 ( (fun real real), sqrt ) 21.71/21.82 ( (fun real real), tan ) 21.71/21.82 ( (fun real real), ln ) 21.71/21.82 ( (fun real real), arctan ) 21.71/21.82 ( (fun real real), arcsin ) 21.71/21.82 ( (fun real real), arccos ) 21.71/21.82 ( (fun nat nat), suc ) 21.71/21.82 ( (fun nat nat), (fact_fact nat) ) 21.71/21.82 ( (fun nat nat), nat_size ) 21.71/21.82 ( (fun nat nat), (size_size nat) ) 21.71/21.82 ( (fun nat nat), fact ) 21.71/21.82 ( (filter nat), sequentially ) 21.71/21.82 ( (fun int (fun int rat)), fract ) 21.71/21.82 ( complex, ii ) 21.71/21.82 ( (fun int bool), zOdd ) 21.71/21.82 ( (fun int bool), zprime ) 21.71/21.82 ( (fun int bool), zEven ) 21.71/21.82 ( (fun int bool), nat_neg ) 21.71/21.82 ( (fun int bool), nat_is_nat ) 21.71/21.82 ( (fun int bool), (even_odd_even int) ) 21.71/21.82 ( (fun int bool), twoSqu1091635170sum2sq ) 21.71/21.82 ( (fun int (fun int int)), legacy_zgcd ) 21.71/21.82 ( (fun int (fun int int)), (gcd_gcd int) ) 21.71/21.82 ( (fun int (fun int int)), inv ) 21.71/21.82 ( (fun int (fun int int)), multInv ) 21.71/21.82 ( (fun int (fun int int)), legendre ) 21.71/21.82 ( (fun int (fun int int)), standardRes ) 21.71/21.82 ( (fun int (fun int int)), nat_tsub ) 21.71/21.82 ( (fun int (fun int int)), z3div ) 21.71/21.82 ( (fun int (fun int int)), z3mod ) 21.71/21.82 ( (fun int (fun int int)), int_lcm ) 21.71/21.82 ( (fun int (fun int int)), int_gcd ) 21.71/21.82 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.71/21.82 ( (fun bool bool), fNot ) 21.71/21.82 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.71/21.82 ( (fun bool (fun bool bool)), fconj ) 21.71/21.82 ( (fun bool (fun bool bool)), fdisj ) 21.71/21.82 ( (fun bool (fun bool bool)), fimplies ) 21.71/21.82 ( (fun int (fun int bool)), quadRes ) 21.71/21.82 ( (fun int (fun int bool)), d22set ) 21.71/21.82 ( (fun int (fun int bool)), norRRset ) 21.71/21.82 ( (fun int (fun int bool)), sRStar ) 21.71/21.82 ( (fun int (fun int bool)), sr ) 21.71/21.82 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.71/21.82 ( (fun nat bool), (even_odd_even nat) ) 21.71/21.82 ( (fun nat bool), prime ) 21.71/21.82 ( (fun real complex), cis ) 21.71/21.82 ( (fun nat (fun nat bool)), coprime ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.71/21.82 ( (fun (product_prod int int) bool), frac_1 ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.71/21.82 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.71/21.82 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.71/21.82 ( (fun (fun int bool) bool), nat_nat_set ) 21.71/21.82 ( (fun nat (fun real real)), root ) 21.71/21.82 ( (fun real (fun real real)), log ) 21.71/21.82 ( (fun real (fun real real)), powr ) 21.71/21.82 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.71/21.82 ( (fun complex complex), cnj ) 21.71/21.82 ( (fun complex complex), expi ) 21.71/21.82 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.71/21.82 ( (fun nat (fun nat nat)), nat_gcd ) 21.71/21.82 ( (fun nat (fun nat nat)), nat_lcm ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.71/21.82 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.71/21.82 ( (fun int (fun (fun int bool) bool)), resSet ) 21.71/21.82 ( (fun int nat), nat_1 ) 21.71/21.82 ( (fun int nat), phi ) 21.71/21.82 ( (fun complex real), re ) 21.71/21.82 ( (fun complex real), im ) 21.71/21.82 ( (fun complex real), arg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.71/21.82 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.71/21.82 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.71/21.82 ( (fun (product_prod nat nat) bool), pred_nat ) 21.71/21.82 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.71/21.82 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.71/21.82 ( (fun (fun int bool) int), (the int) ) 21.71/21.82 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.71/21.82 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.71/21.82 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.71/21.82 ( (fun real (fun real complex)), rcis ) 21.71/21.82 ( (fun real (fun real complex)), complex_1 ) 21.71/21.82 ( (fun int (fun int (fun int bool))), zcong ) 21.71/21.82 ( (fun int (fun int (fun int bool))), wset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), noXRRset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), bnorRset ) 21.71/21.82 ( (fun int (fun int (fun int bool))), zcongm ) 21.71/21.82 ( (fun real nat), natceiling ) 21.71/21.82 ( (fun real nat), natfloor ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.71/21.82 ( (fun int real), (real_1 int) ) 21.71/21.82 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.71/21.82 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.71/21.82 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.71/21.82 ( (fun complex nat), (size_size complex) ) 21.71/21.82 ( (fun complex nat), complex_size ) 21.71/21.82 ( (fun (fun nat rat) bool), vanishes ) 21.71/21.82 ( (fun (product_prod int int) rat), frct ) 21.71/21.82 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.71/21.82 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.71/21.82 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.71/21.82 ( (fun rat real), ratreal ) 21.71/21.82 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.71/21.82 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.71/21.82 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.71/21.82 ( (fun rat (product_prod int int)), quotient_of ) 21.71/21.82 ( (fun int (fun nat nat)), nat_aux ) 21.71/21.82 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.71/21.82 ( (fun int (list int)), quickc666637781d_zero ) 21.71/21.82 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.71/21.82 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.71/21.82 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.71/21.82 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.71/21.82 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.71/21.82 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.71/21.82 ( (fun code_code_numeral int), code_int_of ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113673 $$unsorted) (BOUND_VARIABLE_113674 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_113673)) (hAPP int int (number_number_of int) BOUND_VARIABLE_113674)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_113673) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_113674)))))) ) 21.71/21.82 ( int, (one_one int), pls ) 21.71/21.82 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit1 pls) ) 21.71/21.82 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m), (hAPP int int bit1 pls) ) 21.71/21.82 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 21.71/21.82 ) 21.71/21.82 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_113717 $$unsorted) (BOUND_VARIABLE_113718 $$unsorted) (BOUND_VARIABLE_113728 $$unsorted) (BOUND_VARIABLE_113729 $$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_113717))) (let ((_let_6 (hAPP int X_b _let_2 BOUND_VARIABLE_113718))) (let ((_let_7 (hAPP int X_b _let_2 BOUND_VARIABLE_113728))) (let ((_let_8 (hAPP int X_b _let_2 BOUND_VARIABLE_113729))) (or (not (ord X_b)) (not (number 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)))))))))))))) ) 21.71/21.82 ( int, pls, pls, pls, pls ) 21.71/21.82 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.71/21.82 ( int, min, min, min, min ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( 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))) ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( nat, pls, pls, pls, pls ) 21.71/21.82 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( real, min, min, min, min ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( 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))) ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( 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))) ) 21.71/21.82 ( 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))) ) 21.71/21.82 ( 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)))))))) ) 21.71/21.82 ( complex, min, min, min, min ) 21.71/21.82 ( 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)) ) 21.71/21.82 ( quickcheck_code_int, pls, pls, pls, pls ) 21.71/21.82 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.71/21.82 ( quickcheck_code_int, (one_one int), (one_one int), (one_one int), (one_one int) ) 21.71/21.82 ( code_code_numeral, pls, pls, pls, pls ) 21.71/21.82 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.71/21.82 ) 21.71/21.83 (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)))))))) ) 21.71/21.83 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.71/21.83 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.71/21.83 ( (hAPP nat int (hAPP 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) ) 21.71/21.83 ( (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) ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.71/21.83 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.71/21.83 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 21.71/21.83 ( rat ) 21.71/21.83 ( int ) 21.71/21.83 ( (fun int int) ) 21.71/21.83 ( nat ) 21.71/21.83 ( bool ) 21.71/21.83 ( real ) 21.71/21.83 ( (fun nat real) ) 21.71/21.83 ( (fun real real) ) 21.71/21.83 ( complex ) 21.71/21.83 ( (fun int bool) ) 21.71/21.83 ( (product_prod int int) ) 21.71/21.83 ( (fun (product_prod int int) int) ) 21.71/21.83 ( (fun int (fun int bool)) ) 21.71/21.83 ( (fun nat bool) ) 21.71/21.83 ( (fun (product_prod int int) bool) ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.71/21.83 ( (fun real bool) ) 21.71/21.83 ( code_code_numeral ) 21.71/21.83 ( (fun int (fun int (fun int bool))) ) 21.71/21.83 ( (fun int real) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113760 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (ti X_a BOUND_VARIABLE_113760) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_113760))))) ) 21.71/21.83 ( int, pls ) 21.71/21.83 ( int, (one_one int) ) 21.71/21.83 ( int, min ) 21.71/21.83 ( int, s ) 21.71/21.83 ( int, s1 ) 21.71/21.83 ( int, m ) 21.71/21.83 ( int, t ) 21.71/21.83 ( int, v ) 21.71/21.83 ( int, w ) 21.71/21.83 ( int, y ) 21.71/21.83 ( int, sa ) 21.71/21.83 ( int, x ) 21.71/21.83 ( int, r ) 21.71/21.83 ( int, m1 ) 21.71/21.83 ( int, skv_14 ) 21.71/21.83 ( int, skv_20 ) 21.71/21.83 ( (fun int int), bit1 ) 21.71/21.83 ( (fun int int), bit0 ) 21.71/21.83 ( (fun int int), succ ) 21.71/21.83 ( (fun int int), pred ) 21.71/21.83 ( (fun int int), (fact_fact int) ) 21.71/21.83 ( (fun int int), zfact ) 21.71/21.83 ( nat, n ) 21.71/21.83 ( nat, tn ) 21.71/21.83 ( bool, fTrue ) 21.71/21.83 ( bool, fFalse ) 21.71/21.83 ( real, pi ) 21.71/21.83 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( real, (one_one real) ) 21.71/21.83 ( 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) ) 21.71/21.83 ( (fun nat real), (real_1 nat) ) 21.71/21.83 ( (fun nat real), cos_coeff ) 21.71/21.83 ( (fun nat real), sin_coeff ) 21.71/21.83 ( (fun real real), sin ) 21.71/21.83 ( (fun real real), cos ) 21.71/21.83 ( (fun real real), sqrt ) 21.71/21.83 ( (fun real real), tan ) 21.71/21.83 ( (fun real real), ln ) 21.71/21.83 ( (fun real real), arctan ) 21.71/21.83 ( (fun real real), arcsin ) 21.71/21.83 ( (fun real real), arccos ) 21.71/21.83 ( (fun nat nat), suc ) 21.71/21.83 ( (fun nat nat), (fact_fact nat) ) 21.71/21.83 ( (fun nat nat), nat_size ) 21.71/21.83 ( (fun nat nat), (size_size nat) ) 21.71/21.83 ( (fun nat nat), fact ) 21.71/21.83 ( (filter nat), sequentially ) 21.71/21.83 ( (fun int (fun int rat)), fract ) 21.71/21.83 ( complex, ii ) 21.71/21.83 ( complex, (one_one complex) ) 21.71/21.83 ( (fun int bool), zOdd ) 21.71/21.83 ( (fun int bool), zprime ) 21.71/21.83 ( (fun int bool), zEven ) 21.71/21.83 ( (fun int bool), nat_neg ) 21.71/21.83 ( (fun int bool), nat_is_nat ) 21.71/21.83 ( (fun int bool), (even_odd_even int) ) 21.71/21.83 ( (fun int bool), twoSqu1091635170sum2sq ) 21.71/21.83 ( (fun int (fun int int)), legacy_zgcd ) 21.71/21.83 ( (fun int (fun int int)), (gcd_gcd int) ) 21.71/21.83 ( (fun int (fun int int)), inv ) 21.71/21.83 ( (fun int (fun int int)), multInv ) 21.71/21.83 ( (fun int (fun int int)), legendre ) 21.71/21.83 ( (fun int (fun int int)), standardRes ) 21.71/21.83 ( (fun int (fun int int)), nat_tsub ) 21.71/21.83 ( (fun int (fun int int)), z3div ) 21.71/21.83 ( (fun int (fun int int)), z3mod ) 21.71/21.83 ( (fun int (fun int int)), int_lcm ) 21.71/21.83 ( (fun int (fun int int)), int_gcd ) 21.71/21.83 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.71/21.83 ( (fun bool bool), fNot ) 21.71/21.83 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.71/21.83 ( (fun bool (fun bool bool)), fconj ) 21.71/21.83 ( (fun bool (fun bool bool)), fdisj ) 21.71/21.83 ( (fun bool (fun bool bool)), fimplies ) 21.71/21.83 ( (fun int (fun int bool)), quadRes ) 21.71/21.83 ( (fun int (fun int bool)), d22set ) 21.71/21.83 ( (fun int (fun int bool)), norRRset ) 21.71/21.83 ( (fun int (fun int bool)), sRStar ) 21.71/21.83 ( (fun int (fun int bool)), sr ) 21.71/21.83 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.71/21.83 ( (fun nat bool), (even_odd_even nat) ) 21.71/21.83 ( (fun nat bool), prime ) 21.71/21.83 ( (fun real complex), cis ) 21.71/21.83 ( (fun nat (fun nat bool)), coprime ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.71/21.83 ( (fun (product_prod int int) bool), frac_1 ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.71/21.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.71/21.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.71/21.83 ( (fun (fun int bool) bool), nat_nat_set ) 21.71/21.83 ( (fun nat (fun real real)), root ) 21.71/21.83 ( (fun real (fun real real)), log ) 21.71/21.83 ( (fun real (fun real real)), powr ) 21.71/21.83 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.71/21.83 ( (fun complex complex), cnj ) 21.71/21.83 ( (fun complex complex), expi ) 21.71/21.83 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.71/21.83 ( (fun nat (fun nat nat)), nat_gcd ) 21.71/21.83 ( (fun nat (fun nat nat)), nat_lcm ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.71/21.83 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.71/21.83 ( (fun int (fun (fun int bool) bool)), resSet ) 21.71/21.83 ( (fun int nat), nat_1 ) 21.71/21.83 ( (fun int nat), phi ) 21.71/21.83 ( (fun complex real), re ) 21.71/21.83 ( (fun complex real), im ) 21.71/21.83 ( (fun complex real), arg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.71/21.83 ( (fun (product_prod nat nat) bool), pred_nat ) 21.71/21.83 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.71/21.83 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.71/21.83 ( (fun (fun int bool) int), (the int) ) 21.71/21.83 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.71/21.83 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.71/21.83 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.71/21.83 ( (fun real (fun real complex)), rcis ) 21.71/21.83 ( (fun real (fun real complex)), complex_1 ) 21.71/21.83 ( (fun int (fun int (fun int bool))), zcong ) 21.71/21.83 ( (fun int (fun int (fun int bool))), wset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), noXRRset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), bnorRset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), zcongm ) 21.71/21.83 ( (fun real nat), natceiling ) 21.71/21.83 ( (fun real nat), natfloor ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.71/21.83 ( (fun int real), (real_1 int) ) 21.71/21.83 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.71/21.83 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.71/21.83 ( (fun complex nat), (size_size complex) ) 21.71/21.83 ( (fun complex nat), complex_size ) 21.71/21.83 ( (fun (fun nat rat) bool), vanishes ) 21.71/21.83 ( (fun (product_prod int int) rat), frct ) 21.71/21.83 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.71/21.83 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.71/21.83 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.71/21.83 ( (fun rat real), ratreal ) 21.71/21.83 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.71/21.83 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.71/21.83 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.71/21.83 ( (fun rat (product_prod int int)), quotient_of ) 21.71/21.83 ( (fun int (fun nat nat)), nat_aux ) 21.71/21.83 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.71/21.83 ( (fun int (list int)), quickc666637781d_zero ) 21.71/21.83 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.71/21.83 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.71/21.83 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.71/21.83 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.71/21.83 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.71/21.83 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.71/21.83 ( (fun code_code_numeral int), code_int_of ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (number_number_of int))) (= (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 V) W)) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 V)) (hAPP int int _let_2 W)))))) ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113833 $$unsorted) (BOUND_VARIABLE_113834 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_113833))) (or (not (idom X_a)) (= (or (= (ti X_a BOUND_VARIABLE_113834) _let_2) (= _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_113834))) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113834) BOUND_VARIABLE_113834) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_113833) BOUND_VARIABLE_113833))))))) ) 21.71/21.83 ( int, pls, pls ) 21.71/21.83 ( int, pls, w ) 21.71/21.83 ( int, min, min ) 21.71/21.83 ( int, min, s ) 21.71/21.83 ( int, s, min ) 21.71/21.83 ( int, s1, s1 ) 21.71/21.83 ( int, s1, v ) 21.71/21.83 ( int, m, r ) 21.71/21.83 ( int, t, t ) 21.71/21.83 ( int, t, y ) 21.71/21.83 ( int, v, s1 ) 21.71/21.83 ( int, w, pls ) 21.71/21.83 ( int, y, t ) 21.71/21.83 ( int, sa, m1 ) 21.71/21.83 ( int, x, x ) 21.71/21.83 ( int, x, skv_14 ) 21.71/21.83 ( int, r, m ) 21.71/21.83 ( int, r, r ) 21.71/21.83 ( int, m1, sa ) 21.71/21.83 ( int, m1, m1 ) 21.71/21.83 ( int, skv_14, x ) 21.71/21.83 ( int, skv_20, skv_20 ) 21.71/21.83 ( (fun int int), bit1, (fact_fact int) ) 21.71/21.83 ( (fun int int), bit0, pred ) 21.71/21.83 ( (fun int int), succ, succ ) 21.71/21.83 ( (fun int int), succ, zfact ) 21.71/21.83 ( (fun int int), pred, bit0 ) 21.71/21.83 ( (fun int int), pred, pred ) 21.71/21.83 ( (fun int int), (fact_fact int), bit1 ) 21.71/21.83 ( (fun int int), (fact_fact int), (fact_fact int) ) 21.71/21.83 ( (fun int int), zfact, succ ) 21.71/21.83 ( nat, n, n ) 21.71/21.83 ( nat, n, tn ) 21.71/21.83 ( nat, tn, n ) 21.71/21.83 ( bool, fTrue, fTrue ) 21.71/21.83 ( bool, fTrue, fFalse ) 21.71/21.83 ( bool, fFalse, fTrue ) 21.71/21.83 ( real, pi, pi ) 21.71/21.83 ( (fun nat real), (real_1 nat), (real_1 nat) ) 21.71/21.83 ( (fun nat real), cos_coeff, sin_coeff ) 21.71/21.83 ( (fun nat real), sin_coeff, cos_coeff ) 21.71/21.83 ( (fun nat real), sin_coeff, sin_coeff ) 21.71/21.83 ( (fun real real), sin, sin ) 21.71/21.83 ( (fun real real), sin, ln ) 21.71/21.83 ( (fun real real), cos, cos ) 21.71/21.83 ( (fun real real), cos, arccos ) 21.71/21.83 ( (fun real real), sqrt, arcsin ) 21.71/21.83 ( (fun real real), tan, arctan ) 21.71/21.83 ( (fun real real), ln, sin ) 21.71/21.83 ( (fun real real), arctan, tan ) 21.71/21.83 ( (fun real real), arctan, arctan ) 21.71/21.83 ( (fun real real), arcsin, sqrt ) 21.71/21.83 ( (fun real real), arcsin, arcsin ) 21.71/21.83 ( (fun real real), arccos, cos ) 21.71/21.83 ( (fun nat nat), suc, suc ) 21.71/21.83 ( (fun nat nat), suc, fact ) 21.71/21.83 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 21.71/21.83 ( (fun nat nat), nat_size, nat_size ) 21.71/21.83 ( (fun nat nat), nat_size, (size_size nat) ) 21.71/21.83 ( (fun nat nat), (size_size nat), nat_size ) 21.71/21.83 ( (fun nat nat), fact, suc ) 21.71/21.83 ( (filter nat), sequentially, sequentially ) 21.71/21.83 ( (fun int (fun int rat)), fract, fract ) 21.71/21.83 ( complex, ii, ii ) 21.71/21.83 ( (fun int bool), zOdd, zOdd ) 21.71/21.83 ( (fun int bool), zOdd, zprime ) 21.71/21.83 ( (fun int bool), zprime, zOdd ) 21.71/21.83 ( (fun int bool), zEven, nat_neg ) 21.71/21.83 ( (fun int bool), nat_neg, zEven ) 21.71/21.83 ( (fun int bool), nat_neg, nat_neg ) 21.71/21.83 ( (fun int bool), nat_is_nat, nat_is_nat ) 21.71/21.83 ( (fun int bool), nat_is_nat, twoSqu1091635170sum2sq ) 21.71/21.83 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 21.71/21.83 ( (fun int bool), twoSqu1091635170sum2sq, nat_is_nat ) 21.71/21.83 ( (fun int (fun int int)), legacy_zgcd, z3div ) 21.71/21.83 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 21.71/21.83 ( (fun int (fun int int)), (gcd_gcd int), multInv ) 21.71/21.83 ( (fun int (fun int int)), inv, int_gcd ) 21.71/21.83 ( (fun int (fun int int)), multInv, (gcd_gcd int) ) 21.71/21.83 ( (fun int (fun int int)), legendre, legendre ) 21.71/21.83 ( (fun int (fun int int)), legendre, z3mod ) 21.71/21.83 ( (fun int (fun int int)), standardRes, standardRes ) 21.71/21.83 ( (fun int (fun int int)), standardRes, int_lcm ) 21.71/21.83 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 21.71/21.83 ( (fun int (fun int int)), z3div, legacy_zgcd ) 21.71/21.83 ( (fun int (fun int int)), z3div, z3div ) 21.71/21.83 ( (fun int (fun int int)), z3mod, legendre ) 21.71/21.83 ( (fun int (fun int int)), int_lcm, standardRes ) 21.71/21.83 ( (fun int (fun int int)), int_gcd, inv ) 21.71/21.83 ( (fun int (fun int int)), int_gcd, int_gcd ) 21.71/21.83 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 21.71/21.83 ( (fun bool bool), fNot, fNot ) 21.71/21.83 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 21.71/21.83 ( (fun bool (fun bool bool)), fconj, fdisj ) 21.71/21.83 ( (fun bool (fun bool bool)), fdisj, fconj ) 21.71/21.83 ( (fun bool (fun bool bool)), fdisj, fdisj ) 21.71/21.83 ( (fun bool (fun bool bool)), fimplies, fimplies ) 21.71/21.83 ( (fun int (fun int bool)), quadRes, quadRes ) 21.71/21.83 ( (fun int (fun int bool)), quadRes, sr ) 21.71/21.83 ( (fun int (fun int bool)), d22set, quickc1265749348ro_rel ) 21.71/21.83 ( (fun int (fun int bool)), norRRset, norRRset ) 21.71/21.83 ( (fun int (fun int bool)), norRRset, sRStar ) 21.71/21.83 ( (fun int (fun int bool)), sRStar, norRRset ) 21.71/21.83 ( (fun int (fun int bool)), sr, quadRes ) 21.71/21.83 ( (fun int (fun int bool)), quickc1265749348ro_rel, d22set ) 21.71/21.83 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 21.71/21.83 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 21.71/21.83 ( (fun nat bool), (even_odd_even nat), prime ) 21.71/21.83 ( (fun nat bool), prime, (even_odd_even nat) ) 21.71/21.83 ( (fun real complex), cis, cis ) 21.71/21.83 ( (fun nat (fun nat bool)), coprime, coprime ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 21.71/21.83 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, norm_frac_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, lazy_small_lazy_rel ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 21.71/21.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 21.71/21.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 21.71/21.83 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 21.71/21.83 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 21.71/21.83 ( (fun nat (fun real real)), root, root ) 21.71/21.83 ( (fun real (fun real real)), log, powr ) 21.71/21.83 ( (fun real (fun real real)), powr, log ) 21.71/21.83 ( (fun real (fun real real)), powr, powr ) 21.71/21.83 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 21.71/21.83 ( (fun complex complex), cnj, expi ) 21.71/21.83 ( (fun complex complex), expi, cnj ) 21.71/21.83 ( (fun complex complex), expi, expi ) 21.71/21.83 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 21.71/21.83 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 21.71/21.83 ( (fun nat (fun nat nat)), nat_gcd, nat_lcm ) 21.71/21.83 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 21.71/21.83 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 21.71/21.83 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 21.71/21.83 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 21.71/21.83 ( (fun int nat), nat_1, phi ) 21.71/21.83 ( (fun int nat), phi, nat_1 ) 21.71/21.83 ( (fun int nat), phi, phi ) 21.71/21.83 ( (fun complex real), re, arg ) 21.71/21.83 ( (fun complex real), im, im ) 21.71/21.83 ( (fun complex real), arg, re ) 21.71/21.83 ( (fun complex real), arg, arg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), divmod_int, pdivmod ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), negDivAlg, norm_frac ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), pdivmod, divmod_int ) 21.71/21.83 ( (fun int (fun int (product_prod int int))), norm_frac, negDivAlg ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 21.71/21.83 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 21.71/21.83 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 21.71/21.83 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 21.71/21.83 ( (fun (fun int bool) int), (the int), (the int) ) 21.71/21.83 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 21.71/21.83 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 21.71/21.83 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 21.71/21.83 ( (fun real (fun real complex)), rcis, rcis ) 21.71/21.83 ( (fun real (fun real complex)), rcis, complex_1 ) 21.71/21.83 ( (fun real (fun real complex)), complex_1, rcis ) 21.71/21.83 ( (fun int (fun int (fun int bool))), zcong, zcongm ) 21.71/21.83 ( (fun int (fun int (fun int bool))), wset, wset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 21.71/21.83 ( (fun int (fun int (fun int bool))), zcongm, zcong ) 21.71/21.83 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 21.71/21.83 ( (fun real nat), natceiling, natceiling ) 21.71/21.83 ( (fun real nat), natceiling, natfloor ) 21.71/21.83 ( (fun real nat), natfloor, natceiling ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 21.71/21.83 ( (fun int real), (real_1 int), (real_1 int) ) 21.71/21.83 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 21.71/21.83 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 21.71/21.83 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 21.71/21.83 ( (fun complex nat), (size_size complex), (size_size complex) ) 21.71/21.83 ( (fun complex nat), (size_size complex), complex_size ) 21.71/21.83 ( (fun complex nat), complex_size, (size_size complex) ) 21.71/21.83 ( (fun (fun nat rat) bool), vanishes, vanishes ) 21.71/21.83 ( (fun (product_prod int int) rat), frct, frct ) 21.71/21.83 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 21.71/21.83 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 21.71/21.83 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 21.71/21.83 ( (fun rat real), ratreal, ratreal ) 21.71/21.83 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 21.71/21.83 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 21.71/21.83 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 21.71/21.83 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 21.71/21.83 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 21.71/21.83 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 21.71/21.83 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 21.71/21.83 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 21.71/21.83 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 21.71/21.83 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 21.71/21.83 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 21.71/21.83 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 21.71/21.83 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 21.71/21.83 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 21.71/21.83 ( (fun code_code_numeral int), code_int_of, code_int_of ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (zero_zero real)) (zero_zero X_a))) ) 21.71/21.83 ( rat ) 21.71/21.83 ( int ) 21.71/21.83 ( nat ) 21.71/21.83 ( real ) 21.71/21.83 ( complex ) 21.71/21.83 ( quickcheck_code_int ) 21.71/21.83 ( code_code_numeral ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) (one_one int)) (hAPP int int pred K_4)) ) 21.71/21.83 ( pls ) 21.71/21.83 ( min ) 21.71/21.83 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( y ) 21.71/21.83 ( x ) 21.71/21.83 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.71/21.83 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.71/21.83 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.71/21.83 ( (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))) m1))) ) 21.71/21.83 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (= Ma Na) (= (hAPP nat nat (hAPP nat _let_0 _let_1 Na) K) (hAPP nat nat (hAPP nat _let_0 _let_1 Ma) K))))) ) 21.71/21.83 ( (one_one nat), (one_one nat), (one_one nat) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (or (= (zero_zero nat) M) (= (hAPP nat nat _let_1 M) (hAPP nat nat (hAPP nat _let_0 (times_times nat) M) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) (one_one nat)))))))) ) 21.71/21.83 ( (hAPP int nat nat_1 t) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_113937 $$unsorted) (BOUND_VARIABLE_113938 $$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_113937) BOUND_VARIABLE_113938))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_113937)) (hAPP X_a real _let_0 BOUND_VARIABLE_113938)))))) ) 21.71/21.83 ( 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) ) 21.71/21.83 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.83 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.83 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.83 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.83 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.71/21.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.71/21.83 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.71/21.83 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.83 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.83 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 21.71/21.83 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.71/21.83 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) A_3) B_2))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X_1))))) )) (not (forall ((X_1 $$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 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) (zero_zero real)))))) )) (= (hAPP real real F A_3) (hAPP real real F B_2))) ) 21.71/21.83 ( sin, (zero_zero real), pi ) 21.71/21.83 ( cos, (zero_zero real), skv_2 ) 21.71/21.83 ( sqrt, (zero_zero real), skv_9 ) 21.71/21.83 ( tan, pi, (zero_zero real) ) 21.71/21.83 ( tan, (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)))) ) 21.71/21.83 ( (inverse_inverse real), (zero_zero real), skv_12 ) 21.71/21.83 ( (hAPP 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 bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (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 (hAPP 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))) ) 21.71/21.83 ( arctan, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( arctan, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((P $$unsorted)) (let ((_let_0 (ti bool P))) (or (= fFalse _let_0) (= fTrue _let_0))) ) 21.71/21.83 ( fTrue ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (abs_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 21.71/21.83 ( rat ) 21.71/21.83 ( int ) 21.71/21.83 ( (fun int int) ) 21.71/21.83 ( nat ) 21.71/21.83 ( bool ) 21.71/21.83 ( real ) 21.71/21.83 ( (fun nat real) ) 21.71/21.83 ( (fun real real) ) 21.71/21.83 ( complex ) 21.71/21.83 ( (fun int bool) ) 21.71/21.83 ( (product_prod int int) ) 21.71/21.83 ( (fun (product_prod int int) int) ) 21.71/21.83 ( (fun int (fun int bool)) ) 21.71/21.83 ( (fun nat bool) ) 21.71/21.83 ( (fun (product_prod int int) bool) ) 21.71/21.83 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.71/21.83 ( (fun real bool) ) 21.71/21.83 ( code_code_numeral ) 21.71/21.83 ( (fun int (fun int (fun int bool))) ) 21.71/21.83 ( (fun int real) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= _let_3 (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) N) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) N)))) (hAPP nat real (hAPP real _let_0 _let_1 _let_3) N)))))))) ) 21.71/21.83 ( (zero_zero nat) ) 21.71/21.83 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.83 ( (one_one nat) ) 21.71/21.83 ( n ) 21.71/21.83 ( tn ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114109 $$unsorted) (BOUND_VARIABLE_114110 $$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_114109) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_114110)) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_114109) BOUND_VARIABLE_114110)))) ) 21.71/21.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.83 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.83 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( 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))))))))) ) 21.71/21.83 ( 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))) ) 21.71/21.83 ( 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))) ) 21.71/21.83 ( 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))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (plus_plus real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun (fun nat nat) _let_0))) (let ((_let_6 (combb nat real nat))) (let ((_let_7 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) (combc nat nat nat) (plus_plus nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP real real (exp real) Xa) (hAPP real real (hAPP real _let_1 _let_2 (hAPP real real (hAPP real _let_1 _let_2 (one_one real)) Xa)) (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_0 _let_3 (hAPP (fun real _let_1) (fun _let_0 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 (combb real real nat) (inverse_inverse real)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_5 _let_6 (real_1 nat)) (hAPP (fun nat nat) (fun nat nat) (hAPP (fun nat nat) (fun (fun nat nat) (fun nat nat)) (combb nat nat nat) (fact_fact nat)) _let_7))))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_5 _let_6 (hAPP real _let_0 (power_power real) Xa)) _let_7))))))))))))) ) 21.71/21.83 ( (hAPP int real (number_number_of real) min) ) 21.71/21.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114231 $$unsorted) (BOUND_VARIABLE_114232 $$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_114231) BOUND_VARIABLE_114232) 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_114231)) (hAPP X_a real _let_3 BOUND_VARIABLE_114232)) sequentially))))))) ) 21.71/21.83 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Xa) Ya))) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Ya))) (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X_1) (field_char_0_Rats real)))))) )))) ) 21.71/21.83 ( pi, (zero_zero real) ) 21.71/21.83 ( pi, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 21.71/21.83 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.71/21.83 ( (zero_zero real), pi ) 21.71/21.83 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (zero_zero real), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.71/21.83 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.71/21.83 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.71/21.83 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.71/21.83 ( skv_2, (zero_zero real) ) 21.71/21.83 ( skv_9, (zero_zero real) ) 21.71/21.83 ( skv_12, (zero_zero real) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((L_4 $$unsorted)) (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min))) (= (hAPP int int bit1 (hAPP int int _let_0 L_4)) (hAPP int int _let_0 (hAPP int int bit0 L_4)))) ) 21.71/21.83 ( pls ) 21.71/21.83 ( (hAPP int int bit1 pls) ) 21.71/21.83 ( min ) 21.71/21.83 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.83 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.83 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) Wa))) (= (or (= (ti int Wa) (ti int Z)) (hBOOL (hAPP int bool _let_0 Z))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) Z) (one_one int)))))) ) 21.71/21.83 ( (zero_zero 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) ) 21.71/21.83 ( 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) ) 21.71/21.83 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 21.71/21.83 ( 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) ) 21.71/21.83 ( 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) ) 21.71/21.83 ( skv_5, (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) ) 21.71/21.83 ) 21.71/21.83 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 X) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_0 (plus_plus real) _let_1) X))) X))) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 21.71/21.83 ( (hAPP int real (number_number_of real) min) ) 21.71/21.83 ( pi ) 21.71/21.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.83 ( skv_10 ) 21.71/21.83 ( skv_11 ) 21.71/21.83 ( skv_15 ) 21.71/21.83 ( skv_18 ) 21.71/21.83 ) 21.71/21.84 (instantiation (forall ((X $$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))) (not (= _let_0 (hAPP real real cos X))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (= X (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_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))))))) (hBOOL (hAPP nat bool (even_odd_even nat) N_1)))) )))) ) 21.71/21.84 ( pi ) 21.71/21.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (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)))) ) 21.71/21.84 ( (zero_zero real) ) 21.71/21.84 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (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))))) ) 21.71/21.84 ( (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) ) 21.71/21.84 ( (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))))) ) 21.71/21.84 ( (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)))) ) 21.71/21.84 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.71/21.84 ( skv_10 ) 21.71/21.84 ( skv_11 ) 21.71/21.84 ( skv_15 ) 21.71/21.84 ( skv_18 ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y))))) ) 21.71/21.84 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( v, y ) 21.71/21.84 ( v, sa ) 21.71/21.84 ( v, x ) 21.71/21.84 ( v, r ) 21.71/21.84 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.84 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.84 ( w, y ) 21.71/21.84 ( w, sa ) 21.71/21.84 ( w, x ) 21.71/21.84 ( w, r ) 21.71/21.84 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.84 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.84 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.71/21.84 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.84 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.71/21.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( skv_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))) ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zEven))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Xa))) (= (one_one int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min)) (hAPP int nat nat_1 Xa))))) ) 21.71/21.84 ( pls ) 21.71/21.84 ( (one_one int) ) 21.71/21.84 ( min ) 21.71/21.84 ( (zero_zero int) ) 21.71/21.84 ( s ) 21.71/21.84 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( t ) 21.71/21.84 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.84 ( skv_4 ) 21.71/21.84 ( skv_5 ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X $$unsorted)) (= (hAPP complex real im (hAPP complex complex cnj X)) (hAPP real real (uminus_uminus real) (hAPP complex real im X))) ) 21.71/21.84 ( (zero_zero complex) ) 21.71/21.84 ( ii ) 21.71/21.84 ( (one_one complex) ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114509 $$unsorted) (BOUND_VARIABLE_114510 $$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_114509) BOUND_VARIABLE_114510))) (not (= (ti X_a BOUND_VARIABLE_114510) (ti X_a BOUND_VARIABLE_114509)))) ) 21.71/21.84 ( int, (one_one int), t ) 21.71/21.84 ( int, min, min ) 21.71/21.84 ( int, min, (zero_zero int) ) 21.71/21.84 ( int, (zero_zero int), pls ) 21.71/21.84 ( int, (zero_zero int), (one_one int) ) 21.71/21.84 ( int, (zero_zero int), min ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.84 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( nat, (zero_zero nat), n ) 21.71/21.84 ( nat, (zero_zero nat), tn ) 21.71/21.84 ( real, pi, (zero_zero real) ) 21.71/21.84 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( real, (zero_zero real), pi ) 21.71/21.84 ( 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)))) ) 21.71/21.84 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( real, (zero_zero real), skv_2 ) 21.71/21.84 ( real, (zero_zero real), skv_9 ) 21.71/21.84 ( real, (zero_zero real), skv_12 ) 21.71/21.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.71/21.84 ( 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) ) 21.71/21.84 ( 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 ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114539 $$unsorted) (BOUND_VARIABLE_114540 $$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_114540))) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_114539))) (= (hAPP int X_a _let_1 (hAPP int int (hAPP int (fun int int) (times_times int) BOUND_VARIABLE_114540) BOUND_VARIABLE_114539)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a _let_1 BOUND_VARIABLE_114540)) (hAPP int X_a _let_1 BOUND_VARIABLE_114539)))))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( quickcheck_code_int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( code_code_numeral, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114573 $$unsorted) (BOUND_VARIABLE_114574 $$unsorted) (BOUND_VARIABLE_114575 $$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_inverse_zero X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_114575)) (= (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_114573) BOUND_VARIABLE_114575)) BOUND_VARIABLE_114574) (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_114573) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_114574) BOUND_VARIABLE_114575))) BOUND_VARIABLE_114575)))))) ) 21.71/21.84 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), y, w ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), sa, w ) 21.71/21.84 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114608 $$unsorted) (BOUND_VARIABLE_114609 $$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_114608))) (or (not (comm_monoid_add X_a)) (= (hAPP _let_0 X_a _let_2 (hAPP nat _let_0 _let_1 (hAPP nat nat suc BOUND_VARIABLE_114609))) (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_114609))) (hAPP nat X_a BOUND_VARIABLE_114608 BOUND_VARIABLE_114609))))))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 21.71/21.84 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (semiring_1_of_nat int), (one_one nat) ) 21.71/21.84 ( int, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (semiring_1_of_nat int), n ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) v), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) w), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) x), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2))))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) skv_6), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) skv_7), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) skv_16), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) skv_23), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( int, (hAPP int (fun nat int) (power_power int) skv_24), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (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))) ) 21.71/21.84 ( nat, suc, (zero_zero nat) ) 21.71/21.84 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 21.71/21.84 ( nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.71/21.84 ( nat, (fact_fact nat), (zero_zero nat) ) 21.71/21.84 ( nat, (fact_fact nat), (one_one nat) ) 21.71/21.84 ( nat, nat_size, (zero_zero nat) ) 21.71/21.84 ( nat, (size_size nat), (zero_zero nat) ) 21.71/21.84 ( nat, fact, (zero_zero nat) ) 21.71/21.84 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 21.71/21.84 ( nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (one_one nat) ) 21.71/21.84 ( bool, (even_odd_even nat), (zero_zero nat) ) 21.71/21.84 ( bool, (even_odd_even nat), (one_one nat) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.71/21.84 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.71/21.84 ( bool, prime, (zero_zero nat) ) 21.71/21.84 ( bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.71/21.84 ( real, (real_1 nat), (zero_zero nat) ) 21.71/21.84 ( real, (real_1 nat), (one_one nat) ) 21.71/21.84 ( (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (fun nat nat), (plus_plus nat), (one_one nat) ) 21.71/21.84 ( (fun nat nat), (minus_minus nat), (hAPP int nat nat_1 t) ) 21.71/21.84 ( (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))) ) 21.71/21.84 ( (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) ) 21.71/21.84 ( 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))) ) 21.71/21.84 ( (fun nat bool), (ord_less nat), (zero_zero nat) ) 21.71/21.84 ( (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) ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114632 $$unsorted) (BOUND_VARIABLE_114633 $$unsorted) (BOUND_VARIABLE_114634 $$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_114632))) (or (not (ab_semigroup_mult X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114633) BOUND_VARIABLE_114634)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_114633)) BOUND_VARIABLE_114634)))))) ) 21.71/21.84 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, v ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, w ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, v ) 21.71/21.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, w ) 21.71/21.84 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), m1 ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))) ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.71/21.84 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.71/21.84 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.71/21.84 ( 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))))), (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.71/21.84 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi), ii ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((R_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_3))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (real_1 nat))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) R_3) (hAPP nat real _let_0 N_1)))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP nat real _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N_1) (one_one nat)))) R_3)))))) ))) ) 21.71/21.84 ( pi ) 21.71/21.84 ( (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)))) ) 21.71/21.84 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.84 ( skv_10 ) 21.71/21.84 ( skv_11 ) 21.71/21.84 ( skv_15 ) 21.71/21.84 ( skv_18 ) 21.71/21.84 ) 21.71/21.84 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X))))) ) 21.71/21.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.84 ( (one_one real) ) 21.71/21.84 ( (zero_zero real) ) 21.71/21.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.84 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114699 $$unsorted) (BOUND_VARIABLE_114700 $$unsorted) (BOUND_VARIABLE_114701 $$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 (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_114699))) (or (not (linord581940658strict X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_114700)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_114701))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114700) BOUND_VARIABLE_114701)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_114699))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114699) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114701) BOUND_VARIABLE_114700)))))))))) ) 21.71/21.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (archim2085082626_floor real))) (let ((_let_1 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_1 A_1))) (not (hBOOL (hAPP real bool _let_1 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_0 A_1)) (hAPP real int _let_0 B))) (hAPP real int _let_0 (hAPP real real (hAPP real (fun real real) (times_times real) A_1) B))))))) ) 21.71/21.85 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( 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))))) ) 21.71/21.85 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (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)))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114754 $$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_114754)) (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_114754)) (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_114754)))))))) ) 21.71/21.85 ( int, s ) 21.71/21.85 ( int, s1 ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( int, v ) 21.71/21.85 ( int, w ) 21.71/21.85 ( int, y ) 21.71/21.85 ( int, x ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.71/21.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.85 ( int, skv_6 ) 21.71/21.85 ( int, skv_7 ) 21.71/21.85 ( int, skv_16 ) 21.71/21.85 ( int, skv_23 ) 21.71/21.85 ( int, skv_24 ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) min) ) 21.71/21.85 ( 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)))) ) 21.71/21.85 ( complex, ii ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X)) (hAPP real real sqrt Y)))))) ) 21.71/21.85 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114791 $$unsorted) (BOUND_VARIABLE_114792 $$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_114791)) BOUND_VARIABLE_114792))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114791) BOUND_VARIABLE_114792))))) ) 21.71/21.85 ( int, (one_one int), t ) 21.71/21.85 ( int, min, pls ) 21.71/21.85 ( int, min, min ) 21.71/21.85 ( int, (zero_zero int), pls ) 21.71/21.85 ( int, (zero_zero int), (one_one int) ) 21.71/21.85 ( int, (zero_zero int), min ) 21.71/21.85 ( int, (zero_zero int), s ) 21.71/21.85 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.85 ( int, (zero_zero int), skv_4 ) 21.71/21.85 ( int, (zero_zero int), skv_5 ) 21.71/21.85 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.71/21.85 ( 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))) ) 21.71/21.85 ( real, (zero_zero real), pi ) 21.71/21.85 ( 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)))) ) 21.71/21.85 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( real, (zero_zero real), skv_10 ) 21.71/21.85 ( real, (zero_zero real), skv_11 ) 21.71/21.85 ( real, (zero_zero real), skv_15 ) 21.71/21.85 ( real, (zero_zero real), skv_18 ) 21.71/21.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.71/21.85 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real (hAPP 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_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (uminus_uminus real) _let_0)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) (hAPP real real cos X))))))) ) 21.71/21.85 ( pi ) 21.71/21.85 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (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)))) ) 21.71/21.85 ( (one_one real) ) 21.71/21.85 ( (zero_zero real) ) 21.71/21.85 ( (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 bit0 (hAPP int int bit1 pls))))) ) 21.71/21.85 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.71/21.85 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( (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))))) ) 21.71/21.85 ( (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 (hAPP int int bit1 pls))))) ) 21.71/21.85 ( (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)))) ) 21.71/21.85 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.71/21.85 ( (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)) ) 21.71/21.85 ( skv_10 ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114822 $$unsorted) (BOUND_VARIABLE_114823 $$unsorted) (BOUND_VARIABLE_114824 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_114822))) (or (not (linordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_114823)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_114824)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_114822))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_114823) BOUND_VARIABLE_114824)))))) ) 21.71/21.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((N $$unsorted)) (= (hAPP int nat (number_number_of nat) N) (hAPP real nat natceiling (hAPP int real (number_number_of real) N))) ) 21.71/21.85 ( pls ) 21.71/21.85 ( (hAPP int int bit1 pls) ) 21.71/21.85 ( min ) 21.71/21.85 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.85 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.85 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (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)))))))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (= (not (forall ((N_1 $$unsorted) (F_3 $$unsorted)) (let ((_let_0 (fun nat (fun nat bool)))) (let ((_let_1 (fun X_a bool))) (not (= (ti _let_1 A_2) (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_1))))))) )) (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) A_2))) ) 21.71/21.85 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114894 $$unsorted) (BOUND_VARIABLE_114895 $$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 BOUND_VARIABLE_114895) _let_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) BOUND_VARIABLE_114894))) (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_114895) BOUND_VARIABLE_114894)) _let_1)))))) ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.71/21.85 ( 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)))) ) 21.71/21.85 ( 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))) ) 21.71/21.85 ( 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)))) ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 21.71/21.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.71/21.85 ( 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) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) _let_0) X))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_2 (times_times real))) (let ((_let_3 (real_1 nat))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) X) (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_3 (hAPP nat nat suc N_1))) Y)))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP real real (hAPP real _let_0 _let_2 (hAPP nat real _let_3 N_1)) Y)) X))))))) ))))) ) 21.71/21.85 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( (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)))) ) 21.71/21.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.71/21.85 ( skv_10, skv_2 ) 21.71/21.85 ( skv_11, skv_9 ) 21.71/21.85 ( skv_15, skv_12 ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114945 $$unsorted) (BOUND_VARIABLE_114946 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_char_0 X_a)) (= (= (hAPP nat X_a _let_0 BOUND_VARIABLE_114945) (hAPP nat X_a _let_0 BOUND_VARIABLE_114946)) (= BOUND_VARIABLE_114945 BOUND_VARIABLE_114946)))) ) 21.71/21.85 ( int, (zero_zero nat), (zero_zero nat) ) 21.71/21.85 ( int, (zero_zero nat), n ) 21.71/21.85 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.71/21.85 ( int, (one_one nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.85 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one nat) ) 21.71/21.85 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.85 ( int, n, (zero_zero nat) ) 21.71/21.85 ( int, n, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( real, (zero_zero nat), (one_one nat) ) 21.71/21.85 ( real, (one_one nat), (zero_zero nat) ) 21.71/21.85 ( real, (one_one nat), (one_one nat) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_114962 $$unsorted)) (or (not (ab_sem1668676832m_mult X_a)) (= (ti X_a BOUND_VARIABLE_114962) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_114962) BOUND_VARIABLE_114962))) ) 21.71/21.85 ( int, pls ) 21.71/21.85 ( int, min ) 21.71/21.85 ( int, s ) 21.71/21.85 ( int, s1 ) 21.71/21.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( int, m ) 21.71/21.85 ( 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))) ) 21.71/21.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.85 ( int, t ) 21.71/21.85 ( int, v ) 21.71/21.85 ( int, w ) 21.71/21.85 ( int, y ) 21.71/21.85 ( int, sa ) 21.71/21.85 ( int, x ) 21.71/21.85 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.71/21.85 ( int, r ) 21.71/21.85 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.85 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( int, m1 ) 21.71/21.85 ( int, skv_13 ) 21.71/21.85 ( int, skv_14 ) 21.71/21.85 ( int, skv_19 ) 21.71/21.85 ( int, skv_20 ) 21.71/21.85 ( (fun int int), bit1 ) 21.71/21.85 ( (fun int int), bit0 ) 21.71/21.85 ( (fun int int), succ ) 21.71/21.85 ( (fun int int), pred ) 21.71/21.85 ( (fun int int), (fact_fact int) ) 21.71/21.85 ( (fun int int), zfact ) 21.71/21.85 ( nat, n ) 21.71/21.85 ( nat, tn ) 21.71/21.85 ( bool, fTrue ) 21.71/21.85 ( bool, fFalse ) 21.71/21.85 ( real, pi ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( 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))))) ) 21.71/21.85 ( (fun nat real), (real_1 nat) ) 21.71/21.85 ( (fun nat real), cos_coeff ) 21.71/21.85 ( (fun nat real), sin_coeff ) 21.71/21.85 ( (fun real real), sin ) 21.71/21.85 ( (fun real real), cos ) 21.71/21.85 ( (fun real real), sqrt ) 21.71/21.85 ( (fun real real), tan ) 21.71/21.85 ( (fun real real), ln ) 21.71/21.85 ( (fun real real), arctan ) 21.71/21.85 ( (fun real real), arcsin ) 21.71/21.85 ( (fun real real), arccos ) 21.71/21.85 ( (fun nat nat), suc ) 21.71/21.85 ( (fun nat nat), (fact_fact nat) ) 21.71/21.85 ( (fun nat nat), nat_size ) 21.71/21.85 ( (fun nat nat), (size_size nat) ) 21.71/21.85 ( (fun nat nat), fact ) 21.71/21.85 ( (filter nat), sequentially ) 21.71/21.85 ( (fun int (fun int rat)), fract ) 21.71/21.85 ( complex, ii ) 21.71/21.85 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( 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)) ) 21.71/21.85 ( (fun int bool), zOdd ) 21.71/21.85 ( (fun int bool), zprime ) 21.71/21.85 ( (fun int bool), zEven ) 21.71/21.85 ( (fun int bool), nat_neg ) 21.71/21.85 ( (fun int bool), nat_is_nat ) 21.71/21.85 ( (fun int bool), (even_odd_even int) ) 21.71/21.85 ( (fun int bool), twoSqu1091635170sum2sq ) 21.71/21.85 ( (fun int (fun int int)), legacy_zgcd ) 21.71/21.85 ( (fun int (fun int int)), (gcd_gcd int) ) 21.71/21.85 ( (fun int (fun int int)), inv ) 21.71/21.85 ( (fun int (fun int int)), multInv ) 21.71/21.85 ( (fun int (fun int int)), legendre ) 21.71/21.85 ( (fun int (fun int int)), standardRes ) 21.71/21.85 ( (fun int (fun int int)), nat_tsub ) 21.71/21.85 ( (fun int (fun int int)), z3div ) 21.71/21.85 ( (fun int (fun int int)), z3mod ) 21.71/21.85 ( (fun int (fun int int)), int_lcm ) 21.71/21.85 ( (fun int (fun int int)), int_gcd ) 21.71/21.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.71/21.85 ( (fun bool bool), fNot ) 21.71/21.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.71/21.85 ( (fun bool (fun bool bool)), fconj ) 21.71/21.85 ( (fun bool (fun bool bool)), fdisj ) 21.71/21.85 ( (fun bool (fun bool bool)), fimplies ) 21.71/21.85 ( (fun int (fun int bool)), quadRes ) 21.71/21.85 ( (fun int (fun int bool)), d22set ) 21.71/21.85 ( (fun int (fun int bool)), norRRset ) 21.71/21.85 ( (fun int (fun int bool)), sRStar ) 21.71/21.85 ( (fun int (fun int bool)), sr ) 21.71/21.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.71/21.85 ( (fun nat bool), (even_odd_even nat) ) 21.71/21.85 ( (fun nat bool), prime ) 21.71/21.85 ( (fun real complex), cis ) 21.71/21.85 ( (fun nat (fun nat bool)), coprime ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.71/21.85 ( (fun (product_prod int int) bool), frac_1 ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.71/21.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.71/21.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.71/21.85 ( (fun (fun int bool) bool), nat_nat_set ) 21.71/21.85 ( (fun nat (fun real real)), root ) 21.71/21.85 ( (fun real (fun real real)), log ) 21.71/21.85 ( (fun real (fun real real)), powr ) 21.71/21.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.71/21.85 ( (fun complex complex), cnj ) 21.71/21.85 ( (fun complex complex), expi ) 21.71/21.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.71/21.85 ( (fun nat (fun nat nat)), nat_gcd ) 21.71/21.85 ( (fun nat (fun nat nat)), nat_lcm ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.71/21.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.71/21.85 ( (fun int (fun (fun int bool) bool)), resSet ) 21.71/21.85 ( (fun int nat), nat_1 ) 21.71/21.85 ( (fun int nat), phi ) 21.71/21.85 ( (fun complex real), re ) 21.71/21.85 ( (fun complex real), im ) 21.71/21.85 ( (fun complex real), arg ) 21.71/21.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.71/21.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.71/21.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.71/21.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.71/21.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.71/21.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.71/21.85 ( (fun (product_prod nat nat) bool), pred_nat ) 21.71/21.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.71/21.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.71/21.85 ( (fun (fun int bool) int), (the int) ) 21.71/21.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.71/21.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.71/21.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.71/21.85 ( (fun real (fun real complex)), rcis ) 21.71/21.85 ( (fun real (fun real complex)), complex_1 ) 21.71/21.85 ( (fun int (fun int (fun int bool))), zcong ) 21.71/21.85 ( (fun int (fun int (fun int bool))), wset ) 21.71/21.85 ( (fun int (fun int (fun int bool))), noXRRset ) 21.71/21.85 ( (fun int (fun int (fun int bool))), bnorRset ) 21.71/21.85 ( (fun int (fun int (fun int bool))), zcongm ) 21.71/21.85 ( (fun real nat), natceiling ) 21.71/21.85 ( (fun real nat), natfloor ) 21.71/21.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.71/21.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.71/21.85 ( (fun int real), (real_1 int) ) 21.71/21.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.71/21.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.71/21.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.71/21.85 ( (fun complex nat), (size_size complex) ) 21.71/21.85 ( (fun complex nat), complex_size ) 21.71/21.85 ( (fun (fun nat rat) bool), vanishes ) 21.71/21.85 ( (fun (product_prod int int) rat), frct ) 21.71/21.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.71/21.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.71/21.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.71/21.85 ( (fun rat real), ratreal ) 21.71/21.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.71/21.85 ( (fun (fun int 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X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115140))) (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_115142)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115141) BOUND_VARIABLE_115143)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_115141)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115142) BOUND_VARIABLE_115143))))))) ) 21.71/21.85 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((Xa $$unsorted) (Na $$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)) Na))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Xa) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) Xa) Na)) zEven))))))) ) 21.71/21.85 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ( skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.85 ) 21.71/21.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115226 $$unsorted) (BOUND_VARIABLE_115227 $$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_115226) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_115227) BOUND_VARIABLE_115226)))) ) 21.71/21.85 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.71/21.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.71/21.85 ( 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))) ) 21.71/21.85 ( int, v, y ) 21.71/21.85 ( int, v, sa ) 21.71/21.85 ( int, v, x ) 21.71/21.85 ( int, v, r ) 21.71/21.85 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.86 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.86 ( int, w, y ) 21.71/21.86 ( int, w, sa ) 21.71/21.86 ( int, w, x ) 21.71/21.86 ( int, w, r ) 21.71/21.86 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.86 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.86 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.71/21.86 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.86 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.71/21.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( int, skv_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))) ) 21.71/21.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( 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))))) ) 21.71/21.86 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ( 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)))) ) 21.71/21.86 ( complex, ii, ii ) 21.71/21.86 ( 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)) ) 21.71/21.86 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.86 ) 21.71/21.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115244 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (group_add X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_115244)) (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_115244))))) ) 21.71/21.86 ( int, pls ) 21.71/21.86 ( int, (one_one int) ) 21.71/21.86 ( int, min ) 21.71/21.86 ( int, s ) 21.71/21.86 ( int, s1 ) 21.71/21.86 ( int, m ) 21.71/21.86 ( int, t ) 21.71/21.86 ( int, v ) 21.71/21.86 ( int, w ) 21.71/21.86 ( int, y ) 21.71/21.86 ( int, sa ) 21.71/21.86 ( int, x ) 21.71/21.86 ( int, r ) 21.71/21.86 ( int, m1 ) 21.71/21.86 ( int, skv_14 ) 21.71/21.86 ( int, skv_20 ) 21.71/21.86 ( (fun int int), bit1 ) 21.71/21.86 ( (fun int int), bit0 ) 21.71/21.86 ( (fun int int), succ ) 21.71/21.86 ( (fun int int), pred ) 21.71/21.86 ( (fun int int), (fact_fact int) ) 21.71/21.86 ( (fun int int), zfact ) 21.71/21.86 ( nat, n ) 21.71/21.86 ( nat, tn ) 21.71/21.86 ( bool, fTrue ) 21.71/21.86 ( bool, fFalse ) 21.71/21.86 ( real, pi ) 21.71/21.86 ( 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)))) ) 21.71/21.86 ( real, (one_one real) ) 21.71/21.86 ( 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) ) 21.71/21.86 ( (fun nat real), (real_1 nat) ) 21.71/21.86 ( (fun nat real), cos_coeff ) 21.71/21.86 ( (fun nat real), sin_coeff ) 21.71/21.86 ( (fun real real), sin ) 21.71/21.86 ( (fun real real), cos ) 21.71/21.86 ( (fun real real), sqrt ) 21.71/21.86 ( (fun real real), tan ) 21.71/21.86 ( (fun real real), ln ) 21.71/21.86 ( (fun real real), arctan ) 21.71/21.86 ( (fun real real), arcsin ) 21.71/21.86 ( (fun real real), arccos ) 21.71/21.86 ( (fun nat nat), suc ) 21.71/21.86 ( (fun nat nat), (fact_fact nat) ) 21.71/21.86 ( (fun nat nat), nat_size ) 21.71/21.86 ( (fun nat nat), (size_size nat) ) 21.71/21.86 ( (fun nat nat), fact ) 21.71/21.86 ( (filter nat), sequentially ) 21.71/21.86 ( (fun int (fun int rat)), fract ) 21.71/21.86 ( complex, ii ) 21.71/21.86 ( complex, (one_one complex) ) 21.71/21.86 ( (fun int bool), zOdd ) 21.71/21.86 ( (fun int bool), zprime ) 21.71/21.86 ( (fun int bool), zEven ) 21.71/21.86 ( (fun int bool), nat_neg ) 21.71/21.86 ( (fun int bool), nat_is_nat ) 21.71/21.86 ( (fun int bool), (even_odd_even int) ) 21.71/21.86 ( (fun int bool), twoSqu1091635170sum2sq ) 21.71/21.86 ( (fun int (fun int int)), legacy_zgcd ) 21.71/21.86 ( (fun int (fun int int)), (gcd_gcd int) ) 21.71/21.86 ( (fun int (fun int int)), inv ) 21.71/21.86 ( (fun int (fun int int)), multInv ) 21.71/21.86 ( (fun int (fun int int)), legendre ) 21.71/21.86 ( (fun int (fun int int)), standardRes ) 21.71/21.86 ( (fun int (fun int int)), nat_tsub ) 21.71/21.86 ( (fun int (fun int int)), z3div ) 21.71/21.86 ( (fun int (fun int int)), z3mod ) 21.71/21.86 ( (fun int (fun int int)), int_lcm ) 21.71/21.86 ( (fun int (fun int int)), int_gcd ) 21.71/21.86 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.71/21.86 ( (fun bool bool), fNot ) 21.71/21.86 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.71/21.86 ( (fun bool (fun bool bool)), fconj ) 21.71/21.86 ( (fun bool (fun bool bool)), fdisj ) 21.71/21.86 ( (fun bool (fun bool bool)), fimplies ) 21.71/21.86 ( (fun int (fun int bool)), quadRes ) 21.71/21.86 ( (fun int (fun int bool)), d22set ) 21.71/21.86 ( (fun int (fun int bool)), norRRset ) 21.71/21.86 ( (fun int (fun int bool)), sRStar ) 21.71/21.86 ( (fun int (fun int bool)), sr ) 21.71/21.86 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.71/21.86 ( (fun nat bool), (even_odd_even nat) ) 21.71/21.86 ( (fun nat bool), prime ) 21.71/21.86 ( (fun real complex), cis ) 21.71/21.86 ( (fun nat (fun nat bool)), coprime ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.71/21.86 ( (fun (product_prod int int) bool), frac_1 ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.71/21.86 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.71/21.86 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.71/21.86 ( (fun (fun int bool) bool), nat_nat_set ) 21.71/21.86 ( (fun nat (fun real real)), root ) 21.71/21.86 ( (fun real (fun real real)), log ) 21.71/21.86 ( (fun real (fun real real)), powr ) 21.71/21.86 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.71/21.86 ( (fun complex complex), cnj ) 21.71/21.86 ( (fun complex complex), expi ) 21.71/21.86 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.71/21.86 ( (fun nat (fun nat nat)), nat_gcd ) 21.71/21.86 ( (fun nat (fun nat nat)), nat_lcm ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.71/21.86 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.71/21.86 ( (fun int (fun (fun int bool) bool)), resSet ) 21.71/21.86 ( (fun int nat), nat_1 ) 21.71/21.86 ( (fun int nat), phi ) 21.71/21.86 ( (fun complex real), re ) 21.71/21.86 ( (fun complex real), im ) 21.71/21.86 ( (fun complex real), arg ) 21.71/21.86 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.71/21.86 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.71/21.86 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.71/21.86 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.71/21.86 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.71/21.86 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.71/21.86 ( (fun (product_prod nat nat) bool), pred_nat ) 21.71/21.86 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.71/21.86 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.71/21.86 ( (fun (fun int bool) int), (the int) ) 21.71/21.86 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.71/21.86 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.71/21.86 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.71/21.86 ( (fun real (fun real complex)), rcis ) 21.71/21.86 ( (fun real (fun real complex)), complex_1 ) 21.71/21.86 ( (fun int (fun int (fun int bool))), zcong ) 21.71/21.86 ( (fun int (fun int (fun int bool))), wset ) 21.71/21.86 ( (fun int (fun int (fun int bool))), noXRRset ) 21.71/21.86 ( (fun int (fun int (fun int bool))), bnorRset ) 21.71/21.86 ( (fun int (fun int (fun int bool))), zcongm ) 21.71/21.86 ( (fun real nat), natceiling ) 21.71/21.86 ( (fun real nat), natfloor ) 21.71/21.86 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.71/21.86 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.71/21.86 ( (fun int real), (real_1 int) ) 21.71/21.86 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.71/21.86 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.71/21.86 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.71/21.86 ( (fun complex nat), (size_size complex) ) 21.71/21.86 ( (fun complex nat), complex_size ) 21.71/21.86 ( (fun (fun nat rat) bool), vanishes ) 21.71/21.86 ( (fun (product_prod int int) rat), frct ) 21.71/21.86 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.71/21.86 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.71/21.86 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.71/21.86 ( (fun rat real), ratreal ) 21.71/21.86 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.71/21.86 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.71/21.86 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.71/21.86 ( (fun rat (product_prod int int)), quotient_of ) 21.71/21.86 ( (fun int (fun nat nat)), nat_aux ) 21.71/21.86 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.71/21.86 ( (fun int (list int)), quickc666637781d_zero ) 21.71/21.86 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.71/21.86 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.71/21.86 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.71/21.86 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.71/21.86 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.71/21.86 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.71/21.86 ( (fun code_code_numeral int), code_int_of ) 21.71/21.86 ) 21.71/21.86 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X) _let_1))) (= (hAPP real int (archimedean_ceiling real) X) (ti int N))))) ) 21.71/21.86 ( (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.86 ) 21.71/21.86 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool zprime P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 A_1) P_5))) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP int int (hAPP int _let_0 (times_times int) A_1) (hAPP int int (hAPP int _let_0 inv P_5) A_1))) (one_one int)) P_5)))))) ) 21.71/21.86 ( (one_one int), t ) 21.71/21.86 ( min, min ) 21.71/21.86 ( min, (zero_zero int) ) 21.71/21.86 ( (zero_zero int), pls ) 21.71/21.86 ( (zero_zero int), (one_one int) ) 21.71/21.86 ( (zero_zero int), min ) 21.71/21.86 ( (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))) ) 21.71/21.86 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( 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))) ) 21.71/21.86 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.86 ( 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))) ) 21.71/21.86 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.86 ( 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))) ) 21.71/21.89 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.89 ) 21.71/21.90 (instantiation (forall ((W $$unsorted)) (= (hAPP int nat nat_1 (hAPP int int (number_number_of int) W)) (hAPP int nat (number_number_of nat) W)) ) 21.71/21.90 ( pls ) 21.71/21.90 ( (hAPP int int bit1 pls) ) 21.71/21.90 ( min ) 21.71/21.90 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115386 $$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_115386) (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_115386) BOUND_VARIABLE_115386)))) ) 21.71/21.90 ( int, (one_one int) ) 21.71/21.90 ( 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)))) ) 21.71/21.90 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( 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) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( int, y ) 21.71/21.90 ( int, sa ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.90 ( int, x ) 21.71/21.90 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.71/21.90 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.71/21.90 ( int, r ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.71/21.90 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.71/21.90 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.71/21.90 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.71/21.90 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.71/21.90 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.71/21.90 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.71/21.90 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( int, skv_13 ) 21.71/21.90 ( int, skv_19 ) 21.71/21.90 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( nat, (one_one nat) ) 21.71/21.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( 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))))) ) 21.71/21.90 ( complex, ii ) 21.71/21.90 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( 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)) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((R_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (number_number_of real))) (let ((_let_1 (number_number_of rat))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 R_3)) (hAPP int real _let_0 S_3)) (hAPP rat real ratreal (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_1 R_3)) (hAPP int rat _let_1 S_3)))))) ) 21.71/21.90 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((P_1 $$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_2 $$unsorted) (I_2 $$unsorted)) (let ((_let_2 (hAPP int (fun int bool) P_1 D_2))) (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_2) I_2)))) (and (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) D_2) 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))))) ) 21.71/21.90 ( (ord_less int), (one_one int), t ) 21.71/21.90 ( (ord_less int), min, min ) 21.71/21.90 ( (ord_less int), min, (zero_zero int) ) 21.71/21.90 ( (ord_less int), (zero_zero int), pls ) 21.71/21.90 ( (ord_less int), (zero_zero int), (one_one int) ) 21.71/21.90 ( (ord_less int), (zero_zero int), min ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( (ord_less_eq int), (one_one int), t ) 21.71/21.90 ( (ord_less_eq int), min, pls ) 21.71/21.90 ( (ord_less_eq int), min, min ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), pls ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), min ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), s ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), skv_4 ) 21.71/21.90 ( (ord_less_eq int), (zero_zero int), skv_5 ) 21.71/21.90 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( 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) ) 21.71/21.90 ( (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) (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)) ) 21.71/21.90 ( (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (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))) ) 21.71/21.90 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (division_ring X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 21.71/21.90 ( rat ) 21.71/21.90 ( int ) 21.71/21.90 ( (fun int int) ) 21.71/21.90 ( nat ) 21.71/21.90 ( bool ) 21.71/21.90 ( real ) 21.71/21.90 ( (fun nat real) ) 21.71/21.90 ( (fun real real) ) 21.71/21.90 ( complex ) 21.71/21.90 ( (fun int bool) ) 21.71/21.90 ( (product_prod int int) ) 21.71/21.90 ( (fun (product_prod int int) int) ) 21.71/21.90 ( (fun int (fun int bool)) ) 21.71/21.90 ( (fun nat bool) ) 21.71/21.90 ( (fun (product_prod int int) bool) ) 21.71/21.90 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.71/21.90 ( (fun real bool) ) 21.71/21.90 ( code_code_numeral ) 21.71/21.90 ( (fun int (fun int (fun int bool))) ) 21.71/21.90 ( (fun int real) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int (fun nat int) (power_power int) A_1))) (= (hAPP int int (hAPP int (fun int int) (times_times int) A_1) (hAPP nat int _let_2 (hAPP int nat _let_1 (hAPP int int bit0 _let_0)))) (hAPP nat int _let_2 (hAPP int nat _let_1 (hAPP int int bit1 _let_0))))))) ) 21.71/21.90 ( s ) 21.71/21.90 ( s1 ) 21.71/21.90 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.71/21.90 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ( v ) 21.71/21.90 ( w ) 21.71/21.90 ( y ) 21.71/21.90 ( sa ) 21.71/21.90 ( x ) 21.71/21.90 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 21.71/21.90 ( r ) 21.71/21.90 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.71/21.90 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 21.71/21.90 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 21.71/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.71/21.90 ( skv_6 ) 21.71/21.90 ( skv_7 ) 21.71/21.90 ( skv_13 ) 21.71/21.90 ( skv_16 ) 21.71/21.90 ( skv_19 ) 21.71/21.90 ( skv_23 ) 21.71/21.90 ( skv_24 ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (= N (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc _let_0)))))) ) 21.71/21.90 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( n ) 21.71/21.90 ( tn ) 21.71/21.90 ( (hAPP int nat nat_1 t) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115476 $$unsorted) (BOUND_VARIABLE_115477 $$unsorted) (BOUND_VARIABLE_115478 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (let ((_let_4 (hAPP nat nat suc BOUND_VARIABLE_115477))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_115476) _let_4)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_115478) _let_4)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_115478))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115476) BOUND_VARIABLE_115478)))))))) ) 21.71/21.90 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat nat suc (zero_zero nat)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115525 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun nat _let_0))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (fun _let_0 X_a))) (or (not (metric_space X_a)) (not (comm_monoid_add X_a)) (= (hAPP _let_2 X_a (lim X_a) (hAPP _let_1 _let_2 (hAPP _let_3 (fun _let_1 _let_2) (combb _let_0 X_a nat) (hAPP _let_2 _let_3 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_115525)) (hAPP nat _let_1 (ord_atLeastLessThan nat) (zero_zero nat)))) (hAPP _let_2 X_a (suminf X_a) BOUND_VARIABLE_115525))))))) ) 21.71/21.90 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.71/21.90 ) 21.71/21.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115547 $$unsorted) (BOUND_VARIABLE_115548 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (not (ring_char_0 X_a)) (= (= (hAPP int X_a _let_0 BOUND_VARIABLE_115548) (hAPP int X_a _let_0 BOUND_VARIABLE_115547)) (= (ti int BOUND_VARIABLE_115548) (ti int BOUND_VARIABLE_115547))))) ) 21.71/21.90 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.90 ( int, (hAPP int int bit1 pls), pls ) 21.71/21.90 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 21.71/21.90 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.90 ( int, min, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), min ) 21.71/21.90 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), min ) 21.71/21.90 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( 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))) ) 21.71/21.90 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 21.71/21.90 ( nat, pls, pls ) 21.71/21.90 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.90 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 21.71/21.90 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.71/21.90 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( real, min, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), min ) 21.71/21.90 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.71/21.90 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.71/21.90 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( 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)))))))) ) 21.80/21.90 ( 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 pls)) ) 21.80/21.90 ( complex, min, min ) 21.80/21.90 ( complex, min, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.90 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), min ) 21.80/21.90 ( quickcheck_code_int, pls, pls ) 21.80/21.90 ( quickcheck_code_int, pls, (hAPP int int bit1 pls) ) 21.80/21.90 ( quickcheck_code_int, pls, (one_one int) ) 21.80/21.90 ( quickcheck_code_int, (hAPP int int bit1 pls), pls ) 21.80/21.90 ( quickcheck_code_int, (one_one int), (hAPP int int bit1 pls) ) 21.80/21.90 ( code_code_numeral, pls, pls ) 21.80/21.90 ( code_code_numeral, pls, (hAPP int int bit1 pls) ) 21.80/21.90 ( code_code_numeral, (hAPP int int bit1 pls), pls ) 21.80/21.90 ) 21.80/21.90 (instantiation (forall ((R_3 $$unsorted) (Q_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (zero_zero int)) A_1))) (not (= (hAPP int int (hAPP int _let_0 (plus_plus int) R_3) (hAPP int int (hAPP int _let_0 (times_times int) A_1) Q_3)) (ti int A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 R_3) A_1))) (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (one_one int)) Q_3)))))) ) 21.80/21.90 ( (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.90 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w, y ) 21.80/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.80/21.90 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w, sa ) 21.80/21.90 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.90 ) 21.80/21.90 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115577 $$unsorted) (BOUND_VARIABLE_115578 $$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_115577))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_115578)) (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_115578)))))) ) 21.80/21.90 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.90 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.80/21.90 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.90 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.80/21.90 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.90 ( 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))))))))) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ) 21.80/21.90 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root Na) Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0))))))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ) 21.80/21.90 (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)))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 21.80/21.90 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( (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) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) min), min ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 21.80/21.90 ( nat_neg, (one_one int) ) 21.80/21.90 ( nat_neg, (zero_zero int) ) 21.80/21.90 ( nat_neg, (hAPP int int (number_number_of int) min) ) 21.80/21.90 ( nat_is_nat, (one_one int) ) 21.80/21.90 ( nat_is_nat, (zero_zero int) ) 21.80/21.90 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.90 ( nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 21.80/21.90 ( (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 21.80/21.90 ( (even_odd_even int), (one_one int) ) 21.80/21.90 ( (even_odd_even int), (zero_zero int) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) pls), pls ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) pls), min ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 21.80/21.90 ( 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))) ) 21.80/21.90 ( twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq int) min), min ) 21.80/21.90 ( (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.90 ( (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) (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)) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (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))) ) 21.80/21.90 ( (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.90 ( (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.91 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.91 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (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_1 _let_2 _let_3) P_4))) (not (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) P_4) zOdd))) (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (zero_zero int)) (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_3)))))))) ) 21.80/21.91 ( (one_one int) ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( y ) 21.80/21.91 ( x ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.80/21.91 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.80/21.91 ( (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))) m1))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Y $$unsorted) (R_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less_eq int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 _let_3) B_8)))) (or (not (= (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) B_8) Y)) R_5) (ti int A_9))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 B_8) R_5))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 R_5) _let_3))))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 R_5) B_8))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 _let_3) R_5))))) (= _let_3 (ti int B_8)) (= (hAPP int int (hAPP int _let_0 (div_div int) A_9) B_8) (ti int Y))))))))) ) 21.80/21.91 ( min, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.80/21.91 ( s, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.80/21.91 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 21.80/21.91 ( m, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 21.80/21.91 ( v, x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.80/21.91 ( sa, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.80/21.91 ( r, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 21.80/21.91 ( m1, r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115659 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_115659)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_115659) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_115659))) ) 21.80/21.91 ( int, pls ) 21.80/21.91 ( int, min ) 21.80/21.91 ( int, s ) 21.80/21.91 ( int, s1 ) 21.80/21.91 ( int, m ) 21.80/21.91 ( int, t ) 21.80/21.91 ( int, v ) 21.80/21.91 ( int, w ) 21.80/21.91 ( int, y ) 21.80/21.91 ( int, sa ) 21.80/21.91 ( int, x ) 21.80/21.91 ( int, r ) 21.80/21.91 ( int, m1 ) 21.80/21.91 ( int, skv_14 ) 21.80/21.91 ( int, skv_20 ) 21.80/21.91 ( (fun int int), bit1 ) 21.80/21.91 ( (fun int int), bit0 ) 21.80/21.91 ( (fun int int), succ ) 21.80/21.91 ( (fun int int), pred ) 21.80/21.91 ( (fun int int), (fact_fact int) ) 21.80/21.91 ( (fun int int), zfact ) 21.80/21.91 ( nat, n ) 21.80/21.91 ( nat, tn ) 21.80/21.91 ( bool, fTrue ) 21.80/21.91 ( bool, fFalse ) 21.80/21.91 ( real, pi ) 21.80/21.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( real, (zero_zero real) ) 21.80/21.91 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( 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))))))))) ) 21.80/21.91 ( (fun nat real), (real_1 nat) ) 21.80/21.91 ( (fun nat real), cos_coeff ) 21.80/21.91 ( (fun nat real), sin_coeff ) 21.80/21.91 ( (fun real real), sin ) 21.80/21.91 ( (fun real real), cos ) 21.80/21.91 ( (fun real real), sqrt ) 21.80/21.91 ( (fun real real), tan ) 21.80/21.91 ( (fun real real), ln ) 21.80/21.91 ( (fun real real), arctan ) 21.80/21.91 ( (fun real real), arcsin ) 21.80/21.91 ( (fun real real), arccos ) 21.80/21.91 ( (fun nat nat), suc ) 21.80/21.91 ( (fun nat nat), (fact_fact nat) ) 21.80/21.91 ( (fun nat nat), nat_size ) 21.80/21.91 ( (fun nat nat), (size_size nat) ) 21.80/21.91 ( (fun nat nat), fact ) 21.80/21.91 ( (filter nat), sequentially ) 21.80/21.91 ( (fun int (fun int rat)), fract ) 21.80/21.91 ( complex, ii ) 21.80/21.91 ( (fun int bool), zOdd ) 21.80/21.91 ( (fun int bool), zprime ) 21.80/21.91 ( (fun int bool), zEven ) 21.80/21.91 ( (fun int bool), nat_neg ) 21.80/21.91 ( (fun int bool), nat_is_nat ) 21.80/21.91 ( (fun int bool), (even_odd_even int) ) 21.80/21.91 ( (fun int bool), twoSqu1091635170sum2sq ) 21.80/21.91 ( (fun int (fun int int)), legacy_zgcd ) 21.80/21.91 ( (fun int (fun int int)), (gcd_gcd int) ) 21.80/21.91 ( (fun int (fun int int)), inv ) 21.80/21.91 ( (fun int (fun int int)), multInv ) 21.80/21.91 ( (fun int (fun int int)), legendre ) 21.80/21.91 ( (fun int (fun int int)), standardRes ) 21.80/21.91 ( (fun int (fun int int)), nat_tsub ) 21.80/21.91 ( (fun int (fun int int)), z3div ) 21.80/21.91 ( (fun int (fun int int)), z3mod ) 21.80/21.91 ( (fun int (fun int int)), int_lcm ) 21.80/21.91 ( (fun int (fun int int)), int_gcd ) 21.80/21.91 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.80/21.91 ( (fun bool bool), fNot ) 21.80/21.91 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.80/21.91 ( (fun bool (fun bool bool)), fconj ) 21.80/21.91 ( (fun bool (fun bool bool)), fdisj ) 21.80/21.91 ( (fun bool (fun bool bool)), fimplies ) 21.80/21.91 ( (fun int (fun int bool)), quadRes ) 21.80/21.91 ( (fun int (fun int bool)), d22set ) 21.80/21.91 ( (fun int (fun int bool)), norRRset ) 21.80/21.91 ( (fun int (fun int bool)), sRStar ) 21.80/21.91 ( (fun int (fun int bool)), sr ) 21.80/21.91 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.80/21.91 ( (fun nat bool), (even_odd_even nat) ) 21.80/21.91 ( (fun nat bool), prime ) 21.80/21.91 ( (fun real complex), cis ) 21.80/21.91 ( (fun nat (fun nat bool)), coprime ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.80/21.91 ( (fun (product_prod int int) bool), frac_1 ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.80/21.91 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.80/21.91 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.80/21.91 ( (fun (fun int bool) bool), nat_nat_set ) 21.80/21.91 ( (fun nat (fun real real)), root ) 21.80/21.91 ( (fun real (fun real real)), log ) 21.80/21.91 ( (fun real (fun real real)), powr ) 21.80/21.91 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.80/21.91 ( (fun complex complex), cnj ) 21.80/21.91 ( (fun complex complex), expi ) 21.80/21.91 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.80/21.91 ( (fun nat (fun nat nat)), nat_gcd ) 21.80/21.91 ( (fun nat (fun nat nat)), nat_lcm ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.80/21.91 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.80/21.91 ( (fun int (fun (fun int bool) bool)), resSet ) 21.80/21.91 ( (fun int nat), nat_1 ) 21.80/21.91 ( (fun int nat), phi ) 21.80/21.91 ( (fun complex real), re ) 21.80/21.91 ( (fun complex real), im ) 21.80/21.91 ( (fun complex real), arg ) 21.80/21.91 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.80/21.91 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.80/21.91 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.80/21.91 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.80/21.91 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.80/21.91 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.80/21.91 ( (fun (product_prod nat nat) bool), pred_nat ) 21.80/21.91 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.80/21.91 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.80/21.91 ( (fun (fun int bool) int), (the int) ) 21.80/21.91 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.80/21.91 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.80/21.91 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.80/21.91 ( (fun real (fun real complex)), rcis ) 21.80/21.91 ( (fun real (fun real complex)), complex_1 ) 21.80/21.91 ( (fun int (fun int (fun int bool))), zcong ) 21.80/21.91 ( (fun int (fun int (fun int bool))), wset ) 21.80/21.91 ( (fun int (fun int (fun int bool))), noXRRset ) 21.80/21.91 ( (fun int (fun int (fun int bool))), bnorRset ) 21.80/21.91 ( (fun int (fun int (fun int bool))), zcongm ) 21.80/21.91 ( (fun real nat), natceiling ) 21.80/21.91 ( (fun real nat), natfloor ) 21.80/21.91 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.80/21.91 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.80/21.91 ( (fun int real), (real_1 int) ) 21.80/21.91 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.80/21.91 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.80/21.91 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.80/21.91 ( (fun complex nat), (size_size complex) ) 21.80/21.91 ( (fun complex nat), complex_size ) 21.80/21.91 ( (fun (fun nat rat) bool), vanishes ) 21.80/21.91 ( (fun (product_prod int int) rat), frct ) 21.80/21.91 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.80/21.91 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.80/21.91 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.80/21.91 ( (fun rat real), ratreal ) 21.80/21.91 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.80/21.91 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.80/21.91 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.80/21.91 ( (fun rat (product_prod int int)), quotient_of ) 21.80/21.91 ( (fun int (fun nat nat)), nat_aux ) 21.80/21.91 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.80/21.91 ( (fun int (list int)), quickc666637781d_zero ) 21.80/21.91 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.80/21.91 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.80/21.91 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.80/21.91 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.80/21.91 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.80/21.91 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.80/21.91 ( (fun code_code_numeral int), code_int_of ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((N $$unsorted) (M $$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))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) N) M)))))) ) 21.80/21.91 ( pls, (zero_zero int) ) 21.80/21.91 ( (one_one int), (zero_zero int) ) 21.80/21.91 ( min, min ) 21.80/21.91 ( min, (zero_zero int) ) 21.80/21.91 ( (zero_zero int), min ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.80/21.91 ( t, (one_one int) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (= Ma Na) (= (hAPP nat int _let_0 Na) (hAPP nat int _let_0 Ma)))) ) 21.80/21.91 ( (zero_zero nat), (zero_zero nat) ) 21.80/21.91 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( (zero_zero nat), n ) 21.80/21.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), n ) 21.80/21.91 ( (one_one nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (one_one nat) ) 21.80/21.91 ( (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))) ) 21.80/21.91 ( n, (zero_zero nat) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115709 $$unsorted) (BOUND_VARIABLE_115710 $$unsorted) (BOUND_VARIABLE_115711 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115710) BOUND_VARIABLE_115711))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_115710))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_115710) BOUND_VARIABLE_115709)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_115711) BOUND_VARIABLE_115709)))))))) ) 21.80/21.91 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real im Z_1)) (hAPP complex real (norm_norm complex) Z_1)) (hAPP complex real im (hAPP complex complex (sgn_sgn complex) Z_1))) ) 21.80/21.91 ( ii ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115775 $$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_115775))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115775) _let_2))))))) ) 21.80/21.91 ( int, pls ) 21.80/21.91 ( int, (one_one int) ) 21.80/21.91 ( int, min ) 21.80/21.91 ( int, (zero_zero int) ) 21.80/21.91 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.80/21.91 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.80/21.91 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.80/21.91 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.80/21.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( real, (one_one real) ) 21.80/21.91 ( real, (zero_zero real) ) 21.80/21.91 ( 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) ) 21.80/21.91 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( real, skv_10 ) 21.80/21.91 ( complex, ii ) 21.80/21.91 ( complex, (one_one complex) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((N_3 $$unsorted)) (= (not (forall ((M_2 $$unsorted)) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X_1) N_3))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) X_1) M_2)))) )) )) (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) N_3))) ) 21.80/21.91 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_115803 $$unsorted) (BOUND_VARIABLE_115804 $$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_115803) BOUND_VARIABLE_115804)) (= (ti X_a BOUND_VARIABLE_115803) (ti X_a BOUND_VARIABLE_115804)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_115804) BOUND_VARIABLE_115803))))) ) 21.80/21.91 ( int, pls, (zero_zero int) ) 21.80/21.91 ( int, (one_one int), (zero_zero int) ) 21.80/21.91 ( int, (one_one int), t ) 21.80/21.91 ( int, min, min ) 21.80/21.91 ( int, min, (zero_zero int) ) 21.80/21.91 ( int, (zero_zero int), pls ) 21.80/21.91 ( int, (zero_zero int), (one_one int) ) 21.80/21.91 ( int, (zero_zero int), min ) 21.80/21.91 ( 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))) ) 21.80/21.91 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( 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))) ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 21.80/21.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 21.80/21.91 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 21.80/21.91 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.91 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.80/21.91 ( int, t, (one_one int) ) 21.80/21.91 ( 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))) ) 21.80/21.91 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( 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))) ) 21.80/21.91 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.91 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( nat, (zero_zero nat), n ) 21.80/21.91 ( nat, (zero_zero nat), tn ) 21.80/21.91 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.80/21.91 ( nat, n, (zero_zero nat) ) 21.80/21.91 ( nat, tn, (zero_zero nat) ) 21.80/21.91 ( real, pi, (zero_zero real) ) 21.80/21.91 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( 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)) ) 21.80/21.91 ( 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)))) ) 21.80/21.91 ( real, (hAPP real real (hAPP 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))) ) 21.80/21.91 ( real, (hAPP real real (hAPP 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) ) 21.80/21.91 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( real, (zero_zero real), pi ) 21.80/21.91 ( 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)))) ) 21.80/21.91 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( 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))))) ) 21.80/21.91 ( real, (zero_zero real), skv_2 ) 21.80/21.91 ( real, (zero_zero real), skv_9 ) 21.80/21.91 ( real, (zero_zero real), skv_12 ) 21.80/21.91 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 21.80/21.91 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.80/21.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.80/21.91 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.80/21.91 ( 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) ) 21.80/21.91 ( 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 ) 21.80/21.91 ( real, skv_2, (zero_zero real) ) 21.80/21.91 ( real, skv_9, (zero_zero real) ) 21.80/21.91 ( real, skv_12, (zero_zero real) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int _let_0 _let_1 Z1))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 Z2)) Z3) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 Z2) Z3)))))) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), m1 ) 21.80/21.91 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (forall ((M_2 $$unsorted)) (not (= N (hAPP nat nat suc M_2))) ))) ) 21.80/21.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( n ) 21.80/21.91 ( tn ) 21.80/21.91 ) 21.80/21.91 (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)) ) 21.80/21.91 ( pls ) 21.80/21.91 ( (one_one int) ) 21.80/21.91 ( min ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( (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) ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.80/21.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.80/21.91 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.80/21.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ) 21.80/21.91 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real (real_1 nat) Na)) (zero_zero real))) (= (zero_zero nat) Na)) ) 21.80/21.91 ( (zero_zero nat) ) 21.80/21.91 ( (one_one nat) ) 21.80/21.91 ) 21.80/21.91 (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))) ) 21.80/21.91 ( int, int ) 21.80/21.91 ( int, (product_prod int int) ) 21.80/21.91 ( nat, nat ) 21.80/21.91 ( real, real ) 21.80/21.91 ( (product_prod int int), (product_prod int int) ) 21.80/21.91 ( quickcheck_code_int, quickcheck_code_int ) 21.80/21.91 ( code_code_numeral, code_code_numeral ) 21.80/21.91 ( (product_prod nat nat), (product_prod nat nat) ) 21.80/21.91 ) 21.80/21.91 (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))) ) 21.80/21.91 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 21.80/21.91 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 21.80/21.91 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 21.80/21.91 ( 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))) ) 21.80/21.91 ( int, int, bit1, pls ) 21.80/21.91 ( int, int, bit1, (hAPP int int bit1 pls) ) 21.80/21.91 ( int, int, bit1, min ) 21.80/21.91 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.91 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.80/21.91 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.80/21.91 ( 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)))))) ) 21.80/21.91 ( 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))))))) ) 21.80/21.91 ( int, int, (uminus_uminus int), pls ) 21.80/21.91 ( int, int, (uminus_uminus int), (one_one int) ) 21.80/21.91 ( int, int, (uminus_uminus int), min ) 21.80/21.91 ( int, int, bit0, pls ) 21.80/21.91 ( int, int, bit0, (hAPP int int bit1 pls) ) 21.80/21.91 ( int, int, bit0, min ) 21.80/21.91 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.91 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.80/21.91 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.91 ( int, int, succ, pls ) 21.80/21.91 ( int, int, succ, min ) 21.80/21.91 ( int, int, (number_number_of int), pls ) 21.80/21.91 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 21.80/21.91 ( int, int, (number_number_of int), min ) 21.80/21.91 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.91 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.91 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.80/21.91 ( 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 ) 21.80/21.91 ( 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) ) 21.80/21.91 ( int, int, (abs_abs int), v ) 21.80/21.91 ( int, int, (abs_abs int), w ) 21.80/21.91 ( int, int, (abs_abs int), skv_14 ) 21.80/21.91 ( int, int, (abs_abs int), skv_20 ) 21.80/21.91 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.91 ( int, int, pred, pls ) 21.80/21.91 ( int, int, pred, min ) 21.80/21.91 ( 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)))), (hAPP int int (abs_abs int) w) ) 21.80/21.91 ( 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)))), (hAPP int int (abs_abs int) v) ) 21.80/21.91 ( 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)))), (hAPP int int (abs_abs int) skv_14) ) 21.80/21.91 ( 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)))), (hAPP int int (abs_abs int) skv_20) ) 21.80/21.91 ( int, int, (fact_fact int), (one_one int) ) 21.80/21.91 ( int, int, (fact_fact int), (zero_zero int) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1 ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), skv_3 ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) sa), v ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) sa), w ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP nat int (hAPP int _let_2 _let_3 x) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 y) _let_1))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) x), v ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) x), w ) 21.80/21.91 ( 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) x) v))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) y), v ) 21.80/21.91 ( int, int, (hAPP int (fun int int) (times_times int) y), w ) 21.80/21.91 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 x) v)) (hAPP int int (hAPP int _let_0 _let_2 y) w))) (hAPP int nat (number_number_of nat) (hAPP 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((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.80/21.92 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.80/21.92 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.92 ( int, int, (hAPP int (fun int int) (times_times int) skv_13), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.92 ( int, int, (hAPP int (fun int int) (times_times int) skv_19), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.92 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 21.80/21.92 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (semiring_1_of_nat int), (one_one nat) ) 21.80/21.92 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (semiring_1_of_nat int), n ) 21.80/21.92 ( int, nat, (hAPP int (fun nat int) (power_power int) v), (hAPP int nat 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(power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat 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(hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))))), (hAPP int 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pls))))) m)) (one_one int))) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int 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(hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.80/21.92 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.92 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 21.80/21.92 ( bool, nat, (even_odd_even nat), (one_one nat) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 21.80/21.92 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 21.80/21.92 ( bool, nat, prime, (zero_zero nat) ) 21.80/21.92 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 21.80/21.92 ( 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)))) ) 21.80/21.92 ( 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)))) ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 21.80/21.92 ( 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)))) ) 21.80/21.92 ( 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)))) ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 21.80/21.92 ( bool, 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(hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 21.80/21.92 ( 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)))) ) 21.80/21.92 ( 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))) ) 21.80/21.92 ( 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) ) 21.80/21.92 ( bool, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 21.80/21.92 ( 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 ) 21.80/21.92 ( 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 ) 21.80/21.92 ( 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) ) 21.80/21.92 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( bool, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 21.80/21.92 ( bool, (filter nat), (trivial_limit nat), sequentially ) 21.80/21.92 ( 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)) ) 21.80/21.92 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 21.80/21.92 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 21.80/21.92 ( 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) ) 21.80/21.92 ( 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))))) ) 21.80/21.92 ( real, rat, ratreal, (one_one rat) ) 21.80/21.92 ( real, rat, ratreal, (zero_zero rat) ) 21.80/21.92 ( real, int, (number_number_of real), min ) 21.80/21.92 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.92 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.92 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.80/21.93 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.93 ( 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)))))))) ) 21.80/21.93 ( real, int, (real_1 int), (one_one int) ) 21.80/21.93 ( real, int, (real_1 int), (zero_zero int) ) 21.80/21.93 ( real, nat, (real_1 nat), (zero_zero nat) ) 21.80/21.93 ( real, nat, (real_1 nat), (one_one nat) ) 21.80/21.93 ( real, real, sin, pi ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, sin, (zero_zero real) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.80/21.93 ( real, real, cos, pi ) 21.80/21.93 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, cos, (zero_zero real) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.80/21.93 ( real, real, cos, skv_10 ) 21.80/21.93 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( real, 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)))) ) 21.80/21.93 ( real, real, (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)))) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, (uminus_uminus real), (one_one real) ) 21.80/21.93 ( 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) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( 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))))))))) ) 21.80/21.93 ( real, real, (sgn_sgn real), (zero_zero real) ) 21.80/21.93 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( real, real, sqrt, (one_one real) ) 21.80/21.93 ( real, real, sqrt, (zero_zero real) ) 21.80/21.93 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( real, real, tan, pi ) 21.80/21.93 ( real, real, tan, (zero_zero real) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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)))) ) 21.80/21.93 ( real, real, ln, (one_one real) ) 21.80/21.93 ( real, real, (inverse_inverse real), (zero_zero real) ) 21.80/21.93 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 21.80/21.93 ( real, real, (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.80/21.93 ( real, real, arctan, (one_one real) ) 21.80/21.93 ( real, real, arctan, (zero_zero real) ) 21.80/21.93 ( 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))))) ) 21.80/21.93 ( 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)))))))))) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 21.80/21.93 ( 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)))))) ) 21.80/21.93 ( real, real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))), (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))))))))))) ) 21.80/21.93 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 21.80/21.93 ( real, complex, re, (zero_zero complex) ) 21.80/21.93 ( real, complex, re, ii ) 21.80/21.93 ( real, complex, re, (one_one complex) ) 21.80/21.93 ( real, complex, im, (zero_zero complex) ) 21.80/21.93 ( real, complex, im, ii ) 21.80/21.93 ( real, complex, im, (one_one complex) ) 21.80/21.93 ( real, (fun real bool), (the real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2)))))))))))))) ) 21.80/21.93 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min) ) 21.80/21.93 ( (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)))) ) 21.80/21.93 ( (fun nat real), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), (one_one real) ) 21.80/21.93 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 21.80/21.93 ( (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))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 21.80/21.93 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (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)))))) ) 21.80/21.93 ( (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 ) 21.80/21.93 ( (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)))) ) 21.80/21.93 ( (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 ) 21.80/21.93 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( (fun real real), real, (inverse_divide real), pi ) 21.80/21.93 ( (fun real real), real, (inverse_divide real), (one_one real) ) 21.80/21.93 ( (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)))) ) 21.80/21.93 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.80/21.93 ( (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)))) ) 21.80/21.93 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.80/21.93 ( (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)))) ) 21.80/21.93 ( (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))))) ) 21.80/21.93 ( (fun real real), real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.80/21.93 ( (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 ) 21.80/21.93 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 21.80/21.93 ( (fun nat nat), nat, (minus_minus nat), (hAPP int nat nat_1 t) ) 21.80/21.93 ( (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))) ) 21.80/21.93 ( (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) ) 21.80/21.93 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 21.80/21.93 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 21.80/21.93 ( (fun int rat), int, fract, (one_one int) ) 21.80/21.93 ( (fun int rat), int, fract, (zero_zero int) ) 21.80/21.93 ( complex, int, (number_number_of complex), min ) 21.80/21.93 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 21.80/21.93 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 21.80/21.93 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min) ) 21.80/21.93 ( complex, real, (of_real complex), pi ) 21.80/21.93 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 21.80/21.93 ( complex, real, cis, (zero_zero real) ) 21.80/21.93 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 21.80/21.93 ( complex, complex, cnj, (zero_zero complex) ) 21.80/21.93 ( complex, complex, cnj, ii ) 21.80/21.93 ( complex, complex, cnj, (one_one complex) ) 21.80/21.93 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 21.80/21.93 ( complex, complex, (uminus_uminus complex), ii ) 21.80/21.93 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 21.80/21.93 ( complex, complex, expi, (zero_zero complex) ) 21.80/21.93 ( 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))) ) 21.80/21.93 ( complex, complex, (inverse_inverse complex), ii ) 21.80/21.93 ( 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) ) 21.80/21.93 ( 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 ) 21.80/21.93 ( (fun int bool), int, (ord_less int), (one_one int) ) 21.80/21.93 ( (fun int bool), int, (ord_less int), min ) 21.80/21.93 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 21.80/21.93 ( (fun int bool), int, (ord_less int), s ) 21.80/21.93 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.80/21.93 ( (fun int bool), int, (ord_less int), t ) 21.80/21.93 ( (fun int bool), int, (ord_less int), m1 ) 21.80/21.93 ( (fun int bool), int, (ord_less int), skv_4 ) 21.80/21.93 ( (fun int bool), int, (ord_less int), skv_5 ) 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((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int)))))))), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 21.88/22.03 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (product_snd int int))) (let ((_let_5 (fun _let_2 (fun _let_2 bool)))) (let ((_let_6 (fun _let_2 _let_1))) (let ((_let_7 (fun _let_3 _let_6))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_3 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_6))) (let ((_let_12 (fun _let_3 _let_3))) (let ((_let_13 (fun 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_let_4)))))))))))))))))))), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP _let_3 _let_3 (hAPP (fun bool bool) (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116093 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (inverse_divide X_a))) (or (not (field_inverse_zero X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a (number_number_of X_a) min)) BOUND_VARIABLE_116093) (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_116093)))))) ) 21.88/22.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( 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))))))))) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116135 $$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_116135) BOUND_VARIABLE_116135))) ) 21.88/22.03 ( 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)))) ) 21.88/22.03 ( int, y ) 21.88/22.03 ( int, x ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.88/22.03 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 21.88/22.03 ( 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))) m1))) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 21.88/22.03 ( nat, (hAPP int nat nat_1 t) ) 21.88/22.03 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 21.88/22.03 ( code_code_numeral, (zero_zero code_code_numeral) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (one_one X_a)))) ) 21.88/22.03 ( rat ) 21.88/22.03 ( int ) 21.88/22.03 ( nat ) 21.88/22.03 ( bool ) 21.88/22.03 ( real ) 21.88/22.03 ( (filter nat) ) 21.88/22.03 ( complex ) 21.88/22.03 ( (fun int bool) ) 21.88/22.03 ( (product_prod int int) ) 21.88/22.03 ( (fun nat bool) ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 21.88/22.03 ( quickcheck_code_int ) 21.88/22.03 ( code_code_numeral ) 21.88/22.03 ( (product_prod real real) ) 21.88/22.03 ( (filter real) ) 21.88/22.03 ( (product_prod nat nat) ) 21.88/22.03 ( (fun nat rat) ) 21.88/22.03 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int _let_0 X)) (hAPP nat int _let_0 Y)) (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) X) Y)))) ) 21.88/22.03 ( (one_one nat), (zero_zero nat) ) 21.88/22.03 ( (one_one nat), (one_one nat) ) 21.88/22.03 ( (one_one nat), n ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116164 $$unsorted)) (or (not (linordered_idom X_a)) (= (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_116164)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_116164)) (ti X_a BOUND_VARIABLE_116164))) ) 21.88/22.03 ( rat, (zero_zero rat) ) 21.88/22.03 ( int, pls ) 21.88/22.03 ( int, min ) 21.88/22.03 ( int, s ) 21.88/22.03 ( int, s1 ) 21.88/22.03 ( int, m ) 21.88/22.03 ( int, t ) 21.88/22.03 ( int, v ) 21.88/22.03 ( int, w ) 21.88/22.03 ( int, y ) 21.88/22.03 ( int, sa ) 21.88/22.03 ( int, x ) 21.88/22.03 ( int, r ) 21.88/22.03 ( int, m1 ) 21.88/22.03 ( int, skv_14 ) 21.88/22.03 ( int, skv_20 ) 21.88/22.03 ( (fun int int), bit1 ) 21.88/22.03 ( (fun int int), bit0 ) 21.88/22.03 ( (fun int int), succ ) 21.88/22.03 ( (fun int int), pred ) 21.88/22.03 ( (fun int int), (fact_fact int) ) 21.88/22.03 ( (fun int int), zfact ) 21.88/22.03 ( nat, n ) 21.88/22.03 ( nat, tn ) 21.88/22.03 ( bool, fTrue ) 21.88/22.03 ( bool, fFalse ) 21.88/22.03 ( real, pi ) 21.88/22.03 ( real, (zero_zero real) ) 21.88/22.03 ( (fun nat real), (real_1 nat) ) 21.88/22.03 ( (fun nat real), cos_coeff ) 21.88/22.03 ( (fun nat real), sin_coeff ) 21.88/22.03 ( (fun real real), sin ) 21.88/22.03 ( (fun real real), cos ) 21.88/22.03 ( (fun real real), sqrt ) 21.88/22.03 ( (fun real real), tan ) 21.88/22.03 ( (fun real real), ln ) 21.88/22.03 ( (fun real real), arctan ) 21.88/22.03 ( (fun real real), arcsin ) 21.88/22.03 ( (fun real real), arccos ) 21.88/22.03 ( (fun nat nat), suc ) 21.88/22.03 ( (fun nat nat), (fact_fact nat) ) 21.88/22.03 ( (fun nat nat), nat_size ) 21.88/22.03 ( (fun nat nat), (size_size nat) ) 21.88/22.03 ( (fun nat nat), fact ) 21.88/22.03 ( (filter nat), sequentially ) 21.88/22.03 ( (fun int (fun int rat)), fract ) 21.88/22.03 ( complex, ii ) 21.88/22.03 ( (fun int bool), zOdd ) 21.88/22.03 ( (fun int bool), zprime ) 21.88/22.03 ( (fun int bool), zEven ) 21.88/22.03 ( (fun int bool), nat_neg ) 21.88/22.03 ( (fun int bool), nat_is_nat ) 21.88/22.03 ( (fun int bool), (even_odd_even int) ) 21.88/22.03 ( (fun int bool), twoSqu1091635170sum2sq ) 21.88/22.03 ( (fun int (fun int int)), legacy_zgcd ) 21.88/22.03 ( (fun int (fun int int)), (gcd_gcd int) ) 21.88/22.03 ( (fun int (fun int int)), inv ) 21.88/22.03 ( (fun int (fun int int)), multInv ) 21.88/22.03 ( (fun int (fun int int)), legendre ) 21.88/22.03 ( (fun int (fun int int)), standardRes ) 21.88/22.03 ( (fun int (fun int int)), nat_tsub ) 21.88/22.03 ( (fun int (fun int int)), z3div ) 21.88/22.03 ( (fun int (fun int int)), z3mod ) 21.88/22.03 ( (fun int (fun int int)), int_lcm ) 21.88/22.03 ( (fun int (fun int int)), int_gcd ) 21.88/22.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 21.88/22.03 ( (fun bool bool), fNot ) 21.88/22.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 21.88/22.03 ( (fun bool (fun bool bool)), fconj ) 21.88/22.03 ( (fun bool (fun bool bool)), fdisj ) 21.88/22.03 ( (fun bool (fun bool bool)), fimplies ) 21.88/22.03 ( (fun int (fun int bool)), quadRes ) 21.88/22.03 ( (fun int (fun int bool)), d22set ) 21.88/22.03 ( (fun int (fun int bool)), norRRset ) 21.88/22.03 ( (fun int (fun int bool)), sRStar ) 21.88/22.03 ( (fun int (fun int bool)), sr ) 21.88/22.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 21.88/22.03 ( (fun nat bool), (even_odd_even nat) ) 21.88/22.03 ( (fun nat bool), prime ) 21.88/22.03 ( (fun real complex), cis ) 21.88/22.03 ( (fun nat (fun nat bool)), coprime ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 21.88/22.03 ( (fun (product_prod int int) bool), frac_1 ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 21.88/22.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 21.88/22.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 21.88/22.03 ( (fun (fun int bool) bool), nat_nat_set ) 21.88/22.03 ( (fun nat (fun real real)), root ) 21.88/22.03 ( (fun real (fun real real)), log ) 21.88/22.03 ( (fun real (fun real real)), powr ) 21.88/22.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 21.88/22.03 ( (fun complex complex), cnj ) 21.88/22.03 ( (fun complex complex), expi ) 21.88/22.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 21.88/22.03 ( (fun nat (fun nat nat)), nat_gcd ) 21.88/22.03 ( (fun nat (fun nat nat)), nat_lcm ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 21.88/22.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 21.88/22.03 ( (fun int (fun (fun int bool) bool)), resSet ) 21.88/22.03 ( (fun int nat), nat_1 ) 21.88/22.03 ( (fun int nat), phi ) 21.88/22.03 ( (fun complex real), re ) 21.88/22.03 ( (fun complex real), im ) 21.88/22.03 ( (fun complex real), arg ) 21.88/22.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 21.88/22.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 21.88/22.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 21.88/22.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 21.88/22.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 21.88/22.03 ( (fun (product_prod nat nat) bool), pred_nat ) 21.88/22.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 21.88/22.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 21.88/22.03 ( (fun (fun int bool) int), (the int) ) 21.88/22.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 21.88/22.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 21.88/22.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 21.88/22.03 ( (fun real (fun real complex)), rcis ) 21.88/22.03 ( (fun real (fun real complex)), complex_1 ) 21.88/22.03 ( (fun int (fun int (fun int bool))), zcong ) 21.88/22.03 ( (fun int (fun int (fun int bool))), wset ) 21.88/22.03 ( (fun int (fun int (fun int bool))), noXRRset ) 21.88/22.03 ( (fun int (fun int (fun int bool))), bnorRset ) 21.88/22.03 ( (fun int (fun int (fun int bool))), zcongm ) 21.88/22.03 ( (fun real nat), natceiling ) 21.88/22.03 ( (fun real nat), natfloor ) 21.88/22.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 21.88/22.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 21.88/22.03 ( (fun int real), (real_1 int) ) 21.88/22.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 21.88/22.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 21.88/22.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 21.88/22.03 ( (fun complex nat), (size_size complex) ) 21.88/22.03 ( (fun complex nat), complex_size ) 21.88/22.03 ( (fun (fun nat rat) bool), vanishes ) 21.88/22.03 ( (fun (product_prod int int) rat), frct ) 21.88/22.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 21.88/22.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 21.88/22.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 21.88/22.03 ( (fun rat real), ratreal ) 21.88/22.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 21.88/22.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 21.88/22.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 21.88/22.03 ( (fun rat (product_prod int int)), quotient_of ) 21.88/22.03 ( (fun int (fun nat nat)), nat_aux ) 21.88/22.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 21.88/22.03 ( (fun int (list int)), quickc666637781d_zero ) 21.88/22.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 21.88/22.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 21.88/22.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 21.88/22.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 21.88/22.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 21.88/22.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 21.88/22.03 ( (fun code_code_numeral int), code_int_of ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((R_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_3))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (real_1 nat))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP nat real _let_0 N_1)) R_3))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) R_3) (hAPP nat real _let_0 (hAPP nat nat suc N_1)))))))) ))) ) 21.88/22.03 ( pi ) 21.88/22.03 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( skv_10 ) 21.88/22.03 ( skv_11 ) 21.88/22.03 ( skv_15 ) 21.88/22.03 ( skv_18 ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (or (= X Y) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 X) Y)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Y) X))))) ) 21.88/22.03 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( (zero_zero nat), n ) 21.88/22.03 ( (zero_zero nat), tn ) 21.88/22.03 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 21.88/22.03 ( n, (zero_zero nat) ) 21.88/22.03 ( tn, (zero_zero nat) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116235 $$unsorted) (BOUND_VARIABLE_116236 $$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_116236))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_116235))) (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_116236) BOUND_VARIABLE_116235))))) ) 21.88/22.03 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 21.88/22.03 ( 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))) ) 21.88/22.03 ( int, v, y ) 21.88/22.03 ( int, v, sa ) 21.88/22.03 ( int, v, x ) 21.88/22.03 ( int, v, r ) 21.88/22.03 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.88/22.03 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.88/22.03 ( int, w, y ) 21.88/22.03 ( int, w, sa ) 21.88/22.03 ( int, w, x ) 21.88/22.03 ( int, w, r ) 21.88/22.03 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 21.88/22.03 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 21.88/22.03 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 21.88/22.03 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.03 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, skv_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))) ) 21.88/22.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( 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))))) ) 21.88/22.03 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( 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)))) ) 21.88/22.03 ( complex, ii, ii ) 21.88/22.03 ( 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)) ) 21.88/22.03 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116260 $$unsorted)) (or (not (number_semiring X_a)) (= (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_116260) (hAPP int X_a (number_number_of X_a) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_116260)))) ) 21.88/22.03 ( int, (zero_zero nat) ) 21.88/22.03 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, (one_one nat) ) 21.88/22.03 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.03 ( int, n ) 21.88/22.03 ( nat, (zero_zero nat) ) 21.88/22.03 ( real, (zero_zero nat) ) 21.88/22.03 ( real, (one_one nat) ) 21.88/22.03 ( quickcheck_code_int, (zero_zero nat) ) 21.88/22.03 ( quickcheck_code_int, (one_one nat) ) 21.88/22.03 ( code_code_numeral, (zero_zero nat) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_116290 $$unsorted) (BOUND_VARIABLE_116291 $$unsorted) (BOUND_VARIABLE_116292 $$unsorted) (BOUND_VARIABLE_116293 $$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_116292) BOUND_VARIABLE_116293))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_116290 BOUND_VARIABLE_116293)) BOUND_VARIABLE_116291))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) X_1) Y_1))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_116290 X_1)) (hAPP X_a X_b BOUND_VARIABLE_116290 Y_1)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_116290 BOUND_VARIABLE_116292)) BOUND_VARIABLE_116291)))) ) 21.88/22.03 ( int, int, bit1, pls, (zero_zero int), min ) 21.88/22.03 ( int, int, (uminus_uminus int), min, (zero_zero int), (one_one int) ) 21.88/22.03 ( int, int, bit0, pls, min, (zero_zero int) ) 21.88/22.03 ( int, int, bit0, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int), pls ) 21.88/22.03 ( int, int, succ, (one_one int), min, min ) 21.88/22.03 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), t, (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))) ) 21.88/22.03 ( nat, int, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int int (number_number_of int) (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))) ) 21.88/22.03 ( 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)))), (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 ) 21.88/22.03 ( real, real, sin, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 21.88/22.03 ( real, real, cos, skv_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)))) ) 21.88/22.03 ( real, real, (hAPP 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))) ) 21.88/22.03 ( real, real, (sgn_sgn 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) ) 21.88/22.03 ( real, real, (sgn_sgn real), skv_11, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 21.88/22.03 ( real, real, (sgn_sgn real), skv_15, pi, (zero_zero real) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116335 $$unsorted) (BOUND_VARIABLE_116336 $$unsorted) (BOUND_VARIABLE_116337 $$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_116336) BOUND_VARIABLE_116337))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_116335) BOUND_VARIABLE_116336))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116335) BOUND_VARIABLE_116337))))) ) 21.88/22.03 ( int, (one_one int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( int, min, 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))) ) 21.88/22.03 ( int, (zero_zero 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))) ) 21.88/22.03 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (zero_zero int), (one_one int) ) 21.88/22.03 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), min, min ) 21.88/22.03 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), min, (zero_zero int) ) 21.88/22.03 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (one_one int), t ) 21.88/22.03 ( 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)))) ) 21.88/22.03 ( 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)))), (hAPP real real (hAPP 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))) ) 21.88/22.03 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( 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 ) 21.88/22.03 ( real, skv_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) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real _let_0 (hAPP complex real re X))) (hAPP real real _let_0 (hAPP complex real im X))) (hAPP complex complex (uminus_uminus complex) X))) ) 21.88/22.03 ( (zero_zero complex) ) 21.88/22.03 ( ii ) 21.88/22.03 ( (one_one complex) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116424 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_116424) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_116424)) (one_one int))))) ) 21.88/22.03 ( int, (one_one int) ) 21.88/22.03 ( int, min ) 21.88/22.03 ( int, (zero_zero int) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 21.88/22.03 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( real, (zero_zero real) ) 21.88/22.03 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.03 ( real, skv_10 ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((J $$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))))) ) 21.88/22.03 ( (zero_zero nat), (zero_zero nat), (even_odd_even nat), n ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116479 $$unsorted) (BOUND_VARIABLE_116480 $$unsorted) (BOUND_VARIABLE_116481 $$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_116481))) (= (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_116479) BOUND_VARIABLE_116481)) BOUND_VARIABLE_116480)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_116479) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_116480) BOUND_VARIABLE_116481)))))))) ) 21.88/22.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.03 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.88/22.03 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.88/22.03 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (semiri532925092at_aux X_a))) (or (not (semiring_1 X_a)) (= _let_1 (ti (fun _let_0 (fun nat _let_0)) _let_1))))) ) 21.88/22.03 ( rat ) 21.88/22.03 ( int ) 21.88/22.03 ( (fun int int) ) 21.88/22.03 ( nat ) 21.88/22.03 ( bool ) 21.88/22.03 ( real ) 21.88/22.03 ( (fun nat real) ) 21.88/22.03 ( (fun real real) ) 21.88/22.03 ( complex ) 21.88/22.03 ( (fun int bool) ) 21.88/22.03 ( (product_prod int int) ) 21.88/22.03 ( (fun (product_prod int int) int) ) 21.88/22.03 ( (fun int (fun int bool)) ) 21.88/22.03 ( (fun nat bool) ) 21.88/22.03 ( (fun (product_prod int int) bool) ) 21.88/22.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.88/22.03 ( (fun real bool) ) 21.88/22.03 ( quickcheck_code_int ) 21.88/22.03 ( code_code_numeral ) 21.88/22.03 ( (fun int (fun int (fun int bool))) ) 21.88/22.03 ( (fun int real) ) 21.88/22.03 ) 21.88/22.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116620 $$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_116620)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_116620)) BOUND_VARIABLE_116620)))))) ) 21.88/22.03 ( int, pls ) 21.88/22.03 ( int, (one_one int) ) 21.88/22.03 ( int, min ) 21.88/22.03 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.03 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.03 ( nat, n ) 21.88/22.03 ( nat, tn ) 21.88/22.03 ( real, pi ) 21.88/22.03 ( real, (hAPP real real (hAPP 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(fun real (fun int (fun _let_0 _let_0)))) ) 21.88/22.04 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 21.88/22.04 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 21.88/22.04 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 21.88/22.04 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 21.88/22.04 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 21.88/22.04 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 21.88/22.04 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 21.88/22.04 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 21.88/22.04 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 21.88/22.04 ( (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)))) ) 21.88/22.04 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 21.88/22.04 ( (fun int (fun int real)), (fun int (fun int bool)) ) 21.88/22.04 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 21.88/22.04 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X $$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))) (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))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X))))))) ) 21.88/22.04 ( pi ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (one_one real) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (hAPP real 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))))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.88/22.04 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (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))))) ) 21.88/22.04 ( (hAPP real real (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))))) ) 21.88/22.04 ( (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)))) ) 21.88/22.04 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 21.88/22.04 ( (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)) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116660 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_116660) (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)) BOUND_VARIABLE_116660))) ) 21.88/22.04 ( int, pls ) 21.88/22.04 ( int, (one_one int) ) 21.88/22.04 ( int, min ) 21.88/22.04 ( 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)))) ) 21.88/22.04 ( real, (one_one real) ) 21.88/22.04 ( 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) ) 21.88/22.04 ( complex, ii ) 21.88/22.04 ( complex, (one_one complex) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116706 $$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_116706)) BOUND_VARIABLE_116706))) ) 21.88/22.04 ( int, pls ) 21.88/22.04 ( int, (one_one int) ) 21.88/22.04 ( int, min ) 21.88/22.04 ( 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)))) ) 21.88/22.04 ( real, (one_one real) ) 21.88/22.04 ( 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) ) 21.88/22.04 ( complex, ii ) 21.88/22.04 ( complex, (one_one complex) ) 21.88/22.04 ) 21.88/22.04 (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 $$unsorted)) (or (not (= J_2 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_1) K_1))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) K_1)))) ))) ) 21.88/22.04 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( (zero_zero nat), n ) 21.88/22.04 ( (zero_zero nat), tn ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116772 $$unsorted)) (or (not (number_ring X_a)) (not (real_n2089651433ebra_1 X_a)) (= (hAPP X_a real (norm_norm X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_116772)) (hAPP real real (abs_abs real) (hAPP int real (number_number_of real) BOUND_VARIABLE_116772)))) ) 21.88/22.04 ( int, pls ) 21.88/22.04 ( int, (hAPP int int bit1 pls) ) 21.88/22.04 ( int, min ) 21.88/22.04 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.88/22.04 ( nat, pls ) 21.88/22.04 ( nat, (hAPP int int bit1 pls) ) 21.88/22.04 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.88/22.04 ( real, min ) 21.88/22.04 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 21.88/22.04 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 21.88/22.04 ( complex, min ) 21.88/22.04 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( quickcheck_code_int, pls ) 21.88/22.04 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 21.88/22.04 ( quickcheck_code_int, (one_one int) ) 21.88/22.04 ( code_code_numeral, pls ) 21.88/22.04 ( code_code_numeral, (hAPP int int bit1 pls) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_116792 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (let ((_let_1 (hAPP nat X_a _let_0 (hAPP int nat nat_1 BOUND_VARIABLE_116792)))) (or (not (semiring_1 X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_116792))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_1) _let_1) (hAPP nat X_a _let_0 (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_116792))))))) ) 21.88/22.04 ( int, (one_one int) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$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)))) ) 21.88/22.04 ( rat ) 21.88/22.04 ( int ) 21.88/22.04 ( nat ) 21.88/22.04 ( real ) 21.88/22.04 ( complex ) 21.88/22.04 ( quickcheck_code_int ) 21.88/22.04 ( code_code_numeral ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP real real sin X)) (hAPP real real cos X)) (hAPP real real tan X)) ) 21.88/22.04 ( pi ) 21.88/22.04 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 21.88/22.04 ( skv_10 ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Xa $$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)) Xa))) (hAPP nat nat suc Xa))) ) 21.88/22.04 ( (zero_zero nat) ) 21.88/22.04 ( (hAPP nat nat suc (zero_zero nat)) ) 21.88/22.04 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (diffs X_a))) (or (not (ring_1 X_a)) (= _let_1 (ti (fun _let_0 _let_0) _let_1))))) ) 21.88/22.04 ( rat ) 21.88/22.04 ( int ) 21.88/22.04 ( (fun int int) ) 21.88/22.04 ( nat ) 21.88/22.04 ( bool ) 21.88/22.04 ( real ) 21.88/22.04 ( (fun real real) ) 21.88/22.04 ( (fun nat nat) ) 21.88/22.04 ( complex ) 21.88/22.04 ( (product_prod int int) ) 21.88/22.04 ( (fun bool bool) ) 21.88/22.04 ( (fun nat bool) ) 21.88/22.04 ( (fun nat (fun nat bool)) ) 21.88/22.04 ( (fun nat (product_prod int int)) ) 21.88/22.04 ( (product_prod real real) ) 21.88/22.04 ( (product_prod nat nat) ) 21.88/22.04 ( (fun (product_prod nat nat) bool) ) 21.88/22.04 ( (fun nat (fun (product_prod nat nat) bool)) ) 21.88/22.04 ( (fun nat (product_prod nat nat)) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117078 $$unsorted) (BOUND_VARIABLE_117079 $$unsorted) (BOUND_VARIABLE_117080 $$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_117080))) (= (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_117078) BOUND_VARIABLE_117080)) BOUND_VARIABLE_117079)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117078) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_117079) BOUND_VARIABLE_117080)))))))) ) 21.88/22.04 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.04 ( int, (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.88/22.04 ( 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)), (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.88/22.04 ) 21.88/22.04 (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)))) ) 21.88/22.04 ( rat ) 21.88/22.04 ( int ) 21.88/22.04 ( (fun int int) ) 21.88/22.04 ( nat ) 21.88/22.04 ( bool ) 21.88/22.04 ( real ) 21.88/22.04 ( (fun nat real) ) 21.88/22.04 ( (fun real real) ) 21.88/22.04 ( complex ) 21.88/22.04 ( (fun int bool) ) 21.88/22.04 ( (product_prod int int) ) 21.88/22.04 ( (fun (product_prod int int) int) ) 21.88/22.04 ( (fun int (fun int bool)) ) 21.88/22.04 ( (fun nat bool) ) 21.88/22.04 ( (fun (product_prod int int) bool) ) 21.88/22.04 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 21.88/22.04 ( (fun real bool) ) 21.88/22.04 ( quickcheck_code_int ) 21.88/22.04 ( code_code_numeral ) 21.88/22.04 ( (fun int (fun int (fun int bool))) ) 21.88/22.04 ( (fun int real) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (hAPP complex real re X))) (= (hAPP complex real re (hAPP complex complex (inverse_inverse complex) X)) (hAPP real real (hAPP real _let_2 (inverse_divide real) _let_4) (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 _let_4) _let_3)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real im X)) _let_3))))))))) ) 21.88/22.04 ( (zero_zero complex) ) 21.88/22.04 ( ii ) 21.88/22.04 ( (one_one complex) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((I $$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)))) ) 21.88/22.04 ( (one_one int) ) 21.88/22.04 ( min ) 21.88/22.04 ( (zero_zero int) ) 21.88/22.04 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( t ) 21.88/22.04 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.04 ( (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)))) (hAPP int int (abs_abs int) w)) ) 21.88/22.04 ( (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)))) (hAPP int int (abs_abs int) v)) ) 21.88/22.04 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 21.88/22.04 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117304 $$unsorted) (BOUND_VARIABLE_117305 $$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_117305))) (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_117304) _let_2) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_117304)) _let_2)))))) ) 21.88/22.04 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117330 $$unsorted) (BOUND_VARIABLE_117331 $$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_117330)) BOUND_VARIABLE_117331))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_117331)) BOUND_VARIABLE_117330)))))) ) 21.88/22.04 ( int, pls, pls ) 21.88/22.04 ( int, pls, (one_one int) ) 21.88/22.04 ( int, pls, min ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.04 ( int, (one_one int), pls ) 21.88/22.04 ( int, (one_one int), min ) 21.88/22.04 ( int, (one_one int), (zero_zero int) ) 21.88/22.04 ( int, min, pls ) 21.88/22.04 ( int, min, (one_one int) ) 21.88/22.04 ( int, (zero_zero int), (one_one int) ) 21.88/22.04 ( 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))), pls ) 21.88/22.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), pls ) 21.88/22.04 ( 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) ) 21.88/22.04 ( 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)))), (zero_zero real) ) 21.88/22.04 ( 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)))) ) 21.88/22.04 ( 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 ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (let ((_let_3 (fun int _let_0))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_3 zcong X) Y) M))) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_3 zcong (hAPP nat int (hAPP int _let_1 _let_2 X) Z_1)) (hAPP nat int (hAPP int _let_1 _let_2 Y) Z_1)) M))))))) ) 21.88/22.04 ( (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))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) (one_one real)))) (hBOOL (hAPP _let_0 bool (bseq real) (hAPP real _let_0 (power_power real) Xa))))))) ) 21.88/22.04 ( (hAPP int real (number_number_of real) min) ) 21.88/22.04 ( pi ) 21.88/22.04 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( skv_10 ) 21.88/22.04 ( skv_11 ) 21.88/22.04 ( skv_15 ) 21.88/22.04 ( skv_18 ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Y $$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))) ) 21.88/22.04 ( (one_one real) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (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))))) ) 21.88/22.04 ( (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)))))))))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Y $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real arctan Y)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.04 ( (one_one real) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 21.88/22.04 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((Y $$unsorted)) (= Y (hAPP real real tan (hAPP real real arctan Y))) ) 21.88/22.04 ( (one_one real) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (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))))) ) 21.88/22.04 ( (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)))))))))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117413 $$unsorted) (BOUND_VARIABLE_117414 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_1 X_a)) (= (hAPP int X_a _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) BOUND_VARIABLE_117413) BOUND_VARIABLE_117414)) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_117413)) BOUND_VARIABLE_117414)))) ) 21.88/22.04 ( real, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117443 $$unsorted) (BOUND_VARIABLE_117444 $$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_117444)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_117443)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_117444)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117443) BOUND_VARIABLE_117444)))))) ) 21.88/22.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( 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))))))))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((D_3 $$unsorted) (C_1 $$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_1) (ti int B))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong C_1) D_3) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 D_3) M)))))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( (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))) ) 21.88/22.04 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.04 ( (hAPP int int (number_number_of int) min), (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.04 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.04 ( 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))) ) 21.88/22.04 ( skv_5, s1, s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real sqrt X))))) ) 21.88/22.04 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.04 ( (one_one real) ) 21.88/22.04 ( (zero_zero real) ) 21.88/22.04 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_117601 $$unsorted) (BOUND_VARIABLE_117602 $$unsorted) (BOUND_VARIABLE_117603 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_a)) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_117601) BOUND_VARIABLE_117602) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_117603))) (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_117603)) (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_1) BOUND_VARIABLE_117603))) S_1))) (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_117601 X_1)) BOUND_VARIABLE_117602))) R_1))))) ))) ))) ))))) ) 21.88/22.04 ( 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)))) ) 21.88/22.04 ) 21.88/22.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117733 $$unsorted) (BOUND_VARIABLE_117734 $$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_117734) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_117733) _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_117734) BOUND_VARIABLE_117733)) _let_2)))))) ) 21.88/22.04 ( 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)))) ) 21.88/22.04 ( 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) ) 21.88/22.04 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 21.88/22.04 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 21.88/22.04 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.04 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 21.88/22.04 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 21.88/22.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.88/22.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.88/22.04 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 21.88/22.05 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 21.88/22.05 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 21.88/22.05 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.88/22.05 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 21.88/22.05 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( nat, (one_one nat), (one_one nat) ) 21.88/22.05 ) 21.88/22.05 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2)) (hAPP X_c X_a (hAPP X_b _let_0 F1 A_3) B_2)))) ) 21.88/22.05 ( int, int, rat, fract, (one_one int), (one_one int) ) 21.88/22.05 ( int, int, rat, fract, (zero_zero int), (one_one int) ) 21.88/22.05 ( int, int, int, (plus_plus int), (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 21.88/22.05 ( int, int, int, (plus_plus int), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.88/22.05 ( int, int, int, (plus_plus 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 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int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 21.88/22.05 ( 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 ) 21.88/22.05 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( 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 ) 21.88/22.05 ( 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))), m1 ) 21.88/22.05 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 21.88/22.05 ( 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_21 ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 21.88/22.05 ( int, int, int, (times_times int), y, v ) 21.88/22.05 ( int, int, int, (times_times int), y, w ) 21.88/22.05 ( int, int, int, (times_times int), sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, int, (times_times int), sa, v ) 21.88/22.05 ( int, int, int, (times_times int), sa, w ) 21.88/22.05 ( int, int, int, (times_times int), x, v ) 21.88/22.05 ( int, int, int, (times_times int), x, w ) 21.88/22.05 ( int, int, int, (times_times int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.88/22.05 ( int, int, int, (times_times int), r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, int, (times_times int), r, v ) 21.88/22.05 ( int, int, int, (times_times int), r, w ) 21.88/22.05 ( int, int, int, (times_times int), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 21.88/22.05 ( int, int, int, (times_times int), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 21.88/22.05 ( int, int, int, (times_times int), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 21.88/22.05 ( int, int, int, (times_times int), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 21.88/22.05 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 21.88/22.05 ( int, int, int, (times_times int), skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, int, (times_times int), skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( int, int, int, (minus_minus int), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.05 ( int, int, int, (minus_minus int), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.05 ( int, int, int, (minus_minus int), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.05 ( int, int, int, (minus_minus int), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 21.88/22.05 ( int, int, int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 21.88/22.05 ( int, int, int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 21.88/22.05 ( int, int, int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 21.88/22.05 ( int, int, int, (minus_minus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 21.88/22.05 ( int, int, int, (minus_minus 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 21.88/22.05 ( int, int, int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 21.88/22.05 ( int, int, int, legendre, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( int, int, bool, (ord_less int), (one_one int), t ) 21.88/22.05 ( int, int, bool, (ord_less int), min, min ) 21.88/22.05 ( int, int, bool, (ord_less int), min, (zero_zero int) ) 21.88/22.05 ( int, int, bool, (ord_less int), (zero_zero int), pls ) 21.88/22.05 ( int, int, bool, (ord_less int), (zero_zero int), (one_one int) ) 21.88/22.05 ( int, int, bool, (ord_less int), (zero_zero int), min ) 21.88/22.05 ( int, 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))) ) 21.88/22.05 ( int, int, bool, (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( int, int, bool, (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( int, int, bool, (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), min, pls ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), min, min ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), pls ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), min ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_4 ) 21.88/22.05 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_5 ) 21.88/22.05 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( 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) (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)) ) 21.88/22.05 ( int, int, bool, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( int, int, (fun int bool), zcong, s1, s ) 21.88/22.05 ( int, int, (fun int bool), zcong, s1, skv_4 ) 21.88/22.05 ( int, int, (fun int bool), zcong, s1, skv_5 ) 21.88/22.05 ( 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) ) 21.88/22.05 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 21.88/22.05 ( int, int, (product_prod int int), (product_Pair int int), (one_one int), (one_one int) ) 21.88/22.05 ( int, int, (product_prod int int), (product_Pair int int), (zero_zero int), (one_one int) ) 21.88/22.05 ( int, int, (product_prod int int), (product_Pair int int), s, (one_one int) ) 21.88/22.05 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, nat, int, (power_power int), skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( int, (fun int bool), bool, (member int), (one_one int), zEven ) 21.88/22.05 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 21.88/22.05 ( nat, nat, nat, (minus_minus nat), (hAPP int nat nat_1 t), (one_one nat) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( nat, nat, bool, (ord_less nat), (zero_zero nat), n ) 21.88/22.05 ( nat, nat, bool, (ord_less nat), (zero_zero nat), tn ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 21.88/22.05 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 21.88/22.05 ( real, real, bool, (ord_less real), (zero_zero real), skv_9 ) 21.88/22.05 ( real, real, bool, (ord_less real), (zero_zero real), skv_12 ) 21.88/22.05 ( 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) ) 21.88/22.05 ( 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) ) 21.88/22.05 ( 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 ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_10 ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_11 ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_15 ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_18 ) 21.88/22.05 ( 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) ) 21.88/22.05 ( real, real, bool, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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)))) ) 21.88/22.05 ( 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))))))))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( 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))) ) 21.88/22.05 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 21.88/22.05 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 21.88/22.05 ( 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)))))) ) 21.88/22.05 ( 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 ) 21.88/22.05 ( real, real, real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 21.88/22.05 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 21.88/22.05 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 21.88/22.05 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 21.88/22.05 ( real, (filter nat), bool, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 21.88/22.05 ( 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))))) ) 21.88/22.05 ( (fun nat real), real, bool, (sums real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))), (one_one real) ) 21.88/22.06 ( (fun nat real), real, (fun (filter nat) bool), (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 21.88/22.06 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), suc ) 21.88/22.06 ( (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)))) ) 21.88/22.06 ( (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 ) 21.88/22.06 ( (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) ) 21.88/22.06 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (inverse_inverse real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 21.88/22.06 ( complex, nat, complex, (power_power complex), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 21.88/22.06 ( complex, complex, complex, (times_times complex), ii, ii ) 21.88/22.06 ( 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) ) 21.88/22.06 ( 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 ) 21.88/22.06 ( (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) ) 21.88/22.06 ( (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))))) ) 21.88/22.06 ( (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)))) ) 21.88/22.06 ( (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_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (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))) ) 21.88/22.06 ( (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) ) 21.88/22.06 ( (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))))) ) 21.88/22.06 ( (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))))))) ) 21.88/22.06 ( (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) ) 21.88/22.06 ( (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))) ) 21.88/22.06 ( (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))) ) 21.88/22.06 ( (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))) ) 21.88/22.06 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 21.88/22.06 ( (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 21.88/22.06 ( (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)) ) 21.88/22.06 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP _let_3 _let_3 (hAPP (fun bool bool) (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 21.88/22.06 ( (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)) ) 21.88/22.06 ( (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))))) ) 21.88/22.06 ( (fun int (fun int bool)), int, (fun int bool), (combc int int bool), (fequal int), (zero_zero int) ) 21.88/22.06 ( (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) ) 21.88/22.06 ( (fun nat (fun nat bool)), nat, (fun nat bool), (combc nat nat bool), (fequal nat), (zero_zero nat) ) 21.88/22.06 ( (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 ) 21.88/22.06 ( (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 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_let_2 _let_1))) (let ((_let_7 (fun _let_3 _let_6))) (let ((_let_8 (fun _let_2 _let_3))) (let ((_let_9 (fun _let_3 (fun _let_2 bool)))) (let ((_let_10 (fun _let_2 _let_9))) (let ((_let_11 (fun _let_2 _let_6))) (let ((_let_12 (fun _let_3 _let_3))) (let ((_let_13 (fun _let_2 _let_12))) (let ((_let_14 (fun _let_3 _let_8))) (let ((_let_15 (fun _let_2 _let_0))) (let ((_let_16 (hAPP _let_3 _let_15 (hAPP (fun int _let_0) (fun _let_3 _let_15) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_17 (fun int _let_3))) (hAPP _let_8 _let_5 (hAPP _let_10 (fun _let_8 _let_5) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_11 _let_10 (hAPP (fun _let_6 _let_9) (fun _let_11 _let_10) (combb _let_6 _let_9 _let_2) (combs _let_2 int bool)) (hAPP _let_8 _let_11 (hAPP _let_7 (fun _let_8 _let_11) (combb _let_3 _let_6 _let_2) (hAPP (fun int _let_1) _let_7 (combb int _let_1 _let_2) (fequal int))) (hAPP _let_3 _let_8 (hAPP _let_13 _let_14 (combc _let_2 _let_3 _let_3) (hAPP _let_15 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(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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (real_1 int))) (let ((_let_6 (fun real bool))) (let ((_let_7 (fun real _let_6))) (let ((_let_8 (fun int _let_3))) (let ((_let_9 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_10 (fun int _let_2))) (let ((_let_11 (fun _let_10 _let_8))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun int real))) (let ((_let_14 (fun int _let_0))) (let ((_let_15 (fun _let_13 (fun int bool)))) (let ((_let_16 (fun real (fun int (fun int bool))))) (let ((_let_17 (fun real _let_9))) (let ((_let_18 (fun real _let_8))) (let ((_let_19 (fun real _let_10))) (let ((_let_20 (fun int _let_13))) (let ((_let_21 (fun _let_20 (fun int (fun int bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun real _let_15))) (let ((_let_24 (fun _let_13 _let_13))) (let ((_let_25 (fun int _let_24))) (hAPP _let_18 _let_17 (hAPP (fun _let_8 _let_9) (fun _let_18 _let_17) (combb _let_8 _let_9 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_19 _let_18 (hAPP _let_11 (fun _let_19 _let_18) (combb _let_10 _let_8 real) (hAPP (fun _let_2 _let_3) _let_11 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_16 _let_19 (hAPP _let_12 (fun _let_16 _let_19) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_4 _let_12 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_20 _let_16 (hAPP _let_22 (fun _let_20 _let_16) (combc real _let_20 (fun int (fun int bool))) (hAPP _let_23 _let_22 (hAPP (fun _let_15 _let_21) (fun _let_23 _let_22) (combb _let_15 _let_21 real) (combb _let_13 (fun int bool) int)) (hAPP _let_7 _let_23 (hAPP (fun _let_6 _let_15) (fun _let_7 _let_23) (combb _let_6 _let_15 real) (combb real bool int)) (fequal real)))) (hAPP _let_13 _let_20 (hAPP _let_25 (fun _let_13 _let_20) (combc int _let_13 _let_13) (hAPP _let_14 _let_25 (hAPP (fun _let_0 _let_24) (fun _let_14 _let_25) (combb _let_0 _let_24 int) (combb real real int)) (hAPP _let_13 _let_14 (hAPP (fun real _let_0) (fun _let_13 _let_14) (combb real _let_0 int) (inverse_divide real)) _let_5))) _let_5))))))))))))))))))))))))))))))), (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)))) ) 22.00/22.11 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (real_1 int))) (let ((_let_6 (fun real bool))) (let ((_let_7 (fun real _let_6))) (let ((_let_8 (fun int _let_3))) (let ((_let_9 (fun int _let_2))) (let ((_let_10 (fun _let_9 _let_8))) (let ((_let_11 (fun (fun int (fun int bool)) _let_9))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_0))) (let ((_let_14 (fun _let_12 (fun int bool)))) (let ((_let_15 (fun real (fun int (fun int bool))))) (let ((_let_16 (fun real _let_8))) (let ((_let_17 (fun real _let_9))) (let ((_let_18 (fun int _let_12))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun real _let_14))) (let ((_let_22 (fun _let_12 _let_12))) (let ((_let_23 (fun int _let_22))) (hAPP _let_17 _let_16 (hAPP _let_10 (fun _let_17 _let_16) (combb _let_9 _let_8 real) (hAPP (fun _let_2 _let_3) _let_10 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_15 _let_17 (hAPP _let_11 (fun _let_15 _let_17) (combb (fun int (fun int bool)) _let_9 real) (hAPP _let_4 _let_11 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_18 _let_15 (hAPP _let_20 (fun _let_18 _let_15) (combc real _let_18 (fun int (fun int bool))) (hAPP _let_21 _let_20 (hAPP (fun _let_14 _let_19) (fun _let_21 _let_20) (combb _let_14 _let_19 real) (combb _let_12 (fun int bool) int)) (hAPP _let_7 _let_21 (hAPP (fun _let_6 _let_14) (fun _let_7 _let_21) (combb _let_6 _let_14 real) (combb real bool int)) (fequal real)))) (hAPP _let_12 _let_18 (hAPP _let_23 (fun _let_12 _let_18) (combc int _let_12 _let_12) (hAPP _let_13 _let_23 (hAPP (fun _let_0 _let_22) (fun _let_13 _let_23) (combb _let_0 _let_22 int) (combb real real int)) (hAPP _let_12 _let_13 (hAPP (fun real _let_0) (fun _let_12 _let_13) (combb real _let_0 int) (inverse_divide real)) _let_5))) _let_5)))))))))))))))))))))))))))) ) 22.00/22.11 ( (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 real) (fun int bool)))) (let ((_let_3 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun real _let_2))) (hAPP _let_5 _let_4 (hAPP (fun _let_2 _let_3) (fun _let_5 _let_4) (combb _let_2 _let_3 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_5) (combb _let_0 _let_2 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_0))) (let ((_let_4 (fun int _let_2))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (fun int _let_5))) (hAPP _let_2 _let_4 (hAPP _let_6 (fun _let_2 _let_4) (combc int _let_2 _let_2) (hAPP _let_3 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_3 _let_6) (combb _let_0 _let_5 int) (combb real real int)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 22.00/22.11 ( (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)))))) ) 22.00/22.11 ( (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) ) 22.00/22.11 ( (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 int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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)))))))), (real_1 int) ) 22.00/22.11 ( (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))))) ) 22.00/22.11 ) 22.00/22.11 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (uminus_uminus int))) (let ((_let_1 (number_number_of int))) (= (hAPP int int _let_0 (hAPP int int _let_1 W)) (hAPP int int _let_1 (hAPP int int _let_0 W))))) ) 22.00/22.11 ( pls ) 22.00/22.11 ( (hAPP int int bit1 pls) ) 22.00/22.11 ( (one_one int) ) 22.00/22.11 ( min ) 22.00/22.11 ) 22.00/22.11 (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))) (= (= (hAPP int int _let_1 X2_2) (hAPP int int _let_1 X1_2)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X1_2) X2_2) Ma)))))) ) 22.00/22.11 ( (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)))), (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))) ) 22.00/22.11 ( (hAPP nat int 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((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.00/22.11 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.00/22.11 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.00/22.11 ) 22.00/22.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117879 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archim2085082626_floor X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_117879))) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_117879))) ) 22.00/22.11 ( int, pls ) 22.00/22.11 ( int, (one_one int) ) 22.00/22.11 ( int, min ) 22.00/22.11 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.00/22.11 ( real, (one_one real) ) 22.00/22.11 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.00/22.11 ( complex, ii ) 22.00/22.11 ( complex, (one_one complex) ) 22.00/22.11 ) 22.00/22.11 (instantiation (forall ((N $$unsorted) (X $$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))) (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N))))) ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.00/22.11 ( (hAPP int nat (number_number_of 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_let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.00/22.11 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.00/22.11 ( (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.00/22.11 ( (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.00/22.11 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.00/22.11 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.00/22.11 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.00/22.11 ) 22.00/22.11 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (not (= (zero_zero int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) Z_1)) Z_1))))) ) 22.00/22.11 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.00/22.11 ( (hAPP nat int (semiring_1_of_nat int) n) ) 22.00/22.11 ) 22.00/22.11 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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 F A_3) B_2) (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) F) (hAPP X_c _let_0 (hAPP X_b (fun X_c _let_0) (product_Pair X_b X_c) A_3) B_2))))) ) 22.00/22.11 ( int, int, rat, fract, (one_one int), (one_one int) ) 22.00/22.11 ( int, int, rat, fract, (zero_zero int), (one_one int) ) 22.00/22.11 ( int, int, int, (plus_plus int), (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.00/22.11 ( int, int, int, (plus_plus int), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.00/22.11 ( 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) ) 22.00/22.11 ( 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) ) 22.00/22.11 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.00/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.00/22.11 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.00/22.11 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.00/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.00/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.00/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.02/22.11 ( int, int, int, (plus_plus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.11 ( int, int, int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.11 ( 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 ) 22.02/22.11 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( 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 ) 22.02/22.11 ( 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))), m1 ) 22.02/22.11 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.02/22.11 ( 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_21 ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.02/22.11 ( int, int, int, (times_times int), y, v ) 22.02/22.11 ( int, int, int, (times_times int), y, w ) 22.02/22.11 ( int, int, int, (times_times int), sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, int, (times_times int), sa, v ) 22.02/22.11 ( int, int, int, (times_times int), sa, w ) 22.02/22.11 ( int, int, int, (times_times int), x, v ) 22.02/22.11 ( int, int, int, (times_times int), x, w ) 22.02/22.11 ( int, int, int, (times_times int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.02/22.11 ( int, int, int, (times_times int), r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, int, (times_times int), r, v ) 22.02/22.11 ( int, int, int, (times_times int), r, w ) 22.02/22.11 ( int, int, int, (times_times int), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.02/22.11 ( int, int, int, (times_times int), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.02/22.11 ( int, int, int, (times_times int), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.02/22.11 ( int, int, int, (times_times int), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.11 ( int, int, int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.02/22.11 ( int, int, int, (times_times int), skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, int, (times_times int), skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, int, (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))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), s, (one_one int) ) 22.02/22.11 ( 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) ) 22.02/22.11 ( int, int, int, (minus_minus int), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.11 ( int, int, int, (minus_minus int), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.11 ( int, int, int, (minus_minus int), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.11 ( int, int, int, (minus_minus int), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.11 ( int, int, int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.02/22.11 ( int, int, int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.02/22.11 ( int, int, int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.02/22.11 ( int, int, int, (minus_minus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.02/22.11 ( int, int, int, (minus_minus 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.11 ( int, int, int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.11 ( int, int, int, legendre, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( int, int, bool, (ord_less int), (one_one int), t ) 22.02/22.11 ( int, int, bool, (ord_less int), min, min ) 22.02/22.11 ( int, int, bool, (ord_less int), min, (zero_zero int) ) 22.02/22.11 ( int, int, bool, (ord_less int), (zero_zero int), pls ) 22.02/22.11 ( int, int, bool, (ord_less int), (zero_zero int), (one_one int) ) 22.02/22.11 ( int, int, bool, (ord_less int), (zero_zero int), min ) 22.02/22.11 ( int, 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))) ) 22.02/22.11 ( int, int, bool, (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( int, int, bool, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( int, int, bool, (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( int, int, bool, (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (one_one int), t ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), min, pls ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), min, min ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), pls ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), (one_one int) ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), min ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), s ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_4 ) 22.02/22.11 ( int, int, bool, (ord_less_eq int), (zero_zero int), skv_5 ) 22.02/22.11 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( int, int, bool, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( 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) ) 22.02/22.11 ( 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) (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)) ) 22.02/22.11 ( int, int, bool, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( 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))) ) 22.02/22.11 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( int, int, bool, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.11 ( 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)))) ) 22.02/22.11 ( 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) ) 22.02/22.11 ( int, int, (fun int bool), zcong, s1, s ) 22.02/22.11 ( int, int, (fun int bool), zcong, s1, skv_4 ) 22.02/22.11 ( int, int, (fun int bool), zcong, s1, skv_5 ) 22.02/22.11 ( 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) ) 22.02/22.11 ( int, int, (fun int bool), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 22.02/22.11 ( int, int, (product_prod int int), (product_Pair int int), (one_one int), (one_one int) ) 22.02/22.11 ( int, int, (product_prod int int), (product_Pair int int), (zero_zero int), (one_one int) ) 22.02/22.11 ( int, int, (product_prod int int), (product_Pair int int), s, (one_one int) ) 22.02/22.11 ( int, nat, int, (power_power int), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.11 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, nat, int, (power_power int), skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( int, (fun int bool), bool, (member int), (one_one int), zEven ) 22.02/22.12 ( nat, nat, nat, (plus_plus nat), (one_one nat), (one_one nat) ) 22.02/22.12 ( nat, nat, nat, (minus_minus nat), (hAPP int nat nat_1 t), (one_one nat) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( nat, nat, bool, (ord_less nat), (zero_zero nat), n ) 22.02/22.12 ( nat, nat, bool, (ord_less nat), (zero_zero nat), tn ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.02/22.12 ( nat, real, real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( real, real, bool, (ord_less real), pi, (zero_zero real) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( real, real, bool, (ord_less real), (zero_zero real), pi ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( real, real, bool, (ord_less real), (zero_zero real), skv_2 ) 22.02/22.12 ( real, real, bool, (ord_less real), (zero_zero real), skv_9 ) 22.02/22.12 ( real, real, bool, (ord_less real), (zero_zero real), skv_12 ) 22.02/22.12 ( 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) ) 22.02/22.12 ( 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) ) 22.02/22.12 ( 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 ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (zero_zero real), pi ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_10 ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_11 ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_15 ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), (zero_zero real), skv_18 ) 22.02/22.12 ( 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) ) 22.02/22.12 ( real, real, bool, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( real, real, real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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)))) ) 22.02/22.12 ( 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))))))))) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( 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))) ) 22.02/22.12 ( real, real, real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.02/22.12 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.02/22.12 ( 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)))))) ) 22.02/22.12 ( 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 ) 22.02/22.12 ( real, real, real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.02/22.12 ( real, real, complex, complex_1, (one_one real), (zero_zero real) ) 22.02/22.12 ( real, real, complex, complex_1, (zero_zero real), (one_one real) ) 22.02/22.12 ( real, real, complex, complex_1, (zero_zero real), (zero_zero real) ) 22.02/22.12 ( real, (filter nat), bool, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 22.02/22.12 ( 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))))) ) 22.02/22.12 ( (fun nat real), real, bool, (sums real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))), (one_one real) ) 22.02/22.12 ( (fun nat real), real, (fun (filter nat) bool), (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.02/22.12 ( (fun nat real), (fun nat nat), (fun nat real), (combb nat real nat), (real_1 nat), suc ) 22.02/22.12 ( (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)))) ) 22.02/22.12 ( (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 ) 22.02/22.12 ( (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) ) 22.02/22.12 ( (fun real real), (fun nat real), (fun nat real), (combb real real nat), (inverse_inverse real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 22.02/22.12 ( complex, nat, complex, (power_power complex), ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.12 ( complex, complex, complex, (times_times complex), ii, ii ) 22.02/22.12 ( 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) ) 22.02/22.12 ( 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 ) 22.02/22.12 ( (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) ) 22.02/22.12 ( (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))))) ) 22.02/22.12 ( (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)))) ) 22.02/22.12 ( (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_0))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (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))) ) 22.02/22.12 ( (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) ) 22.02/22.12 ( (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))))) ) 22.02/22.12 ( (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))))))) ) 22.02/22.12 ( (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) ) 22.02/22.12 ( (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))) ) 22.02/22.12 ( (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))) ) 22.02/22.12 ( (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))) ) 22.02/22.12 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 22.02/22.12 ( (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 22.02/22.12 ( (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)) ) 22.02/22.12 ( (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 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP _let_3 _let_3 (hAPP (fun bool bool) (fun _let_3 _let_3) (combb bool bool _let_1) fNot) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int)))))))) ) 22.02/22.12 ( (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)) ) 22.02/22.12 ( (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))))) ) 22.02/22.12 ( (fun int (fun int bool)), int, (fun int bool), (combc int int bool), (fequal int), (zero_zero int) ) 22.02/22.12 ( (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) ) 22.02/22.12 ( (fun nat (fun nat bool)), nat, (fun nat bool), (combc nat nat bool), (fequal nat), (zero_zero nat) ) 22.02/22.12 ( (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 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(let ((_let_11 (fun int _let_3))) (let ((_let_12 (fun int _let_0))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun nat bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_2 _let_10 (hAPP (fun _let_1 _let_9) (fun _let_2 _let_10) (combb _let_1 _let_9 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_6 (hAPP _let_11 (fun (fun nat real) _let_6) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_11 (hAPP (fun _let_0 _let_3) (fun _let_12 _let_11) (combb _let_0 _let_3 int) (combb real real nat)) (hAPP _let_4 _let_12 (hAPP (fun real _let_0) (fun _let_4 _let_12) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 22.02/22.13 ( (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 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(combb real real nat)) (hAPP _let_2 _let_5 (hAPP (fun real _let_0) (fun _let_2 _let_5) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))) ) 22.02/22.13 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat bool))) (fun (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1))))), (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 real))) (let ((_let_1 (fun nat bool))) (combb (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) 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)))))) ) 22.02/22.13 ( (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) ) 22.02/22.13 ( (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_1))) (let ((_let_4 (fun int _let_0))) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_1) (fun _let_4 _let_3) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_4 (hAPP (fun real _let_0) (fun _let_2 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))))))), (real_1 nat) ) 22.02/22.13 ( (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))))) ) 22.02/22.13 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (real_1 int))) (let ((_let_6 (fun real bool))) (let ((_let_7 (fun real _let_6))) (let ((_let_8 (fun int _let_3))) (let ((_let_9 (fun (fun int bool) (fun int (fun int bool))))) (let ((_let_10 (fun int _let_2))) (let ((_let_11 (fun _let_10 _let_8))) (let ((_let_12 (fun (fun int (fun int bool)) _let_10))) (let ((_let_13 (fun int real))) (let ((_let_14 (fun int _let_0))) (let ((_let_15 (fun _let_13 (fun int bool)))) (let ((_let_16 (fun real (fun int (fun int bool))))) (let ((_let_17 (fun real _let_9))) (let ((_let_18 (fun real _let_8))) (let ((_let_19 (fun real _let_10))) (let ((_let_20 (fun int _let_13))) (let ((_let_21 (fun _let_20 (fun int (fun int bool))))) (let ((_let_22 (fun real _let_21))) (let ((_let_23 (fun real _let_15))) (let ((_let_24 (fun _let_13 _let_13))) (let ((_let_25 (fun int _let_24))) (hAPP _let_18 _let_17 (hAPP (fun _let_8 _let_9) (fun _let_18 _let_17) (combb _let_8 _let_9 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_19 _let_18 (hAPP _let_11 (fun _let_19 _let_18) (combb _let_10 _let_8 real) (hAPP (fun _let_2 _let_3) _let_11 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_16 _let_19 (hAPP _let_12 (fun _let_16 _let_19) (combb (fun int (fun int bool)) _let_10 real) (hAPP _let_4 _let_12 (combb (fun int bool) _let_2 int) (hAPP 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_let_0 _let_0 (combc int int bool) (fequal int)) (zero_zero int)))) ) 22.02/22.13 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (real_1 int))) (let ((_let_6 (fun real bool))) (let ((_let_7 (fun real _let_6))) (let ((_let_8 (fun int _let_3))) (let ((_let_9 (fun int _let_2))) (let ((_let_10 (fun _let_9 _let_8))) (let ((_let_11 (fun (fun int (fun int bool)) _let_9))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int 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((_let_5 (fun real _let_2))) (hAPP _let_5 _let_4 (hAPP (fun _let_2 _let_3) (fun _let_5 _let_4) (combb _let_2 _let_3 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_5) (combb _let_0 _let_2 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_0))) (let ((_let_4 (fun int _let_2))) (let ((_let_5 (fun _let_2 _let_2))) (let ((_let_6 (fun int _let_5))) (hAPP _let_2 _let_4 (hAPP _let_6 (fun _let_2 _let_4) (combc int _let_2 _let_2) (hAPP _let_3 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_3 _let_6) (combb _let_0 _let_5 int) (combb real real int)) (hAPP _let_2 _let_3 (hAPP (fun real _let_0) (fun _let_2 _let_3) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))) ) 22.02/22.13 ( (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 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(instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_117915 $$unsorted) (BOUND_VARIABLE_117916 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117916) BOUND_VARIABLE_117915)) (= (ti X_a BOUND_VARIABLE_117916) (ti X_a BOUND_VARIABLE_117915))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_117915) BOUND_VARIABLE_117916))))))) ) 22.02/22.13 ( int, pls, (zero_zero int) ) 22.02/22.13 ( int, (one_one int), (zero_zero int) ) 22.02/22.13 ( int, (one_one int), t ) 22.02/22.13 ( int, min, min ) 22.02/22.13 ( int, min, (zero_zero int) ) 22.02/22.13 ( int, (zero_zero int), pls ) 22.02/22.13 ( int, (zero_zero int), (one_one int) ) 22.02/22.13 ( int, (zero_zero int), min ) 22.02/22.13 ( 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 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m)) (one_one int))), skv_4 ) 22.02/22.13 ( 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_5 ) 22.02/22.13 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.02/22.13 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.13 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.02/22.13 ( int, t, (one_one int) ) 22.02/22.13 ( 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))) ) 22.02/22.13 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.13 ( 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))) ) 22.02/22.13 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.13 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.13 ( nat, (zero_zero nat), n ) 22.02/22.13 ( nat, (zero_zero nat), tn ) 22.02/22.13 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.02/22.13 ( nat, n, (zero_zero nat) ) 22.02/22.13 ( nat, tn, (zero_zero nat) ) 22.02/22.13 ( real, pi, (zero_zero real) ) 22.02/22.13 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.13 ( 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)) ) 22.02/22.13 ( 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)))) ) 22.02/22.13 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.13 ( 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)))), (zero_zero real) ) 22.02/22.13 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.13 ( real, (zero_zero real), pi ) 22.02/22.13 ( 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)))) ) 22.02/22.13 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.13 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.13 ( 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))))) ) 22.02/22.13 ( real, (zero_zero real), skv_2 ) 22.02/22.13 ( real, (zero_zero real), skv_9 ) 22.02/22.13 ( real, (zero_zero real), skv_12 ) 22.02/22.13 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.02/22.13 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.02/22.13 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.02/22.13 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.02/22.13 ( 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) ) 22.02/22.13 ( 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 ) 22.02/22.13 ( real, skv_2, (zero_zero real) ) 22.02/22.13 ( real, skv_9, (zero_zero real) ) 22.02/22.13 ( real, skv_12, (zero_zero real) ) 22.02/22.13 ) 22.02/22.13 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (preorder T_1)) (preorder (fun T_2 T_1))) ) 22.02/22.13 ( rat, real ) 22.02/22.13 ( rat, (product_prod int int) ) 22.02/22.13 ( int, rat ) 22.02/22.13 ( int, int ) 22.02/22.13 ( int, (fun int int) ) 22.02/22.13 ( int, nat ) 22.02/22.13 ( int, bool ) 22.02/22.13 ( int, real ) 22.02/22.13 ( int, (fun nat real) ) 22.02/22.13 ( int, (fun real real) ) 22.02/22.13 ( int, (fun nat nat) ) 22.02/22.13 ( int, (fun int rat) ) 22.02/22.13 ( int, (fun int bool) ) 22.02/22.13 ( int, (product_prod int int) ) 22.02/22.13 ( int, (fun (product_prod int int) int) ) 22.02/22.13 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.02/22.13 ( int, (fun nat int) ) 22.02/22.13 ( int, (fun bool bool) ) 22.02/22.13 ( int, (fun int (fun bool bool)) ) 22.02/22.13 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.02/22.13 ( int, (fun int (fun int bool)) ) 22.02/22.13 ( int, (fun nat bool) ) 22.02/22.13 ( int, (fun (product_prod int int) bool) ) 22.02/22.13 ( int, (fun int (fun (product_prod int int) bool)) ) 22.02/22.13 ( int, quickcheck_code_int ) 22.02/22.13 ( int, (fun (fun int bool) bool) ) 22.02/22.13 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.02/22.13 ( int, (product_prod int (product_prod int int)) ) 22.02/22.13 ( int, (fun int (product_prod int (product_prod int int))) ) 22.02/22.13 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 22.02/22.13 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.02/22.13 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.02/22.13 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.02/22.13 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.02/22.13 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.02/22.13 ( int, (fun nat (fun bool bool)) ) 22.02/22.13 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.02/22.13 ( int, (fun int (product_prod int int)) ) 22.02/22.13 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.02/22.13 ( int, (fun int (fun (fun int bool) bool)) ) 22.02/22.13 ( int, (fun (fun int int) (fun int bool)) ) 22.02/22.13 ( int, (list int) ) 22.02/22.13 ( int, (fun int (fun int (fun int bool))) ) 22.02/22.13 ( int, (fun int real) ) 22.02/22.13 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.02/22.13 ( (fun int int), (fun int int) ) 22.02/22.13 ( (fun int int), (fun int bool) ) 22.02/22.13 ( (fun int int), (fun int (fun int int)) ) 22.02/22.13 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.02/22.13 ( (fun int int), (fun int (fun int bool)) ) 22.02/22.13 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.02/22.13 ( nat, rat ) 22.02/22.13 ( nat, int ) 22.02/22.13 ( nat, (fun int int) ) 22.02/22.13 ( nat, nat ) 22.02/22.13 ( nat, bool ) 22.02/22.13 ( nat, real ) 22.02/22.13 ( nat, (fun real real) ) 22.02/22.13 ( nat, (fun nat nat) ) 22.02/22.13 ( nat, complex ) 22.02/22.13 ( nat, (product_prod int int) ) 22.02/22.13 ( nat, (fun bool bool) ) 22.02/22.13 ( nat, (fun nat bool) ) 22.02/22.13 ( nat, (fun nat (fun nat bool)) ) 22.02/22.13 ( nat, (fun nat (product_prod int int)) ) 22.02/22.13 ( nat, (product_prod real real) ) 22.02/22.13 ( nat, (product_prod nat nat) ) 22.02/22.13 ( nat, (fun (product_prod nat nat) bool) ) 22.02/22.13 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 22.02/22.13 ( nat, (fun nat (product_prod nat nat)) ) 22.02/22.13 ( bool, bool ) 22.02/22.13 ( bool, (fun bool bool) ) 22.02/22.13 ( real, nat ) 22.02/22.13 ( real, bool ) 22.02/22.13 ( real, real ) 22.02/22.13 ( real, (fun nat real) ) 22.02/22.13 ( real, (fun real real) ) 22.02/22.13 ( real, (fun (filter nat) bool) ) 22.02/22.13 ( real, complex ) 22.02/22.13 ( real, (fun int bool) ) 22.02/22.13 ( real, (fun bool bool) ) 22.02/22.13 ( real, (fun int (fun int bool)) ) 22.02/22.13 ( real, (fun real complex) ) 22.02/22.13 ( real, (fun real bool) ) 22.02/22.13 ( real, (fun nat (product_prod real real)) ) 22.02/22.13 ( real, (fun real (fun nat (product_prod real real))) ) 22.02/22.13 ( real, (fun (filter real) bool) ) 22.02/22.13 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.02/22.13 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 22.02/22.13 ( real, (fun int (fun int (fun bool bool))) ) 22.02/22.13 ( real, (fun int (fun nat bool)) ) 22.02/22.13 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 22.02/22.13 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.02/22.13 ( real, (fun int (fun nat (fun bool bool))) ) 22.02/22.13 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.02/22.13 ( real, (fun (fun nat real) (fun nat bool)) ) 22.02/22.13 ( real, (fun (fun int real) (fun int bool)) ) 22.02/22.13 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.02/22.13 ( (fun nat real), (fun nat real) ) 22.02/22.13 ( (fun nat real), (fun nat bool) ) 22.02/22.13 ( (fun nat real), (fun nat (fun real real)) ) 22.02/22.13 ( (fun nat real), (fun int (fun nat real)) ) 22.02/22.13 ( (fun real real), (fun real real) ) 22.02/22.14 ( (fun real real), (fun real (fun real bool)) ) 22.02/22.14 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (fun real real), (fun real (fun real real)) ) 22.02/22.14 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (fun nat nat), (fun nat real) ) 22.02/22.14 ( (fun nat nat), (fun nat (fun nat bool)) ) 22.02/22.14 ( (fun nat nat), (fun nat (fun nat nat)) ) 22.02/22.14 ( (filter nat), bool ) 22.02/22.14 ( complex, nat ) 22.02/22.14 ( complex, real ) 22.02/22.14 ( complex, complex ) 22.02/22.14 ( (fun int bool), int ) 22.02/22.14 ( (fun int bool), bool ) 22.02/22.14 ( (fun int bool), (fun int bool) ) 22.02/22.14 ( (fun int bool), (fun int (fun int int)) ) 22.02/22.14 ( (fun int bool), (fun int (fun bool bool)) ) 22.02/22.14 ( (fun int bool), (fun int (fun int bool)) ) 22.02/22.14 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 22.02/22.14 ( (fun int bool), (fun real (fun int (fun int bool))) ) 22.02/22.14 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 22.02/22.14 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 22.02/22.14 ( (product_prod int int), rat ) 22.02/22.14 ( (product_prod int int), int ) 22.02/22.14 ( (product_prod int int), (fun int int) ) 22.02/22.14 ( (product_prod int int), bool ) 22.02/22.14 ( (product_prod int int), (fun int bool) ) 22.02/22.14 ( (product_prod int int), (product_prod int int) ) 22.02/22.14 ( (product_prod int int), (fun (product_prod int int) int) ) 22.02/22.14 ( (product_prod int int), (fun bool bool) ) 22.02/22.14 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.02/22.14 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 22.02/22.14 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.02/22.14 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 22.02/22.14 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 22.02/22.14 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 22.02/22.14 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 22.02/22.14 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 22.02/22.14 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.02/22.14 ( (fun int (fun int bool)), (fun int bool) ) 22.02/22.14 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 22.02/22.14 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 22.02/22.14 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 22.02/22.14 ( (fun nat bool), bool ) 22.02/22.14 ( (fun nat bool), (fun nat bool) ) 22.02/22.14 ( (fun nat bool), (fun nat (fun bool bool)) ) 22.02/22.14 ( (fun nat bool), (fun int (fun nat bool)) ) 22.02/22.14 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 22.02/22.14 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 22.02/22.14 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 22.02/22.14 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 22.02/22.14 ( (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))) ) 22.02/22.14 ( (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))) ) 22.02/22.14 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.02/22.14 ( (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))) ) 22.02/22.17 ( (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)))) ) 22.02/22.17 ( (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)))) ) 22.02/22.17 ( (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))) ) 22.02/22.17 ( (fun real bool), real ) 22.02/22.17 ( (fun real bool), (fun real bool) ) 22.02/22.17 ( (fun real bool), (fun real (fun bool bool)) ) 22.02/22.17 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 22.02/22.17 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 22.02/22.17 ( quickcheck_code_int, int ) 22.02/22.17 ( quickcheck_code_int, nat ) 22.02/22.17 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 22.02/22.17 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 22.02/22.17 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 22.02/22.17 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 22.02/22.17 ( code_code_numeral, int ) 22.02/22.17 ( code_code_numeral, nat ) 22.02/22.17 ( code_code_numeral, (fun nat nat) ) 22.02/22.17 ( code_code_numeral, code_code_numeral ) 22.02/22.17 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 22.02/22.17 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.02/22.17 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.02/22.17 ( (product_prod real real), bool ) 22.02/22.17 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 22.02/22.17 ( (filter real), bool ) 22.02/22.17 ( (product_prod nat nat), bool ) 22.02/22.17 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 22.02/22.17 ( (fun nat rat), bool ) 22.02/22.17 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 22.02/22.17 ( (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))) ) 22.02/22.17 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.02/22.17 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 22.02/22.17 ( (fun int real), (fun int bool) ) 22.02/22.17 ( (fun int real), (fun int real) ) 22.02/22.17 ( (fun int real), (fun int (fun real real)) ) 22.02/22.17 ( (fun int real), (fun int (fun int real)) ) 22.02/22.17 ( (fun real (fun int bool)), (fun real bool) ) 22.02/22.17 ( (fun int (fun nat bool)), (fun int bool) ) 22.02/22.17 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 22.02/22.17 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 22.02/22.17 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 22.02/22.17 ( (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))) ) 22.02/22.17 ( (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)))) ) 22.02/22.17 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.02/22.17 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.02/22.17 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 22.02/22.17 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 22.02/22.17 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.02/22.17 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 22.02/22.17 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 22.02/22.17 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 22.02/22.17 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.02/22.17 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 22.02/22.17 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 22.02/22.17 ( (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)))) ) 22.02/22.17 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.02/22.17 ( (fun int (fun int real)), (fun int (fun int bool)) ) 22.02/22.17 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 22.02/22.17 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real _let_0 (hAPP real real tan X)) (hAPP real real tan (hAPP real real _let_0 X)))) ) 22.02/22.17 ( (hAPP real 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))))) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real ln (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) X))) X))))) ) 22.02/22.17 ( pi ) 22.02/22.17 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( skv_10 ) 22.02/22.17 ( skv_11 ) 22.02/22.17 ( skv_15 ) 22.02/22.17 ( skv_18 ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((N $$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))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 N) P_5))) (= (one_one int) (hAPP int int (hAPP int (fun int int) legacy_zgcd N) P_5))))) ) 22.02/22.17 ( (one_one int), t ) 22.02/22.17 ( min, min ) 22.02/22.17 ( min, (zero_zero int) ) 22.02/22.17 ( (zero_zero int), pls ) 22.02/22.17 ( (zero_zero int), (one_one int) ) 22.02/22.17 ( (zero_zero int), min ) 22.02/22.17 ( (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))) ) 22.02/22.17 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.17 ( 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))) ) 22.02/22.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.17 ( 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))) ) 22.02/22.17 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.17 ( 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))) ) 22.02/22.17 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (ring_1_of_int rat))) (= (hAPP int rat (hAPP int (fun int rat) fract K_4) L_4) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (hAPP int rat _let_0 K_4)) (hAPP int rat _let_0 L_4)))) ) 22.02/22.17 ( (one_one int), (one_one int) ) 22.02/22.17 ( (zero_zero int), (one_one int) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((I $$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)))))) ) 22.02/22.17 ( min ) 22.02/22.17 ( s ) 22.02/22.17 ( s1 ) 22.02/22.17 ( m ) 22.02/22.17 ( t ) 22.02/22.17 ( v ) 22.02/22.17 ( w ) 22.02/22.17 ( y ) 22.02/22.17 ( sa ) 22.02/22.17 ( x ) 22.02/22.17 ( r ) 22.02/22.17 ( m1 ) 22.02/22.17 ( skv_14 ) 22.02/22.17 ( skv_20 ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) X) (hAPP nat nat suc _let_1)))) (= _let_1 X) (= _let_0 X)))) ) 22.02/22.17 ( (zero_zero nat) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (plus_plus real))) (let ((_let_4 (abs_abs real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 (ord_less_eq real) (hAPP real real _let_4 X)) _let_1))) (not (hBOOL (hAPP real bool (hAPP real _let_2 (ord_less real) (hAPP real real _let_4 Y)) _let_1))) (= (hAPP real real arctan (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real (hAPP real _let_0 _let_3 X) Y)) (hAPP real real (hAPP real _let_0 (minus_minus real) _let_1) (hAPP real real (hAPP real _let_0 (times_times real) X) Y)))) (hAPP real real (hAPP real _let_0 _let_3 (hAPP real real arctan X)) (hAPP real real arctan Y))))))))) ) 22.02/22.17 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.17 ( 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))))) ) 22.02/22.17 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.17 ( (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)))) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted)) (let ((_let_0 (big_co1399186613setsum X_a X_c))) (or (not (comm_monoid_add X_c)) (= _let_0 (ti (fun (fun X_a X_c) (fun (fun X_a bool) X_c)) _let_0)))) ) 22.02/22.17 ( int, int ) 22.02/22.17 ( int, bool ) 22.02/22.17 ( int, (fun int bool) ) 22.02/22.17 ( int, (fun int (fun int int)) ) 22.02/22.17 ( int, (fun int (fun bool bool)) ) 22.02/22.17 ( int, (fun int (fun int bool)) ) 22.02/22.17 ( int, (fun (fun int int) (fun int bool)) ) 22.02/22.17 ( int, (fun real (fun int (fun int bool))) ) 22.02/22.17 ( nat, bool ) 22.02/22.17 ( nat, (fun nat bool) ) 22.02/22.17 ( nat, (fun nat (fun bool bool)) ) 22.02/22.17 ( nat, (fun int (fun nat bool)) ) 22.02/22.17 ( nat, (fun real (fun int (fun nat bool))) ) 22.02/22.17 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.02/22.17 ( real, real ) 22.02/22.17 ( real, (fun real bool) ) 22.02/22.17 ( real, (fun real (fun bool bool)) ) 22.02/22.17 ( real, (fun (fun nat real) (fun nat bool)) ) 22.02/22.17 ( real, (fun (fun int real) (fun int bool)) ) 22.02/22.17 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.02/22.17 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 22.02/22.17 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X_a $$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)))))) ) 22.02/22.17 ( rat ) 22.02/22.17 ( int ) 22.02/22.17 ( nat ) 22.02/22.17 ( real ) 22.02/22.17 ( complex ) 22.02/22.17 ( quickcheck_code_int ) 22.02/22.17 ( code_code_numeral ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((M $$unsorted) (N $$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))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N)))) ) 22.02/22.17 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.17 ( (zero_zero nat), n ) 22.02/22.17 ( (zero_zero nat), tn ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP nat nat suc _let_0) N) (= _let_0 N))) ) 22.02/22.17 ( (zero_zero nat) ) 22.02/22.17 ) 22.02/22.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118082 $$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 (plus_plus X_a) BOUND_VARIABLE_118082) BOUND_VARIABLE_118082) (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_118082)))) ) 22.02/22.17 ( int, (one_one int) ) 22.02/22.17 ( 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)))) ) 22.02/22.17 ( 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) ) 22.02/22.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.17 ( int, (hAPP int int (abs_abs int) w) ) 22.02/22.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.17 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.17 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.17 ( int, (hAPP int int (abs_abs int) v) ) 22.02/22.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.02/22.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( int, (hAPP int int (abs_abs int) skv_14) ) 22.02/22.17 ( int, (hAPP int int (abs_abs int) skv_20) ) 22.02/22.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.17 ( nat, (one_one nat) ) 22.02/22.17 ( real, pi ) 22.02/22.17 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.02/22.17 ( complex, (hAPP real complex (of_real complex) pi) ) 22.02/22.17 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118098 $$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_118098)) (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_118098)) (zero_zero X_a)) sequentially))))) ) 22.02/22.18 ( int, s ) 22.02/22.18 ( int, s1 ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.18 ( int, v ) 22.02/22.18 ( int, w ) 22.02/22.18 ( int, y ) 22.02/22.18 ( int, x ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.02/22.18 ( int, skv_6 ) 22.02/22.18 ( int, skv_7 ) 22.02/22.18 ( int, skv_16 ) 22.02/22.18 ( int, skv_23 ) 22.02/22.18 ( int, skv_24 ) 22.02/22.18 ( real, (hAPP int real (number_number_of real) min) ) 22.02/22.18 ( 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)))) ) 22.02/22.18 ( complex, ii ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((Na $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 Na))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) K_1) Na))) (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 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) I_2) K_1))) (not (hBOOL (hAPP nat bool P_1 I_2)))) ))) ))) ) 22.02/22.18 ( (zero_zero nat), (even_odd_even nat) ) 22.02/22.18 ( (zero_zero nat), prime ) 22.02/22.18 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 22.02/22.18 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 22.02/22.18 ( (one_one nat), (even_odd_even nat) ) 22.02/22.18 ( (hAPP nat nat suc (zero_zero nat)), prime ) 22.02/22.18 ( n, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 22.02/22.18 ( tn, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118149 $$unsorted) (BOUND_VARIABLE_118150 $$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_118149)) (hAPP int int (number_number_of int) BOUND_VARIABLE_118150)) (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_118149) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_118150)))))) ) 22.02/22.18 ( int, (one_one int), pls ) 22.02/22.18 ( 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)))), (hAPP int int bit1 pls) ) 22.02/22.18 ( 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), (hAPP int int bit1 pls) ) 22.02/22.18 ( nat, (one_one nat), (hAPP int int bit1 pls) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118178 $$unsorted) (BOUND_VARIABLE_118179 $$unsorted) (BOUND_VARIABLE_118180 $$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_118180) (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_118178) BOUND_VARIABLE_118180)) BOUND_VARIABLE_118179)) (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_118179) BOUND_VARIABLE_118180)) BOUND_VARIABLE_118178))))))) ) 22.02/22.18 ( int, pls, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, s, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.02/22.18 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, skv_4, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( int, skv_5, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.18 ( 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))) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118216 $$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_118216) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_118216)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_118216)) _let_3))))))) ) 22.02/22.18 ( int, pls ) 22.02/22.18 ( int, min ) 22.02/22.18 ( int, s ) 22.02/22.18 ( int, s1 ) 22.02/22.18 ( int, m ) 22.02/22.18 ( int, t ) 22.02/22.18 ( int, v ) 22.02/22.18 ( int, w ) 22.02/22.18 ( int, y ) 22.02/22.18 ( int, sa ) 22.02/22.18 ( int, x ) 22.02/22.18 ( int, r ) 22.02/22.18 ( int, m1 ) 22.02/22.18 ( int, skv_14 ) 22.02/22.18 ( int, skv_20 ) 22.02/22.18 ( (fun int int), bit1 ) 22.02/22.18 ( (fun int int), bit0 ) 22.02/22.18 ( (fun int int), succ ) 22.02/22.18 ( (fun int int), pred ) 22.02/22.18 ( (fun int int), (fact_fact int) ) 22.02/22.18 ( (fun int int), zfact ) 22.02/22.18 ( nat, n ) 22.02/22.18 ( nat, tn ) 22.02/22.18 ( bool, fTrue ) 22.02/22.18 ( bool, fFalse ) 22.02/22.18 ( real, pi ) 22.02/22.18 ( real, (zero_zero real) ) 22.02/22.18 ( (fun nat real), (real_1 nat) ) 22.02/22.18 ( (fun nat real), cos_coeff ) 22.02/22.18 ( (fun nat real), sin_coeff ) 22.02/22.18 ( (fun real real), sin ) 22.02/22.18 ( (fun real real), cos ) 22.02/22.18 ( (fun real real), sqrt ) 22.02/22.18 ( (fun real real), tan ) 22.02/22.18 ( (fun real real), ln ) 22.02/22.18 ( (fun real real), arctan ) 22.02/22.18 ( (fun real real), arcsin ) 22.02/22.18 ( (fun real real), arccos ) 22.02/22.18 ( (fun nat nat), suc ) 22.02/22.18 ( (fun nat nat), (fact_fact nat) ) 22.02/22.18 ( (fun nat nat), nat_size ) 22.02/22.18 ( (fun nat nat), (size_size nat) ) 22.02/22.18 ( (fun nat nat), fact ) 22.02/22.18 ( (filter nat), sequentially ) 22.02/22.18 ( (fun int (fun int rat)), fract ) 22.02/22.18 ( complex, ii ) 22.02/22.18 ( (fun int bool), zOdd ) 22.02/22.18 ( (fun int bool), zprime ) 22.02/22.18 ( (fun int bool), zEven ) 22.02/22.18 ( (fun int bool), nat_neg ) 22.02/22.18 ( (fun int bool), nat_is_nat ) 22.02/22.18 ( (fun int bool), (even_odd_even int) ) 22.02/22.18 ( (fun int bool), twoSqu1091635170sum2sq ) 22.02/22.18 ( (fun int (fun int int)), legacy_zgcd ) 22.02/22.18 ( (fun int (fun int int)), (gcd_gcd int) ) 22.02/22.18 ( (fun int (fun int int)), inv ) 22.02/22.18 ( (fun int (fun int int)), multInv ) 22.02/22.18 ( (fun int (fun int int)), legendre ) 22.02/22.18 ( (fun int (fun int int)), standardRes ) 22.02/22.18 ( (fun int (fun int int)), nat_tsub ) 22.02/22.18 ( (fun int (fun int int)), z3div ) 22.02/22.18 ( (fun int (fun int int)), z3mod ) 22.02/22.18 ( (fun int (fun int int)), int_lcm ) 22.02/22.18 ( (fun int (fun int int)), int_gcd ) 22.02/22.18 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.02/22.18 ( (fun bool bool), fNot ) 22.02/22.18 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.02/22.18 ( (fun bool (fun bool bool)), fconj ) 22.02/22.18 ( (fun bool (fun bool bool)), fdisj ) 22.02/22.18 ( (fun bool (fun bool bool)), fimplies ) 22.02/22.18 ( (fun int (fun int bool)), quadRes ) 22.02/22.18 ( (fun int (fun int bool)), d22set ) 22.02/22.18 ( (fun int (fun int bool)), norRRset ) 22.02/22.18 ( (fun int (fun int bool)), sRStar ) 22.02/22.18 ( (fun int (fun int bool)), sr ) 22.02/22.18 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.02/22.18 ( (fun nat bool), (even_odd_even nat) ) 22.02/22.18 ( (fun nat bool), prime ) 22.02/22.18 ( (fun real complex), cis ) 22.02/22.18 ( (fun nat (fun nat bool)), coprime ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.02/22.18 ( (fun (product_prod int int) bool), frac_1 ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.02/22.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.02/22.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.02/22.18 ( (fun (fun int bool) bool), nat_nat_set ) 22.02/22.18 ( (fun nat (fun real real)), root ) 22.02/22.18 ( (fun real (fun real real)), log ) 22.02/22.18 ( (fun real (fun real real)), powr ) 22.02/22.18 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.02/22.18 ( (fun complex complex), cnj ) 22.02/22.18 ( (fun complex complex), expi ) 22.02/22.18 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.02/22.18 ( (fun nat (fun nat nat)), nat_gcd ) 22.02/22.18 ( (fun nat (fun nat nat)), nat_lcm ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.02/22.18 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.02/22.18 ( (fun int (fun (fun int bool) bool)), resSet ) 22.02/22.18 ( (fun int nat), nat_1 ) 22.02/22.18 ( (fun int nat), phi ) 22.02/22.18 ( (fun complex real), re ) 22.02/22.18 ( (fun complex real), im ) 22.02/22.18 ( (fun complex real), arg ) 22.02/22.18 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.02/22.18 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.02/22.18 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.02/22.18 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.02/22.18 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.02/22.18 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.02/22.18 ( (fun (product_prod nat nat) bool), pred_nat ) 22.02/22.18 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.02/22.18 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.02/22.18 ( (fun (fun int bool) int), (the int) ) 22.02/22.18 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.02/22.18 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.02/22.18 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.02/22.18 ( (fun real (fun real complex)), rcis ) 22.02/22.18 ( (fun real (fun real complex)), complex_1 ) 22.02/22.18 ( (fun int (fun int (fun int bool))), zcong ) 22.02/22.18 ( (fun int (fun int (fun int bool))), wset ) 22.02/22.18 ( (fun int (fun int (fun int bool))), noXRRset ) 22.02/22.18 ( (fun int (fun int (fun int bool))), bnorRset ) 22.02/22.18 ( (fun int (fun int (fun int bool))), zcongm ) 22.02/22.18 ( (fun real nat), natceiling ) 22.02/22.18 ( (fun real nat), natfloor ) 22.02/22.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.02/22.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.02/22.18 ( (fun int real), (real_1 int) ) 22.02/22.18 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.02/22.18 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.02/22.18 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.02/22.18 ( (fun complex nat), (size_size complex) ) 22.02/22.18 ( (fun complex nat), complex_size ) 22.02/22.18 ( (fun (fun nat rat) bool), vanishes ) 22.02/22.18 ( (fun (product_prod int int) rat), frct ) 22.02/22.18 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.02/22.18 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.02/22.18 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.02/22.18 ( (fun rat real), ratreal ) 22.02/22.18 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.02/22.18 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.02/22.18 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.02/22.18 ( (fun rat (product_prod int int)), quotient_of ) 22.02/22.18 ( (fun int (fun nat nat)), nat_aux ) 22.02/22.18 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.02/22.18 ( (fun int (list int)), quickc666637781d_zero ) 22.02/22.18 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.02/22.18 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.02/22.18 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.02/22.18 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.02/22.18 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.02/22.18 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.02/22.18 ( (fun code_code_numeral int), code_int_of ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M) N))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N))) ) 22.02/22.18 ( (hAPP int nat nat_1 t), (one_one nat) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int _let_2 W))) (let ((_let_4 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) _let_3)))) (let ((_let_5 (hAPP int (fun int _let_1) posDivAlg (one_one int)))) (let ((_let_6 (hAPP int _let_1 _let_5 _let_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_3))) (and (or (not _let_4) (= (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) (one_one int)) _let_6)) (or _let_4 (= _let_6 (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust _let_3) (hAPP int _let_1 _let_5 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_3)))))))))))))) ) 22.02/22.18 ( pls ) 22.02/22.18 ( (hAPP int int bit1 pls) ) 22.02/22.18 ( min ) 22.02/22.18 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.18 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.18 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) (hAPP _let_0 nat (finite_card X_a) A_2)))) (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_2)))) ) 22.02/22.18 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118319 $$unsorted) (BOUND_VARIABLE_118320 $$unsorted) (BOUND_VARIABLE_118321 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_118320))) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_118321))) (not (= (ti X_a BOUND_VARIABLE_118321) (ti X_a BOUND_VARIABLE_118319))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_118319)))) ) 22.02/22.18 ( int, pls, (zero_zero int), s ) 22.02/22.18 ( int, min, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.18 ( int, s, min, min ) 22.02/22.18 ( int, s1, (zero_zero int), (one_one int) ) 22.02/22.18 ( int, m, (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.18 ( int, t, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.18 ( int, v, (one_one int), t ) 22.02/22.18 ( int, w, (zero_zero int), skv_4 ) 22.02/22.18 ( int, y, (zero_zero int), min ) 22.02/22.18 ( int, sa, (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.18 ( int, x, (zero_zero int), skv_5 ) 22.02/22.18 ( int, r, (zero_zero int), pls ) 22.02/22.18 ( int, m1, min, pls ) 22.02/22.18 ( int, skv_14, (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.18 ( int, skv_20, (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.18 ( real, pi, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (times_times real) A_1) X) (hAPP real real (hAPP real _let_0 (scaleR_scaleR real) A_1) X))) ) 22.02/22.18 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.02/22.18 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.02/22.18 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.18 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0))))), pi ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) M))) (or (not (hBOOL (hAPP nat bool _let_0 N))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc N))))) ) 22.02/22.18 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118371 $$unsorted) (BOUND_VARIABLE_118372 $$unsorted) (BOUND_VARIABLE_118373 $$unsorted)) (or (not (order X_a)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_118373 N_1)) (hAPP nat X_a BOUND_VARIABLE_118373 (hAPP nat nat suc N_1)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_118371) BOUND_VARIABLE_118372))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_118373 BOUND_VARIABLE_118371)) (hAPP nat X_a BOUND_VARIABLE_118373 BOUND_VARIABLE_118372)))) ) 22.02/22.18 ( 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) ) 22.02/22.18 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 22.02/22.18 ( 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) ) 22.02/22.18 ( 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))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((M $$unsorted)) (= (hAPP int int (hAPP int (fun int int) legacy_zgcd (zero_zero int)) M) (hAPP int int (abs_abs int) M)) ) 22.02/22.18 ( v ) 22.02/22.18 ( w ) 22.02/22.18 ( skv_14 ) 22.02/22.18 ( skv_20 ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118467 $$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_118467) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP X_a int _let_0 BOUND_VARIABLE_118467)) (one_one int))))) ) 22.02/22.18 ( int, (one_one int) ) 22.02/22.18 ( 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)))) ) 22.02/22.18 ( 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) ) 22.02/22.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.18 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.18 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.02/22.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( nat, (one_one nat) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex real re (hAPP real complex (of_real complex) Z_1))) ) 22.02/22.18 ( (hAPP int real (number_number_of real) min) ) 22.02/22.18 ( pi ) 22.02/22.18 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (inverse_inverse real) (hAPP rat real ratreal X)) (hAPP rat real ratreal (hAPP rat rat (inverse_inverse rat) X))) ) 22.02/22.18 ( (zero_zero rat) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118526 $$unsorted) (BOUND_VARIABLE_118527 $$unsorted)) (let ((_let_0 (ti X_a BOUND_VARIABLE_118527))) (or (not (division_ring X_a)) (= (zero_zero X_a) _let_0) (= (= _let_0 (ti X_a BOUND_VARIABLE_118526)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_118526) BOUND_VARIABLE_118527))))) ) 22.02/22.18 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.18 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.18 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.18 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( 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))))))))) ) 22.02/22.18 ( 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))) ) 22.02/22.18 ( 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))) ) 22.02/22.18 ( 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))) ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= (hAPP complex complex cnj Xa) (hAPP complex complex cnj Ya)) (= Xa Ya)) ) 22.02/22.18 ( (zero_zero complex), (zero_zero complex) ) 22.02/22.18 ( (zero_zero complex), (one_one complex) ) 22.02/22.18 ( ii, (zero_zero complex) ) 22.02/22.18 ( (one_one complex), (zero_zero complex) ) 22.02/22.18 ( (one_one complex), ii ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (hBOOL (hAPP real bool (hAPP _let_0 (fun real bool) (isCont real real) (hAPP nat _let_0 root Na)) (zero_zero real))))) ) 22.02/22.18 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.18 ( n ) 22.02/22.18 ( tn ) 22.02/22.18 ) 22.02/22.18 (instantiation (forall ((V_2 $$unsorted) (V $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_2) pls)))) (let ((_let_2 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 V_2)))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (and (or (not _let_1) (= (hAPP int nat _let_0 V) _let_2)) (or _let_1 (= _let_2 (hAPP int nat _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) V) V_2))))))))) ) 22.02/22.18 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.02/22.18 ( (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)))) ) 22.02/22.18 ( (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) ) 22.02/22.18 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.02/22.18 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.02/22.18 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.18 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.18 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.02/22.18 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.18 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.02/22.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.02/22.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.18 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.18 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.02/22.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.02/22.18 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.02/22.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((V_2 $$unsorted) (V $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int nat _let_0 V_2))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V)) _let_1))))) ) 22.02/22.19 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118570 $$unsorted) (BOUND_VARIABLE_118571 $$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_118570)) (hAPP int int (number_number_of int) BOUND_VARIABLE_118571))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_118570) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_118571))))) ) 22.02/22.19 ( int, min, pls ) 22.02/22.19 ( int, (zero_zero int), pls ) 22.02/22.19 ( int, (zero_zero int), (hAPP int int bit1 pls) ) 22.02/22.19 ( nat, (zero_zero nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.19 ( real, pi, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( 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 int bit0 (hAPP int int bit1 pls)) ) 22.02/22.19 ) 22.02/22.19 (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_atMost nat) K_1))))) ))) ) 22.02/22.19 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118599 $$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_118599)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_118599)))))) ) 22.02/22.19 ( rat, (zero_zero rat) ) 22.02/22.19 ( int, pls ) 22.02/22.19 ( int, (one_one int) ) 22.02/22.19 ( int, min ) 22.02/22.19 ( 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)))) ) 22.02/22.19 ( real, (one_one real) ) 22.02/22.19 ( real, (zero_zero real) ) 22.02/22.19 ( 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) ) 22.02/22.19 ( complex, ii ) 22.02/22.19 ( complex, (one_one complex) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (= (= (ti int Na) (ti int Ma)) (= (hAPP int quickcheck_code_int quickcheck_of_int Na) (hAPP int quickcheck_code_int quickcheck_of_int Ma))) ) 22.02/22.19 ( pls, w ) 22.02/22.19 ( pls, y ) 22.02/22.19 ( min, s ) 22.02/22.19 ( min, m ) 22.02/22.19 ( s, m ) 22.02/22.19 ( s1, s1 ) 22.02/22.19 ( s1, v ) 22.02/22.19 ( m, min ) 22.02/22.19 ( m, m ) 22.02/22.19 ( t, m1 ) 22.02/22.19 ( v, s1 ) 22.02/22.19 ( v, r ) 22.02/22.19 ( w, y ) 22.02/22.19 ( y, pls ) 22.02/22.19 ( y, y ) 22.02/22.19 ( sa, t ) 22.02/22.19 ( sa, m1 ) 22.02/22.19 ( x, x ) 22.02/22.19 ( x, skv_14 ) 22.02/22.19 ( r, s1 ) 22.02/22.19 ( m1, sa ) 22.02/22.19 ( m1, m1 ) 22.02/22.19 ( skv_14, x ) 22.02/22.19 ( skv_14, skv_20 ) 22.02/22.19 ( skv_20, x ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118616 $$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_118616) BOUND_VARIABLE_118616)) (zero_zero X_a))))) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( 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))) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, y ) 22.02/22.19 ( int, sa ) 22.02/22.19 ( int, x ) 22.02/22.19 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.02/22.19 ( int, r ) 22.02/22.19 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.02/22.19 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( int, skv_13 ) 22.02/22.19 ( int, skv_19 ) 22.02/22.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( 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))))) ) 22.02/22.19 ( complex, ii ) 22.02/22.19 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( 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)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X))))))) ) 22.02/22.19 ( pi ) 22.02/22.19 ( (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)))) ) 22.02/22.19 ( (one_one real) ) 22.02/22.19 ( (zero_zero real) ) 22.02/22.19 ( (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))))) ) 22.02/22.19 ( (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) ) 22.02/22.19 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( (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))))) ) 22.02/22.19 ( (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))))) ) 22.02/22.19 ( (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)))) ) 22.02/22.19 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.02/22.19 ( (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)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118634 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (one_one X_a))) (or (not (linord1117847801e_zero X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_118634) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_118634))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_118634)) _let_2))))))) ) 22.02/22.19 ( int, min ) 22.02/22.19 ( int, (zero_zero int) ) 22.02/22.19 ( int, t ) 22.02/22.19 ( real, (zero_zero real) ) 22.02/22.19 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( complex, ii ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118669 $$unsorted) (BOUND_VARIABLE_118670 $$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_118669) BOUND_VARIABLE_118670)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_118669)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_118670))))))) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.02/22.19 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( 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 ) 22.02/22.19 ( 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))), m1 ) 22.02/22.19 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.02/22.19 ( 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_21 ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.02/22.19 ( int, y, v ) 22.02/22.19 ( int, y, w ) 22.02/22.19 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, sa, v ) 22.02/22.19 ( int, sa, w ) 22.02/22.19 ( int, x, v ) 22.02/22.19 ( int, x, w ) 22.02/22.19 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.02/22.19 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, r, v ) 22.02/22.19 ( int, r, w ) 22.02/22.19 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.02/22.19 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.02/22.19 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.02/22.19 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.02/22.19 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.02/22.19 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.02/22.19 ( 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)))))) ) 22.02/22.19 ( 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 ) 22.02/22.19 ( complex, ii, ii ) 22.02/22.19 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.02/22.19 ( 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 ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_3) B_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (hAPP int (fun int rat) fract A_3) B_2)) (one_one rat)))))) ) 22.02/22.19 ( (one_one int), (one_one int) ) 22.02/22.19 ( (one_one int), t ) 22.02/22.19 ( min, pls ) 22.02/22.19 ( min, min ) 22.02/22.19 ( (zero_zero int), pls ) 22.02/22.19 ( (zero_zero int), (one_one int) ) 22.02/22.19 ( (zero_zero int), min ) 22.02/22.19 ( (zero_zero int), s ) 22.02/22.19 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.19 ( (zero_zero int), skv_4 ) 22.02/22.19 ( (zero_zero int), skv_5 ) 22.02/22.19 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((Va $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int _let_2 Va))) (let ((_let_4 (hBOOL (hAPP int bool nat_neg _let_3)))) (let ((_let_5 (hBOOL (hAPP int bool nat_neg (hAPP int int _let_2 V_1))))) (= (and (or (not _let_4) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_2 V_1)) _let_1))) (or _let_4 (and (or (not _let_5) (= _let_1 _let_3)) (or _let_5 (= (ti int V_1) (ti int Va)))))) (= (hAPP int nat _let_0 Va) (hAPP int nat _let_0 V_1))))))))) ) 22.02/22.19 ( pls, pls ) 22.02/22.19 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.02/22.19 ( min, min ) 22.02/22.19 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.19 ( (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))) ) 22.02/22.19 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118760 $$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 _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_118760)) (hAPP X_a _let_0 (power_power X_a) (zero_zero X_a)))) (hAPP nat X_a BOUND_VARIABLE_118760 (zero_zero nat))))))) ) 22.02/22.19 ( int, (semiring_1_of_nat int) ) 22.02/22.19 ( nat, suc ) 22.02/22.19 ( nat, (fact_fact nat) ) 22.02/22.19 ( nat, nat_size ) 22.02/22.19 ( nat, (size_size nat) ) 22.02/22.19 ( nat, fact ) 22.02/22.19 ( bool, (even_odd_even nat) ) 22.02/22.19 ( bool, prime ) 22.02/22.19 ( real, (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) ) 22.02/22.19 ( real, (real_1 nat) ) 22.02/22.19 ( (fun nat bool), (ord_less nat) ) 22.02/22.19 ( (fun nat bool), (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) B_5) Q_5)) R_4)) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 _let_3) R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 _let_3) B_5))) (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 Q_5) _let_3)))))))) ) 22.02/22.19 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 22.02/22.19 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.19 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 22.02/22.19 ( x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.02/22.19 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 22.02/22.19 ( r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.02/22.19 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.02/22.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118864 $$unsorted) (BOUND_VARIABLE_118865 $$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_118864) BOUND_VARIABLE_118865)) BOUND_VARIABLE_118865)))) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.02/22.19 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( 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 ) 22.02/22.19 ( 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))), m1 ) 22.02/22.19 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.02/22.19 ( 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_21 ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.02/22.19 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.02/22.19 ( int, y, v ) 22.02/22.19 ( int, y, w ) 22.02/22.19 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, sa, v ) 22.02/22.19 ( int, sa, w ) 22.02/22.19 ( int, x, v ) 22.02/22.19 ( int, x, w ) 22.02/22.19 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.02/22.19 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, r, v ) 22.02/22.19 ( int, r, w ) 22.02/22.19 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.02/22.19 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.02/22.19 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.02/22.19 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.02/22.19 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.02/22.19 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.02/22.19 ( 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)))))) ) 22.02/22.19 ( 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 ) 22.02/22.19 ( complex, ii, ii ) 22.02/22.19 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.02/22.19 ( 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 ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_118953 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_118953))) (or (not (linord219039673up_add X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_118953))) (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a)))))) ) 22.02/22.19 ( int, pls ) 22.02/22.19 ( int, (one_one int) ) 22.02/22.19 ( int, min ) 22.02/22.19 ( int, (zero_zero int) ) 22.02/22.19 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.02/22.19 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.02/22.19 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.02/22.19 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.02/22.19 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.19 ( 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)))) ) 22.02/22.19 ( real, (one_one real) ) 22.02/22.19 ( real, (zero_zero real) ) 22.02/22.19 ( 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) ) 22.02/22.19 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( real, skv_10 ) 22.02/22.19 ( complex, ii ) 22.02/22.19 ( complex, (one_one complex) ) 22.02/22.19 ) 22.02/22.19 (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))))) ) 22.02/22.19 ( pls, (zero_zero int) ) 22.02/22.19 ( (one_one int), (zero_zero int) ) 22.02/22.19 ( min, min ) 22.02/22.19 ( min, (zero_zero int) ) 22.02/22.19 ( (zero_zero int), min ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.02/22.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.02/22.19 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.02/22.19 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.02/22.19 ( t, (one_one int) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) (zero_zero int)) (ti int A_1)) ) 22.02/22.19 ( pls ) 22.02/22.19 ( min ) 22.02/22.19 ( s ) 22.02/22.19 ( s1 ) 22.02/22.19 ( m ) 22.02/22.19 ( t ) 22.02/22.19 ( v ) 22.02/22.19 ( w ) 22.02/22.19 ( y ) 22.02/22.19 ( sa ) 22.02/22.19 ( x ) 22.02/22.19 ( r ) 22.02/22.19 ( m1 ) 22.02/22.19 ( skv_14 ) 22.02/22.19 ( skv_20 ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (hAPP int complex (number_number_of complex) W))) (= _let_0 (hAPP complex complex cnj _let_0))) ) 22.02/22.19 ( min ) 22.02/22.19 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_119121 $$unsorted) (BOUND_VARIABLE_119122 $$unsorted) (BOUND_VARIABLE_119123 $$unsorted) (BOUND_VARIABLE_119124 $$unsorted) (BOUND_VARIABLE_119125 $$unsorted) (BOUND_VARIABLE_119126 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_c))) (let ((_let_3 (fun X_a X_b))) (let ((_let_4 (fun X_b X_c))) (let ((_let_5 (filter X_b))) (let ((_let_6 (fun _let_5 bool))) (let ((_let_7 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_119125))) (or (not (topological_space X_b)) (not (topological_space X_c)) (not (metric_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_3 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_119123) BOUND_VARIABLE_119124) _let_7))) (not (hBOOL (hAPP _let_5 bool (hAPP X_c _let_6 (hAPP _let_4 (fun X_c _let_6) (tendsto X_b X_c) BOUND_VARIABLE_119121) BOUND_VARIABLE_119122) (hAPP X_b _let_5 (at X_b) BOUND_VARIABLE_119124)))) (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP _let_2 (fun X_c _let_1) (tendsto X_a X_c) (hAPP _let_3 _let_2 (hAPP _let_4 (fun _let_3 _let_2) (combb X_b X_c X_a) BOUND_VARIABLE_119121) BOUND_VARIABLE_119123)) BOUND_VARIABLE_119122) _let_7)) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_119125)) (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_1) BOUND_VARIABLE_119125)) BOUND_VARIABLE_119126))) (not (= (ti X_b BOUND_VARIABLE_119124) (hAPP X_a X_b BOUND_VARIABLE_119123 X_1)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_119126)))))))))))) ) 22.02/22.19 ( 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)))), pi ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((Xa $$unsorted)) (= (= (zero_zero int) (ti int Xa)) (= (zero_zero real) (hAPP int real (real_1 int) Xa))) ) 22.02/22.19 ( pls ) 22.02/22.19 ( (one_one int) ) 22.02/22.19 ( min ) 22.02/22.19 ( (zero_zero int) ) 22.02/22.19 ( s ) 22.02/22.19 ( s1 ) 22.02/22.19 ( m ) 22.02/22.19 ( t ) 22.02/22.19 ( v ) 22.02/22.19 ( w ) 22.02/22.19 ( y ) 22.02/22.19 ( sa ) 22.02/22.19 ( x ) 22.02/22.19 ( r ) 22.02/22.19 ( m1 ) 22.02/22.19 ( skv_14 ) 22.02/22.19 ( skv_20 ) 22.02/22.19 ) 22.02/22.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119214 $$unsorted) (BOUND_VARIABLE_119215 $$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_119215) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119214) _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_119215) BOUND_VARIABLE_119214)) _let_2)))))) ) 22.02/22.19 ( 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)))) ) 22.02/22.19 ( 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) ) 22.02/22.19 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.02/22.19 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.02/22.19 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.19 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.02/22.19 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.02/22.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.02/22.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.19 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.02/22.20 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( nat, (one_one nat), (one_one nat) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119242 $$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 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2)) BOUND_VARIABLE_119242) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119242) BOUND_VARIABLE_119242)))))) ) 22.02/22.20 ( int, (one_one int) ) 22.02/22.20 ( 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)))) ) 22.02/22.20 ( 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) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.02/22.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.02/22.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( nat, (one_one nat) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (one X_a)) (= _let_0 (ti X_a _let_0)))) ) 22.02/22.20 ( rat ) 22.02/22.20 ( int ) 22.02/22.20 ( nat ) 22.02/22.20 ( real ) 22.02/22.20 ( complex ) 22.02/22.20 ( quickcheck_code_int ) 22.02/22.20 ( code_code_numeral ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun real real) root Na))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (= (hAPP real real _let_0 Ya) (hAPP real real _let_0 Xa)) (= Xa Ya)))) ) 22.02/22.20 ( (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 int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (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))) ) 22.02/22.20 ( (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))) ) 22.02/22.20 ( (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))) ) 22.02/22.20 ( (zero_zero real), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (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 int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 (gcd_gcd int) K_4) N))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) M) N)))) (hBOOL (hAPP int bool _let_1 M))))) ) 22.02/22.20 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_21 ) 22.02/22.20 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119280 $$unsorted) (BOUND_VARIABLE_119281 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_lessThan X_a))) (or (not (linorder X_a)) (= (= (ti X_a BOUND_VARIABLE_119280) (ti X_a BOUND_VARIABLE_119281)) (= (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119280) (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119281)))))) ) 22.02/22.20 ( int, pls, w ) 22.02/22.20 ( int, pls, y ) 22.02/22.20 ( int, min, s ) 22.02/22.20 ( int, min, m ) 22.02/22.20 ( int, s, m ) 22.02/22.20 ( int, s1, s1 ) 22.02/22.20 ( int, s1, v ) 22.02/22.20 ( int, m, min ) 22.02/22.20 ( int, m, m ) 22.02/22.20 ( int, t, m1 ) 22.02/22.20 ( int, v, s1 ) 22.02/22.20 ( int, v, r ) 22.02/22.20 ( int, w, y ) 22.02/22.20 ( int, y, pls ) 22.02/22.20 ( int, y, y ) 22.02/22.20 ( int, sa, t ) 22.02/22.20 ( int, sa, m1 ) 22.02/22.20 ( int, x, x ) 22.02/22.20 ( int, x, skv_14 ) 22.02/22.20 ( int, r, s1 ) 22.02/22.20 ( int, m1, sa ) 22.02/22.20 ( int, m1, m1 ) 22.02/22.20 ( int, skv_14, x ) 22.02/22.20 ( int, skv_14, skv_20 ) 22.02/22.20 ( int, skv_20, x ) 22.02/22.20 ( (fun int int), bit1, bit0 ) 22.02/22.20 ( (fun int int), bit0, bit0 ) 22.02/22.20 ( (fun int int), bit0, (fact_fact int) ) 22.02/22.20 ( (fun int int), succ, succ ) 22.02/22.20 ( (fun int int), succ, zfact ) 22.02/22.20 ( (fun int int), pred, succ ) 22.02/22.20 ( (fun int int), (fact_fact int), bit1 ) 22.02/22.20 ( (fun int int), (fact_fact int), bit0 ) 22.02/22.20 ( (fun int int), zfact, succ ) 22.02/22.20 ( (fun int int), zfact, pred ) 22.02/22.20 ( nat, n, n ) 22.02/22.20 ( nat, n, tn ) 22.02/22.20 ( nat, tn, n ) 22.02/22.20 ( bool, fTrue, fTrue ) 22.02/22.20 ( bool, fTrue, fFalse ) 22.02/22.20 ( bool, fFalse, fTrue ) 22.02/22.20 ( real, pi, pi ) 22.02/22.20 ( (fun nat real), (real_1 nat), sin_coeff ) 22.02/22.20 ( (fun nat real), cos_coeff, (real_1 nat) ) 22.02/22.20 ( (fun nat real), cos_coeff, sin_coeff ) 22.02/22.20 ( (fun nat real), sin_coeff, cos_coeff ) 22.02/22.20 ( (fun nat real), sin_coeff, sin_coeff ) 22.02/22.20 ( (fun real real), sin, sin ) 22.02/22.20 ( (fun real real), sin, ln ) 22.02/22.20 ( (fun real real), cos, tan ) 22.02/22.20 ( (fun real real), cos, arccos ) 22.02/22.20 ( (fun real real), sqrt, arcsin ) 22.02/22.20 ( (fun real real), tan, cos ) 22.02/22.20 ( (fun real real), tan, tan ) 22.02/22.20 ( (fun real real), ln, sin ) 22.02/22.20 ( (fun real real), ln, arctan ) 22.02/22.20 ( (fun real real), arctan, sin ) 22.02/22.20 ( (fun real real), arcsin, sqrt ) 22.02/22.20 ( (fun real real), arcsin, arcsin ) 22.02/22.20 ( (fun real real), arccos, tan ) 22.02/22.20 ( (fun nat nat), suc, nat_size ) 22.02/22.20 ( (fun nat nat), (fact_fact nat), fact ) 22.02/22.20 ( (fun nat nat), nat_size, nat_size ) 22.02/22.20 ( (fun nat nat), nat_size, (size_size nat) ) 22.02/22.20 ( (fun nat nat), (size_size nat), suc ) 22.02/22.20 ( (fun nat nat), (size_size nat), nat_size ) 22.02/22.20 ( (fun nat nat), fact, (fact_fact nat) ) 22.02/22.20 ( (fun nat nat), fact, fact ) 22.02/22.20 ( (filter nat), sequentially, sequentially ) 22.02/22.20 ( (fun int (fun int rat)), fract, fract ) 22.02/22.20 ( complex, ii, ii ) 22.02/22.20 ( (fun int bool), zOdd, zOdd ) 22.02/22.20 ( (fun int bool), zOdd, zprime ) 22.02/22.20 ( (fun int bool), zprime, zOdd ) 22.02/22.20 ( (fun int bool), zprime, nat_is_nat ) 22.02/22.20 ( (fun int bool), zEven, twoSqu1091635170sum2sq ) 22.02/22.20 ( (fun int bool), nat_neg, zEven ) 22.02/22.20 ( (fun int bool), nat_neg, twoSqu1091635170sum2sq ) 22.02/22.20 ( (fun int bool), nat_is_nat, zOdd ) 22.02/22.20 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 22.02/22.20 ( (fun int bool), twoSqu1091635170sum2sq, nat_neg ) 22.02/22.20 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.02/22.20 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 22.02/22.20 ( (fun int (fun int int)), legacy_zgcd, nat_tsub ) 22.02/22.20 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 22.02/22.20 ( (fun int (fun int int)), (gcd_gcd int), multInv ) 22.02/22.20 ( (fun int (fun int int)), inv, z3div ) 22.02/22.20 ( (fun int (fun int int)), inv, int_gcd ) 22.02/22.20 ( (fun int (fun int int)), multInv, (gcd_gcd int) ) 22.02/22.20 ( (fun int (fun int int)), multInv, standardRes ) 22.02/22.20 ( (fun int (fun int int)), legendre, z3mod ) 22.02/22.20 ( (fun int (fun int int)), legendre, int_lcm ) 22.02/22.20 ( (fun int (fun int int)), standardRes, (gcd_gcd int) ) 22.02/22.20 ( (fun int (fun int int)), nat_tsub, legacy_zgcd ) 22.02/22.20 ( (fun int (fun int int)), z3div, int_gcd ) 22.02/22.20 ( (fun int (fun int int)), z3mod, int_lcm ) 22.02/22.20 ( (fun int (fun int int)), int_lcm, legendre ) 22.02/22.20 ( (fun int (fun int int)), int_lcm, int_lcm ) 22.02/22.20 ( (fun int (fun int int)), int_gcd, inv ) 22.02/22.20 ( (fun int (fun int int)), int_gcd, int_gcd ) 22.02/22.20 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.02/22.20 ( (fun bool bool), fNot, fNot ) 22.02/22.20 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 22.02/22.20 ( (fun bool (fun bool bool)), fconj, fdisj ) 22.02/22.20 ( (fun bool (fun bool bool)), fconj, fimplies ) 22.02/22.20 ( (fun bool (fun bool bool)), fdisj, fconj ) 22.02/22.20 ( (fun bool (fun bool bool)), fdisj, fdisj ) 22.02/22.20 ( (fun bool (fun bool bool)), fimplies, fdisj ) 22.02/22.20 ( (fun int (fun int bool)), quadRes, norRRset ) 22.02/22.20 ( (fun int (fun int bool)), d22set, sr ) 22.02/22.20 ( (fun int (fun int bool)), norRRset, norRRset ) 22.02/22.20 ( (fun int (fun int bool)), norRRset, sRStar ) 22.02/22.20 ( (fun int (fun int bool)), sRStar, quadRes ) 22.02/22.20 ( (fun int (fun int bool)), sRStar, norRRset ) 22.02/22.20 ( (fun int (fun int bool)), sr, sr ) 22.02/22.20 ( (fun int (fun int bool)), sr, quickc1265749348ro_rel ) 22.02/22.20 ( (fun int (fun int bool)), quickc1265749348ro_rel, d22set ) 22.02/22.20 ( (fun int (fun int bool)), quickc1265749348ro_rel, sr ) 22.02/22.20 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 22.02/22.20 ( (fun nat bool), (even_odd_even nat), prime ) 22.02/22.20 ( (fun nat bool), prime, (even_odd_even nat) ) 22.02/22.20 ( (fun real complex), cis, cis ) 22.02/22.20 ( (fun nat (fun nat bool)), coprime, coprime ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 22.02/22.20 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, norm_frac_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, lazy_small_lazy_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, negDivAlg_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, upto_rel ) 22.02/22.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 22.02/22.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 22.02/22.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 22.02/22.20 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 22.02/22.20 ( (fun nat (fun real real)), root, root ) 22.02/22.20 ( (fun real (fun real real)), log, powr ) 22.02/22.20 ( (fun real (fun real real)), powr, log ) 22.02/22.20 ( (fun real (fun real real)), powr, powr ) 22.02/22.20 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 22.02/22.20 ( (fun complex complex), cnj, expi ) 22.02/22.20 ( (fun complex complex), expi, cnj ) 22.02/22.20 ( (fun complex complex), expi, expi ) 22.02/22.20 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_gcd ) 22.02/22.20 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 22.02/22.20 ( (fun nat (fun nat nat)), nat_gcd, nat_lcm ) 22.02/22.20 ( (fun nat (fun nat nat)), nat_lcm, (gcd_gcd nat) ) 22.02/22.20 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 22.02/22.20 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 22.02/22.20 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 22.02/22.20 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 22.02/22.20 ( (fun int nat), nat_1, phi ) 22.02/22.20 ( (fun int nat), phi, nat_1 ) 22.02/22.20 ( (fun int nat), phi, phi ) 22.02/22.20 ( (fun complex real), re, im ) 22.02/22.20 ( (fun complex real), re, arg ) 22.02/22.20 ( (fun complex real), im, arg ) 22.02/22.20 ( (fun complex real), arg, re ) 22.02/22.20 ( (fun complex real), arg, arg ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), divmod_int, pdivmod ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), posDivAlg, norm_frac ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), negDivAlg, divmod_int ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), pdivmod, divmod_int ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), pdivmod, negDivAlg ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), norm_frac, posDivAlg ) 22.02/22.20 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 22.02/22.20 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 22.02/22.20 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 22.02/22.20 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 22.02/22.20 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 22.02/22.20 ( (fun (fun int bool) int), (the int), (the int) ) 22.02/22.20 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 22.02/22.20 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 22.02/22.20 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 22.02/22.20 ( (fun real (fun real complex)), rcis, rcis ) 22.02/22.20 ( (fun real (fun real complex)), rcis, complex_1 ) 22.02/22.20 ( (fun real (fun real complex)), complex_1, rcis ) 22.02/22.20 ( (fun int (fun int (fun int bool))), zcong, zcong ) 22.02/22.20 ( (fun int (fun int (fun int bool))), zcong, noXRRset ) 22.02/22.20 ( (fun int (fun int (fun int bool))), wset, wset ) 22.02/22.20 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 22.02/22.20 ( (fun int (fun int (fun int bool))), noXRRset, zcong ) 22.02/22.20 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 22.02/22.20 ( (fun int (fun int (fun int bool))), bnorRset, zcongm ) 22.02/22.20 ( (fun int (fun int (fun int bool))), zcongm, wset ) 22.02/22.20 ( (fun real nat), natceiling, natceiling ) 22.02/22.20 ( (fun real nat), natceiling, natfloor ) 22.02/22.20 ( (fun real nat), natfloor, natceiling ) 22.02/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 22.02/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 22.02/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 22.02/22.20 ( (fun int real), (real_1 int), (real_1 int) ) 22.02/22.20 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 22.02/22.20 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 22.02/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 22.02/22.20 ( (fun complex nat), (size_size complex), (size_size complex) ) 22.02/22.20 ( (fun complex nat), (size_size complex), complex_size ) 22.02/22.20 ( (fun complex nat), complex_size, (size_size complex) ) 22.02/22.20 ( (fun (fun nat rat) bool), vanishes, vanishes ) 22.02/22.20 ( (fun (product_prod int int) rat), frct, frct ) 22.02/22.20 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 22.02/22.20 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 22.02/22.20 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.02/22.20 ( (fun rat real), ratreal, ratreal ) 22.02/22.20 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 22.02/22.20 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 22.02/22.20 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 22.02/22.20 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 22.02/22.20 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 22.02/22.20 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 22.02/22.20 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 22.02/22.20 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 22.02/22.20 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.02/22.20 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 22.02/22.20 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 22.02/22.20 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 22.02/22.20 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 22.02/22.20 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 22.02/22.20 ( (fun code_code_numeral int), code_int_of, code_int_of ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119300 $$unsorted) (BOUND_VARIABLE_119301 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119300) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119301)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119301) (hAPP X_a X_a _let_2 BOUND_VARIABLE_119300))))))) ) 22.02/22.20 ( int, pls, min ) 22.02/22.20 ( int, pls, (zero_zero int) ) 22.02/22.20 ( int, (one_one int), min ) 22.02/22.20 ( int, (one_one int), (zero_zero int) ) 22.02/22.20 ( int, min, pls ) 22.02/22.20 ( int, min, (one_one int) ) 22.02/22.20 ( int, (zero_zero int), pls ) 22.02/22.20 ( int, (zero_zero int), (one_one int) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (or (not (forall ((I_2 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_2) P_4))) (not (hBOOL (hAPP nat bool P_1 I_2))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) (hAPP nat nat suc I_2)) P_4)))) )) (not (hBOOL (hAPP nat bool P_1 I))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I) P_4))) (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) ) 22.02/22.20 ( (zero_zero nat), (even_odd_even nat), n ) 22.02/22.20 ( (zero_zero nat), prime, tn ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119393 $$unsorted) (BOUND_VARIABLE_119394 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (or (not (divisi14063676e_zero X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_119393) (hAPP X_a X_a _let_0 BOUND_VARIABLE_119394))) (= (ti X_a BOUND_VARIABLE_119393) (ti X_a BOUND_VARIABLE_119394)))) ) 22.02/22.20 ( real, (zero_zero real), (zero_zero real) ) 22.02/22.20 ( complex, ii, ii ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)) (hAPP nat nat suc N)) ) 22.02/22.20 ( (zero_zero nat) ) 22.02/22.20 ( (one_one nat) ) 22.02/22.20 ( (hAPP nat nat suc (zero_zero nat)) ) 22.02/22.20 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((V_2 $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) V_2))) (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_2))))) ) 22.02/22.20 ( pls ) 22.02/22.20 ( (hAPP int int bit1 pls) ) 22.02/22.20 ( min ) 22.02/22.20 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.20 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((V_2 $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V_2)))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) _let_0) (hAPP int nat (number_number_of nat) V_2))))) ) 22.02/22.20 ( pls ) 22.02/22.20 ( (hAPP int int bit1 pls) ) 22.02/22.20 ( min ) 22.02/22.20 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.02/22.20 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119440 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archim2085082626_floor X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_119440)) (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_119440))) ) 22.02/22.20 ( int, (zero_zero nat) ) 22.02/22.20 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( int, (one_one nat) ) 22.02/22.20 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.20 ( int, n ) 22.02/22.20 ( real, (zero_zero nat) ) 22.02/22.20 ( real, (one_one nat) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP int real _let_0 min)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real _let_0 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real arcsin Y))))))) ) 22.02/22.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (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)))) ) 22.02/22.20 ( (zero_zero real) ) 22.02/22.20 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( skv_10 ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((N $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP int real (real_1 int) N)) (ti int N)) ) 22.02/22.20 ( pls ) 22.02/22.20 ( (one_one int) ) 22.02/22.20 ( min ) 22.02/22.20 ( (zero_zero int) ) 22.02/22.20 ( s ) 22.02/22.20 ( s1 ) 22.02/22.20 ( m ) 22.02/22.20 ( t ) 22.02/22.20 ( v ) 22.02/22.20 ( w ) 22.02/22.20 ( y ) 22.02/22.20 ( sa ) 22.02/22.20 ( x ) 22.02/22.20 ( r ) 22.02/22.20 ( m1 ) 22.02/22.20 ( skv_14 ) 22.02/22.20 ( skv_20 ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_0 (big_co302546470etprod X_a X_b))) (or (not (comm_monoid_mult X_b)) (= _let_0 (ti (fun (fun X_a X_b) (fun (fun X_a bool) X_b)) _let_0)))) ) 22.02/22.20 ( int, int ) 22.02/22.20 ( int, bool ) 22.02/22.20 ( int, (fun int bool) ) 22.02/22.20 ( int, (fun int (fun int int)) ) 22.02/22.20 ( int, (fun int (fun bool bool)) ) 22.02/22.20 ( int, (fun int (fun int bool)) ) 22.02/22.20 ( int, (fun (fun int int) (fun int bool)) ) 22.02/22.20 ( int, (fun real (fun int (fun int bool))) ) 22.02/22.20 ( nat, bool ) 22.02/22.20 ( nat, (fun nat bool) ) 22.02/22.20 ( nat, (fun nat (fun bool bool)) ) 22.02/22.20 ( nat, (fun int (fun nat bool)) ) 22.02/22.20 ( nat, (fun real (fun int (fun nat bool))) ) 22.02/22.20 ( bool, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.02/22.20 ( real, real ) 22.02/22.20 ( real, (fun real bool) ) 22.02/22.20 ( real, (fun real (fun bool bool)) ) 22.02/22.20 ( real, (fun (fun nat real) (fun nat bool)) ) 22.02/22.20 ( real, (fun (fun int real) (fun int bool)) ) 22.02/22.20 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.02/22.20 ( (product_prod int int), (fun (product_prod int int) (fun bool bool)) ) 22.02/22.20 ( (product_prod real real), (fun real (fun real (fun nat (product_prod real real)))) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X $$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))) (= (ti int X) (hAPP int int (hAPP int _let_0 (times_times int) _let_1) (hAPP int int (hAPP int _let_0 (div_div int) X) _let_1)))))) ) 22.02/22.20 ( pls ) 22.02/22.20 ( (one_one int) ) 22.02/22.20 ( min ) 22.02/22.20 ( (zero_zero int) ) 22.02/22.20 ( s ) 22.02/22.20 ( s1 ) 22.02/22.20 ( m ) 22.02/22.20 ( t ) 22.02/22.20 ( v ) 22.02/22.20 ( w ) 22.02/22.20 ( y ) 22.02/22.20 ( sa ) 22.02/22.20 ( x ) 22.02/22.20 ( r ) 22.02/22.20 ( m1 ) 22.02/22.20 ( skv_14 ) 22.02/22.20 ( skv_20 ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((N $$unsorted) (X $$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)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 X)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) N) X)))) ) 22.02/22.20 ( (one_one int), t ) 22.02/22.20 ( min, pls ) 22.02/22.20 ( min, min ) 22.02/22.20 ( (zero_zero int), pls ) 22.02/22.20 ( (zero_zero int), (one_one int) ) 22.02/22.20 ( (zero_zero int), min ) 22.02/22.20 ( (zero_zero int), s ) 22.02/22.20 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.02/22.20 ( (zero_zero int), skv_4 ) 22.02/22.20 ( (zero_zero int), skv_5 ) 22.02/22.20 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.20 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.20 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.20 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.02/22.20 ) 22.02/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119511 $$unsorted) (BOUND_VARIABLE_119512 $$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_119511) BOUND_VARIABLE_119512))) (= (ti X_a BOUND_VARIABLE_119512) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_119511))) ) 22.02/22.20 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.02/22.20 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.02/22.20 ( 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) ) 22.02/22.20 ( 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) ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.02/22.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.02/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.12/22.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.12/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.20 ( nat, (one_one nat), (one_one nat) ) 22.12/22.20 ) 22.12/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119533 $$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_119533) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_119533))) ) 22.12/22.20 ( int, pls ) 22.12/22.20 ( int, min ) 22.12/22.20 ( int, s ) 22.12/22.20 ( int, s1 ) 22.12/22.20 ( int, m ) 22.12/22.20 ( int, t ) 22.12/22.20 ( int, v ) 22.12/22.20 ( int, w ) 22.12/22.20 ( int, y ) 22.12/22.20 ( int, sa ) 22.12/22.20 ( int, x ) 22.12/22.20 ( int, r ) 22.12/22.20 ( int, m1 ) 22.12/22.20 ( int, skv_14 ) 22.12/22.20 ( int, skv_20 ) 22.12/22.20 ( (fun int int), bit1 ) 22.12/22.20 ( (fun int int), bit0 ) 22.12/22.20 ( (fun int int), succ ) 22.12/22.20 ( (fun int int), pred ) 22.12/22.20 ( (fun int int), (fact_fact int) ) 22.12/22.20 ( (fun int int), zfact ) 22.12/22.20 ( nat, n ) 22.12/22.20 ( nat, tn ) 22.12/22.20 ( bool, fTrue ) 22.12/22.20 ( bool, fFalse ) 22.12/22.20 ( real, pi ) 22.12/22.20 ( (fun nat real), (real_1 nat) ) 22.12/22.20 ( (fun nat real), cos_coeff ) 22.12/22.20 ( (fun nat real), sin_coeff ) 22.12/22.20 ( (fun real real), sin ) 22.12/22.20 ( (fun real real), cos ) 22.12/22.20 ( (fun real real), sqrt ) 22.12/22.20 ( (fun real real), tan ) 22.12/22.20 ( (fun real real), ln ) 22.12/22.20 ( (fun real real), arctan ) 22.12/22.20 ( (fun real real), arcsin ) 22.12/22.20 ( (fun real real), arccos ) 22.12/22.20 ( (fun nat nat), suc ) 22.12/22.20 ( (fun nat nat), (fact_fact nat) ) 22.12/22.20 ( (fun nat nat), nat_size ) 22.12/22.20 ( (fun nat nat), (size_size nat) ) 22.12/22.20 ( (fun nat nat), fact ) 22.12/22.20 ( (filter nat), sequentially ) 22.12/22.20 ( (fun int (fun int rat)), fract ) 22.12/22.20 ( complex, ii ) 22.12/22.20 ( (fun int bool), zOdd ) 22.12/22.20 ( (fun int bool), zprime ) 22.12/22.20 ( (fun int bool), zEven ) 22.12/22.20 ( (fun int bool), nat_neg ) 22.12/22.20 ( (fun int bool), nat_is_nat ) 22.12/22.20 ( (fun int bool), (even_odd_even int) ) 22.12/22.20 ( (fun int bool), twoSqu1091635170sum2sq ) 22.12/22.20 ( (fun int (fun int int)), legacy_zgcd ) 22.12/22.20 ( (fun int (fun int int)), (gcd_gcd int) ) 22.12/22.20 ( (fun int (fun int int)), inv ) 22.12/22.20 ( (fun int (fun int int)), multInv ) 22.12/22.20 ( (fun int (fun int int)), legendre ) 22.12/22.20 ( (fun int (fun int int)), standardRes ) 22.12/22.20 ( (fun int (fun int int)), nat_tsub ) 22.12/22.20 ( (fun int (fun int int)), z3div ) 22.12/22.20 ( (fun int (fun int int)), z3mod ) 22.12/22.20 ( (fun int (fun int int)), int_lcm ) 22.12/22.20 ( (fun int (fun int int)), int_gcd ) 22.12/22.20 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.12/22.20 ( (fun bool bool), fNot ) 22.12/22.20 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.12/22.20 ( (fun bool (fun bool bool)), fconj ) 22.12/22.20 ( (fun bool (fun bool bool)), fdisj ) 22.12/22.20 ( (fun bool (fun bool bool)), fimplies ) 22.12/22.20 ( (fun int (fun int bool)), quadRes ) 22.12/22.20 ( (fun int (fun int bool)), d22set ) 22.12/22.20 ( (fun int (fun int bool)), norRRset ) 22.12/22.20 ( (fun int (fun int bool)), sRStar ) 22.12/22.20 ( (fun int (fun int bool)), sr ) 22.12/22.20 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.12/22.20 ( (fun nat bool), (even_odd_even nat) ) 22.12/22.20 ( (fun nat bool), prime ) 22.12/22.20 ( (fun real complex), cis ) 22.12/22.20 ( (fun nat (fun nat bool)), coprime ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.12/22.20 ( (fun (product_prod int int) bool), frac_1 ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.12/22.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.12/22.20 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.12/22.20 ( (fun (fun int bool) bool), nat_nat_set ) 22.12/22.20 ( (fun nat (fun real real)), root ) 22.12/22.20 ( (fun real (fun real real)), log ) 22.12/22.20 ( (fun real (fun real real)), powr ) 22.12/22.20 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.12/22.20 ( (fun complex complex), cnj ) 22.12/22.20 ( (fun complex complex), expi ) 22.12/22.20 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.12/22.20 ( (fun nat (fun nat nat)), nat_gcd ) 22.12/22.20 ( (fun nat (fun nat nat)), nat_lcm ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.12/22.20 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.12/22.20 ( (fun int (fun (fun int bool) bool)), resSet ) 22.12/22.20 ( (fun int nat), nat_1 ) 22.12/22.20 ( (fun int nat), phi ) 22.12/22.20 ( (fun complex real), re ) 22.12/22.20 ( (fun complex real), im ) 22.12/22.20 ( (fun complex real), arg ) 22.12/22.20 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.12/22.20 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.12/22.20 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.12/22.20 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.12/22.20 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.12/22.20 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.12/22.20 ( (fun (product_prod nat nat) bool), pred_nat ) 22.12/22.20 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.12/22.20 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.12/22.20 ( (fun (fun int bool) int), (the int) ) 22.12/22.20 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.12/22.20 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.12/22.20 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.12/22.20 ( (fun real (fun real complex)), rcis ) 22.12/22.20 ( (fun real (fun real complex)), complex_1 ) 22.12/22.20 ( (fun int (fun int (fun int bool))), zcong ) 22.12/22.20 ( (fun int (fun int (fun int bool))), wset ) 22.12/22.20 ( (fun int (fun int (fun int bool))), noXRRset ) 22.12/22.20 ( (fun int (fun int (fun int bool))), bnorRset ) 22.12/22.20 ( (fun int (fun int (fun int bool))), zcongm ) 22.12/22.20 ( (fun real nat), natceiling ) 22.12/22.20 ( (fun real nat), natfloor ) 22.12/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.12/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.12/22.20 ( (fun int real), (real_1 int) ) 22.12/22.20 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.12/22.20 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.12/22.20 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.12/22.20 ( (fun complex nat), (size_size complex) ) 22.12/22.20 ( (fun complex nat), complex_size ) 22.12/22.20 ( (fun (fun nat rat) bool), vanishes ) 22.12/22.20 ( (fun (product_prod int int) rat), frct ) 22.12/22.20 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.12/22.20 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.12/22.20 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.12/22.20 ( (fun rat real), ratreal ) 22.12/22.20 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.12/22.20 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.12/22.20 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.12/22.20 ( (fun rat (product_prod int int)), quotient_of ) 22.12/22.20 ( (fun int (fun nat nat)), nat_aux ) 22.12/22.20 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.12/22.20 ( (fun int (list int)), quickc666637781d_zero ) 22.12/22.20 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.12/22.20 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.12/22.20 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.12/22.20 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.12/22.20 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.12/22.20 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.12/22.20 ( (fun code_code_numeral int), code_int_of ) 22.12/22.20 ) 22.12/22.20 (instantiation (forall ((Ma $$unsorted) (K $$unsorted) (Na $$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) Na))) (= (hBOOL (hAPP int bool _let_1 Ma)) (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) Ma) Na))))))) ) 22.12/22.20 ( (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.12/22.20 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.12/22.20 ) 22.12/22.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119583 $$unsorted) (BOUND_VARIABLE_119584 $$unsorted) (BOUND_VARIABLE_119585 $$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_119583))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_119585)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119585) _let_2)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_119583) BOUND_VARIABLE_119585))) (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_119584) BOUND_VARIABLE_119585))) (and (or _let_4 (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119584) _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_119584))))))))))))) ) 22.12/22.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.21 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.12/22.21 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.12/22.21 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.12/22.21 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (ti X_a Xa) (hAPP _let_0 X_a (hilbert_Eps X_a) (hAPP X_a _let_0 (fequal X_a) Xa)))) ) 22.12/22.21 ( int, pls ) 22.12/22.21 ( int, min ) 22.12/22.21 ( int, s ) 22.12/22.21 ( int, s1 ) 22.12/22.21 ( int, m ) 22.12/22.21 ( int, t ) 22.12/22.21 ( int, v ) 22.12/22.21 ( int, w ) 22.12/22.21 ( int, y ) 22.12/22.21 ( int, sa ) 22.12/22.21 ( int, x ) 22.12/22.21 ( int, r ) 22.12/22.21 ( int, m1 ) 22.12/22.21 ( int, skv_14 ) 22.12/22.21 ( int, skv_20 ) 22.12/22.21 ( (fun int int), bit1 ) 22.12/22.21 ( (fun int int), bit0 ) 22.12/22.21 ( (fun int int), succ ) 22.12/22.21 ( (fun int int), pred ) 22.12/22.21 ( (fun int int), (fact_fact int) ) 22.12/22.21 ( (fun int int), zfact ) 22.12/22.21 ( nat, n ) 22.12/22.21 ( nat, tn ) 22.12/22.21 ( bool, fTrue ) 22.12/22.21 ( bool, fFalse ) 22.12/22.21 ( real, pi ) 22.12/22.21 ( (fun nat real), (real_1 nat) ) 22.12/22.21 ( (fun nat real), cos_coeff ) 22.12/22.21 ( (fun nat real), sin_coeff ) 22.12/22.21 ( (fun real real), sin ) 22.12/22.21 ( (fun real real), cos ) 22.12/22.21 ( (fun real real), sqrt ) 22.12/22.21 ( (fun real real), tan ) 22.12/22.21 ( (fun real real), ln ) 22.12/22.21 ( (fun real real), arctan ) 22.12/22.21 ( (fun real real), arcsin ) 22.12/22.21 ( (fun real real), arccos ) 22.12/22.21 ( (fun nat nat), suc ) 22.12/22.21 ( (fun nat nat), (fact_fact nat) ) 22.12/22.21 ( (fun nat nat), nat_size ) 22.12/22.21 ( (fun nat nat), (size_size nat) ) 22.12/22.21 ( (fun nat nat), fact ) 22.12/22.21 ( (filter nat), sequentially ) 22.12/22.21 ( (fun int (fun int rat)), fract ) 22.12/22.21 ( complex, ii ) 22.12/22.21 ( (fun int bool), zOdd ) 22.12/22.21 ( (fun int bool), zprime ) 22.12/22.21 ( (fun int bool), zEven ) 22.12/22.21 ( (fun int bool), nat_neg ) 22.12/22.21 ( (fun int bool), nat_is_nat ) 22.12/22.21 ( (fun int bool), (even_odd_even int) ) 22.12/22.21 ( (fun int bool), twoSqu1091635170sum2sq ) 22.12/22.21 ( (fun int (fun int int)), legacy_zgcd ) 22.12/22.21 ( (fun int (fun int int)), (gcd_gcd int) ) 22.12/22.21 ( (fun int (fun int int)), inv ) 22.12/22.21 ( (fun int (fun int int)), multInv ) 22.12/22.21 ( (fun int (fun int int)), legendre ) 22.12/22.21 ( (fun int (fun int int)), standardRes ) 22.12/22.21 ( (fun int (fun int int)), nat_tsub ) 22.12/22.21 ( (fun int (fun int int)), z3div ) 22.12/22.21 ( (fun int (fun int int)), z3mod ) 22.12/22.21 ( (fun int (fun int int)), int_lcm ) 22.12/22.21 ( (fun int (fun int int)), int_gcd ) 22.12/22.21 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.12/22.21 ( (fun bool bool), fNot ) 22.12/22.21 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.12/22.21 ( (fun bool (fun bool bool)), fconj ) 22.12/22.21 ( (fun bool (fun bool bool)), fdisj ) 22.12/22.21 ( (fun bool (fun bool bool)), fimplies ) 22.12/22.21 ( (fun int (fun int bool)), quadRes ) 22.12/22.21 ( (fun int (fun int bool)), d22set ) 22.12/22.21 ( (fun int (fun int bool)), norRRset ) 22.12/22.21 ( (fun int (fun int bool)), sRStar ) 22.12/22.21 ( (fun int (fun int bool)), sr ) 22.12/22.21 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.12/22.21 ( (fun nat bool), (even_odd_even nat) ) 22.12/22.21 ( (fun nat bool), prime ) 22.12/22.21 ( (fun real complex), cis ) 22.12/22.21 ( (fun nat (fun nat bool)), coprime ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.12/22.21 ( (fun (product_prod int int) bool), frac_1 ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.12/22.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.12/22.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.12/22.21 ( (fun (fun int bool) bool), nat_nat_set ) 22.12/22.21 ( (fun nat (fun real real)), root ) 22.12/22.21 ( (fun real (fun real real)), log ) 22.12/22.21 ( (fun real (fun real real)), powr ) 22.12/22.21 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.12/22.21 ( (fun complex complex), cnj ) 22.12/22.21 ( (fun complex complex), expi ) 22.12/22.21 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.12/22.21 ( (fun nat (fun nat nat)), nat_gcd ) 22.12/22.21 ( (fun nat (fun nat nat)), nat_lcm ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.12/22.21 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.12/22.21 ( (fun int (fun (fun int bool) bool)), resSet ) 22.12/22.21 ( (fun int nat), nat_1 ) 22.12/22.21 ( (fun int nat), phi ) 22.12/22.21 ( (fun complex real), re ) 22.12/22.21 ( (fun complex real), im ) 22.12/22.21 ( (fun complex real), arg ) 22.12/22.21 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.12/22.21 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.12/22.21 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.12/22.21 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.12/22.21 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.12/22.21 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.12/22.21 ( (fun (product_prod nat nat) bool), pred_nat ) 22.12/22.21 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.12/22.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.12/22.21 ( (fun (fun int bool) int), (the int) ) 22.12/22.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.12/22.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.12/22.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.12/22.21 ( (fun real (fun real complex)), rcis ) 22.12/22.21 ( (fun real (fun real complex)), complex_1 ) 22.12/22.21 ( (fun int (fun int (fun int bool))), zcong ) 22.12/22.21 ( (fun int (fun int (fun int bool))), wset ) 22.12/22.21 ( (fun int (fun int (fun int bool))), noXRRset ) 22.12/22.21 ( (fun int (fun int (fun int bool))), bnorRset ) 22.12/22.21 ( (fun int (fun int (fun int bool))), zcongm ) 22.12/22.21 ( (fun real nat), natceiling ) 22.12/22.21 ( (fun real nat), natfloor ) 22.12/22.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.12/22.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.12/22.21 ( (fun int real), (real_1 int) ) 22.12/22.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.12/22.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.12/22.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.12/22.21 ( (fun complex nat), (size_size complex) ) 22.12/22.21 ( (fun complex nat), complex_size ) 22.12/22.21 ( (fun (fun nat rat) bool), vanishes ) 22.12/22.21 ( (fun (product_prod int int) rat), frct ) 22.12/22.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.12/22.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.12/22.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.12/22.21 ( (fun rat real), ratreal ) 22.12/22.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.12/22.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.12/22.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.12/22.21 ( (fun rat (product_prod int int)), quotient_of ) 22.12/22.21 ( (fun int (fun nat nat)), nat_aux ) 22.12/22.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.12/22.21 ( (fun int (list int)), quickc666637781d_zero ) 22.12/22.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.12/22.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.12/22.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.12/22.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.12/22.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.12/22.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.12/22.21 ( (fun code_code_numeral int), code_int_of ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119629 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (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_0 _let_4 (hAPP (fun real _let_3) (fun _let_0 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_119629))) (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_119629))))))))) ) 22.12/22.21 ( int, s ) 22.12/22.21 ( int, s1 ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.21 ( int, v ) 22.12/22.21 ( int, w ) 22.12/22.21 ( int, y ) 22.12/22.21 ( int, x ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.12/22.21 ( int, skv_6 ) 22.12/22.21 ( int, skv_7 ) 22.12/22.21 ( int, skv_16 ) 22.12/22.21 ( int, skv_23 ) 22.12/22.21 ( int, skv_24 ) 22.12/22.21 ( real, (hAPP int real (number_number_of real) min) ) 22.12/22.21 ( 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)))) ) 22.12/22.21 ( complex, ii ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119647 $$unsorted) (BOUND_VARIABLE_119648 $$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_119647) BOUND_VARIABLE_119648))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119648) BOUND_VARIABLE_119647)))))) ) 22.12/22.21 ( int, pls, (zero_zero int) ) 22.12/22.21 ( int, (one_one int), (zero_zero int) ) 22.12/22.21 ( int, (one_one int), t ) 22.12/22.21 ( int, min, min ) 22.12/22.21 ( int, min, (zero_zero int) ) 22.12/22.21 ( int, (zero_zero int), pls ) 22.12/22.21 ( int, (zero_zero int), (one_one int) ) 22.12/22.21 ( int, (zero_zero int), min ) 22.12/22.21 ( 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))) ) 22.12/22.21 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.21 ( 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))) ) 22.12/22.21 ( 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))), (zero_zero int) ) 22.12/22.21 ( 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 ) 22.12/22.21 ( 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 int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.21 ( 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 ) 22.12/22.21 ( 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 ) 22.12/22.21 ( 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_5 ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.12/22.21 ( int, t, (one_one int) ) 22.12/22.21 ( 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))) ) 22.12/22.21 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.21 ( 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))) ) 22.12/22.21 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.21 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( nat, (zero_zero nat), n ) 22.12/22.21 ( nat, (zero_zero nat), tn ) 22.12/22.21 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.12/22.21 ( nat, n, (zero_zero nat) ) 22.12/22.21 ( nat, tn, (zero_zero nat) ) 22.12/22.21 ( real, pi, (zero_zero real) ) 22.12/22.21 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( 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)) ) 22.12/22.21 ( 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)))) ) 22.12/22.21 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( 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) ) 22.12/22.21 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( real, (zero_zero real), pi ) 22.12/22.21 ( 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)))) ) 22.12/22.21 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( 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))))) ) 22.12/22.21 ( real, (zero_zero real), skv_2 ) 22.12/22.21 ( real, (zero_zero real), skv_9 ) 22.12/22.21 ( real, (zero_zero real), skv_12 ) 22.12/22.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.12/22.21 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.12/22.21 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.21 ( 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) ) 22.12/22.21 ( 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 ) 22.12/22.21 ( real, skv_2, (zero_zero real) ) 22.12/22.21 ( real, skv_9, (zero_zero real) ) 22.12/22.21 ( real, skv_12, (zero_zero real) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119691 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_119691)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_119691))))) ) 22.12/22.21 ( int, pls ) 22.12/22.21 ( int, (hAPP int int bit1 pls) ) 22.12/22.21 ( int, min ) 22.12/22.21 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.21 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.12/22.21 ( nat, pls ) 22.12/22.21 ( nat, (hAPP int int bit1 pls) ) 22.12/22.21 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.21 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.12/22.21 ( real, min ) 22.12/22.21 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.21 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.12/22.21 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.21 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 22.12/22.21 ( complex, min ) 22.12/22.21 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.21 ( quickcheck_code_int, pls ) 22.12/22.21 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.12/22.21 ( quickcheck_code_int, (one_one int) ) 22.12/22.21 ( code_code_numeral, pls ) 22.12/22.21 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((B $$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))))))) ) 22.12/22.21 ( 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 ) 22.12/22.21 ( (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)))) ) 22.12/22.21 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 22.12/22.21 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 22.12/22.21 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( 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 ) 22.12/22.21 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119722 $$unsorted) (BOUND_VARIABLE_119723 $$unsorted) (BOUND_VARIABLE_119724 $$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 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (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_119722) BOUND_VARIABLE_119723)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_119724) BOUND_VARIABLE_119723)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_119723))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_119722) BOUND_VARIABLE_119724))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119754 $$unsorted) (BOUND_VARIABLE_119755 $$unsorted) (BOUND_VARIABLE_119756 $$unsorted) (BOUND_VARIABLE_119757 $$unsorted) (BOUND_VARIABLE_119758 $$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_119754) BOUND_VARIABLE_119755)) BOUND_VARIABLE_119756) (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_119757) BOUND_VARIABLE_119755)) BOUND_VARIABLE_119758)) (= (ti X_a BOUND_VARIABLE_119758) (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_119754) BOUND_VARIABLE_119757)) BOUND_VARIABLE_119755)) BOUND_VARIABLE_119756))))))) ) 22.12/22.21 ( int, (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) ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.21 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w, sa, w ) 22.12/22.21 ( int, x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), x, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.12/22.21 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v, r, v ) 22.12/22.21 ( int, r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), r, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.21 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119786 $$unsorted)) (or (not (ring_char_0 X_a)) (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 BOUND_VARIABLE_119786)))))) ) 22.12/22.21 ( int, pls ) 22.12/22.21 ( int, (hAPP int int bit1 pls) ) 22.12/22.21 ( int, min ) 22.12/22.21 ( nat, pls ) 22.12/22.21 ( nat, (hAPP int int bit1 pls) ) 22.12/22.21 ( real, (hAPP int int bit1 pls) ) 22.12/22.21 ( real, min ) 22.12/22.21 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.21 ( 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))))))) ) 22.12/22.21 ( complex, min ) 22.12/22.21 ( quickcheck_code_int, pls ) 22.12/22.21 ( code_code_numeral, pls ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119802 $$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_119802)) (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_119802) (one_one X_a)))))) ) 22.12/22.21 ( int, (one_one int) ) 22.12/22.21 ( 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)))) ) 22.12/22.21 ( 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) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.12/22.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.21 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( nat, (one_one nat) ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (pow X_a))) (= _let_1 (ti (fun _let_0 (fun _let_0 bool)) _let_1)))) ) 22.12/22.21 ( int ) 22.12/22.21 ( nat ) 22.12/22.21 ) 22.12/22.21 (instantiation (forall ((P_5 $$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)) P_5)))) ) 22.12/22.21 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.21 ( (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))) ) 22.12/22.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.21 ( y ) 22.12/22.21 ( x ) 22.12/22.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.12/22.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.12/22.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.21 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.12/22.21 ( (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))) m1))) ) 22.12/22.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.12/22.21 ) 22.12/22.22 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_119916 $$unsorted) (BOUND_VARIABLE_119917 $$unsorted) (BOUND_VARIABLE_119918 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_a)) (not (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((S_1 $$unsorted)) (or (not (forall ((X_1 $$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 (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_1) BOUND_VARIABLE_119918))) S_1))) (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_119918)) (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_119916 X_1)) BOUND_VARIABLE_119917))) R_1))))) )) (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_119916) BOUND_VARIABLE_119917) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_119918)))))) ) 22.12/22.22 ( 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)))) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_119977 $$unsorted) (BOUND_VARIABLE_119978 $$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_119978))) (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_119977) _let_2))) (or (and (not (= _let_0 (ti X_a BOUND_VARIABLE_119977))) _let_3) (and (not _let_3) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_119977))) (= (zero_zero nat) _let_2)))))))) ) 22.12/22.22 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120011 $$unsorted) (BOUND_VARIABLE_120012 $$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_120011) BOUND_VARIABLE_120012))) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_120012) BOUND_VARIABLE_120011))) ) 22.12/22.22 ( 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))), (hAPP 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)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120042 $$unsorted) (BOUND_VARIABLE_120043 $$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_120042) BOUND_VARIABLE_120043))) (= _let_0 (ti X_a BOUND_VARIABLE_120043)) (= _let_0 (ti X_a BOUND_VARIABLE_120042)))) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.12/22.22 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( 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 ) 22.12/22.22 ( 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))), m1 ) 22.12/22.22 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.12/22.22 ( 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_21 ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.12/22.22 ( int, y, v ) 22.12/22.22 ( int, y, w ) 22.12/22.22 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, sa, v ) 22.12/22.22 ( int, sa, w ) 22.12/22.22 ( int, x, v ) 22.12/22.22 ( int, x, w ) 22.12/22.22 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.22 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, r, v ) 22.12/22.22 ( int, r, w ) 22.12/22.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.12/22.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.12/22.22 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.12/22.22 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.12/22.22 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.12/22.22 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.12/22.22 ( 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)))))) ) 22.12/22.22 ( 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 ) 22.12/22.22 ( complex, ii, ii ) 22.12/22.22 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.12/22.22 ( 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 ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((N $$unsorted) (M $$unsorted) (R_3 $$unsorted)) (let ((_let_0 (real_1 int))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP int real _let_0 M)) R_3))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) R_3) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 N)) (one_one real))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) M) N))))) ) 22.12/22.22 ( (one_one int), (zero_zero int), pi ) 22.12/22.22 ( (zero_zero int), (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120152 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_120152) BOUND_VARIABLE_120152) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_120152) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.22 ( int, s ) 22.12/22.22 ( int, s1 ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, v ) 22.12/22.22 ( int, w ) 22.12/22.22 ( int, y ) 22.12/22.22 ( int, sa ) 22.12/22.22 ( int, x ) 22.12/22.22 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.12/22.22 ( int, r ) 22.12/22.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.22 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.12/22.22 ( int, skv_6 ) 22.12/22.22 ( int, skv_7 ) 22.12/22.22 ( int, skv_13 ) 22.12/22.22 ( int, skv_16 ) 22.12/22.22 ( int, skv_19 ) 22.12/22.22 ( int, skv_23 ) 22.12/22.22 ( int, skv_24 ) 22.12/22.22 ( real, (hAPP int real (number_number_of real) min) ) 22.12/22.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( 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)))) ) 22.12/22.22 ( 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))))) ) 22.12/22.22 ( complex, ii ) 22.12/22.22 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( 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)) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) Xa))) (or (hBOOL (hAPP _let_0 bool _let_1 zOdd)) (hBOOL (hAPP _let_0 bool _let_1 zEven))))) ) 22.12/22.22 ( (one_one int) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X $$unsorted)) (= (hAPP int int (abs_abs int) X) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) (zero_zero int)) X)) ) 22.12/22.22 ( v ) 22.12/22.22 ( w ) 22.12/22.22 ( skv_14 ) 22.12/22.22 ( skv_20 ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP rat real ratreal X)) (hAPP rat int (archim2085082626_floor rat) X)) ) 22.12/22.22 ( (one_one rat) ) 22.12/22.22 ( (zero_zero rat) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120232 $$unsorted) (BOUND_VARIABLE_120233 $$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_120232)) BOUND_VARIABLE_120233))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_120233)) BOUND_VARIABLE_120232)))))) ) 22.12/22.22 ( int, pls, pls ) 22.12/22.22 ( int, pls, (one_one int) ) 22.12/22.22 ( int, pls, min ) 22.12/22.22 ( int, pls, s ) 22.12/22.22 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, pls, skv_4 ) 22.12/22.22 ( int, pls, skv_5 ) 22.12/22.22 ( int, (one_one int), pls ) 22.12/22.22 ( int, (one_one int), min ) 22.12/22.22 ( int, min, pls ) 22.12/22.22 ( int, min, (one_one int) ) 22.12/22.22 ( int, s, pls ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 22.12/22.22 ( int, skv_4, pls ) 22.12/22.22 ( int, skv_5, pls ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120319 $$unsorted) (BOUND_VARIABLE_120320 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (no_zero_divisors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_120320)) (= _let_0 (ti X_a BOUND_VARIABLE_120319)) (not (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_120320) BOUND_VARIABLE_120319))))) ) 22.12/22.22 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, v, y ) 22.12/22.22 ( int, v, sa ) 22.12/22.22 ( int, v, x ) 22.12/22.22 ( int, v, r ) 22.12/22.22 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.22 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.22 ( int, w, y ) 22.12/22.22 ( int, w, sa ) 22.12/22.22 ( int, w, x ) 22.12/22.22 ( int, w, r ) 22.12/22.22 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.22 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.22 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.12/22.22 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.22 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.12/22.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, skv_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))) ) 22.12/22.22 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( 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))))) ) 22.12/22.22 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( 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)))) ) 22.12/22.22 ( complex, ii, ii ) 22.12/22.22 ( 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)) ) 22.12/22.22 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ) 22.12/22.22 (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))) ) 22.12/22.22 ( pls ) 22.12/22.22 ( (one_one int) ) 22.12/22.22 ( min ) 22.12/22.22 ( (zero_zero int) ) 22.12/22.22 ( s ) 22.12/22.22 ( s1 ) 22.12/22.22 ( m ) 22.12/22.22 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( t ) 22.12/22.22 ( v ) 22.12/22.22 ( w ) 22.12/22.22 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.22 ( y ) 22.12/22.22 ( sa ) 22.12/22.22 ( x ) 22.12/22.22 ( r ) 22.12/22.22 ( m1 ) 22.12/22.22 ( skv_4 ) 22.12/22.22 ( skv_5 ) 22.12/22.22 ( skv_14 ) 22.12/22.22 ( skv_20 ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120351 $$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_120351) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_120351))) ) 22.12/22.22 ( int, pls ) 22.12/22.22 ( int, (one_one int) ) 22.12/22.22 ( int, min ) 22.12/22.22 ( 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)))) ) 22.12/22.22 ( real, (one_one real) ) 22.12/22.22 ( 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) ) 22.12/22.22 ( complex, ii ) 22.12/22.22 ( complex, (one_one complex) ) 22.12/22.22 ( code_code_numeral, (one_one code_code_numeral) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120464 $$unsorted) (BOUND_VARIABLE_120465 $$unsorted) (BOUND_VARIABLE_120466 $$unsorted) (BOUND_VARIABLE_120467 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_120464))) (let ((_let_4 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_120466))) (or (not (semiri456707255roduct X_a)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_120465)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_120467)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_120467)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_120465))) (or (= (ti X_a BOUND_VARIABLE_120466) (ti X_a BOUND_VARIABLE_120464)) (= (ti X_a BOUND_VARIABLE_120467) (ti X_a BOUND_VARIABLE_120465)))))))))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.22 ( int, x, v, y, w ) 22.12/22.22 ( int, x, w, y, v ) 22.12/22.22 ( int, r, v, sa, w ) 22.12/22.22 ( int, r, w, sa, v ) 22.12/22.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.12/22.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120494 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_120494))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_120494))) (hBOOL (hAPP X_a bool _let_0 (zero_zero X_a)))))) ) 22.12/22.22 ( int, pls ) 22.12/22.22 ( int, (one_one int) ) 22.12/22.22 ( int, min ) 22.12/22.22 ( int, (zero_zero int) ) 22.12/22.22 ( int, s ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, t ) 22.12/22.22 ( int, m1 ) 22.12/22.22 ( int, skv_4 ) 22.12/22.22 ( int, skv_5 ) 22.12/22.22 ( nat, (zero_zero nat) ) 22.12/22.22 ( real, pi ) 22.12/22.22 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( real, (one_one real) ) 22.12/22.22 ( real, (zero_zero real) ) 22.12/22.22 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.12/22.22 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.12/22.22 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 22.12/22.22 ( complex, ii ) 22.12/22.22 ( complex, (one_one complex) ) 22.12/22.22 ) 22.12/22.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120514 $$unsorted) (BOUND_VARIABLE_120515 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (preorder X_a)) (= (and (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120515) BOUND_VARIABLE_120514))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120514) BOUND_VARIABLE_120515))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_120514) BOUND_VARIABLE_120515)))))) ) 22.12/22.22 ( int, pls, min ) 22.12/22.22 ( int, pls, (zero_zero int) ) 22.12/22.22 ( int, (one_one int), (zero_zero int) ) 22.12/22.22 ( int, (one_one int), t ) 22.12/22.22 ( int, min, pls ) 22.12/22.22 ( int, min, min ) 22.12/22.22 ( int, min, (zero_zero int) ) 22.12/22.22 ( int, (zero_zero int), pls ) 22.12/22.22 ( int, (zero_zero int), (one_one int) ) 22.12/22.22 ( int, (zero_zero int), min ) 22.12/22.22 ( int, (zero_zero int), s ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.22 ( int, (zero_zero int), skv_4 ) 22.12/22.22 ( int, (zero_zero int), skv_5 ) 22.12/22.22 ( int, s, (zero_zero int) ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.12/22.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.12/22.22 ( int, t, (one_one int) ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.12/22.22 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( int, skv_4, (zero_zero int) ) 22.12/22.22 ( 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))) ) 22.12/22.22 ( int, skv_5, (zero_zero int) ) 22.12/22.22 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.22 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.22 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( nat, (zero_zero nat), n ) 22.12/22.22 ( nat, (zero_zero nat), tn ) 22.12/22.22 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.22 ( real, pi, (zero_zero real) ) 22.12/22.22 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.12/22.23 ( 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)))) ) 22.12/22.23 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( 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)))), (zero_zero real) ) 22.12/22.23 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( real, (zero_zero real), pi ) 22.12/22.23 ( 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)))) ) 22.12/22.23 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( real, (zero_zero real), skv_2 ) 22.12/22.23 ( real, (zero_zero real), skv_9 ) 22.12/22.23 ( real, (zero_zero real), skv_10 ) 22.12/22.23 ( real, (zero_zero real), skv_11 ) 22.12/22.23 ( real, (zero_zero real), skv_12 ) 22.12/22.23 ( real, (zero_zero real), skv_15 ) 22.12/22.23 ( real, (zero_zero real), skv_18 ) 22.12/22.23 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.23 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.23 ( 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) ) 22.12/22.23 ( 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 ) 22.12/22.23 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.23 ( real, skv_10, (zero_zero real) ) 22.12/22.23 ( real, skv_11, (zero_zero real) ) 22.12/22.23 ( real, skv_15, (zero_zero real) ) 22.12/22.23 ( real, skv_18, (zero_zero real) ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120568 $$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_120568)) BOUND_VARIABLE_120568) sequentially))))) ) 22.12/22.23 ( bool, fTrue ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120593 $$unsorted) (BOUND_VARIABLE_120594 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_120593) BOUND_VARIABLE_120594))) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_120593) (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_120594))) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120593) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2))))))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120617 $$unsorted) (BOUND_VARIABLE_120618 $$unsorted) (BOUND_VARIABLE_120619 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (cancel_semigroup_add X_a)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120617) BOUND_VARIABLE_120618) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120619) BOUND_VARIABLE_120618)) (= (ti X_a BOUND_VARIABLE_120617) (ti X_a BOUND_VARIABLE_120619)))))) ) 22.12/22.23 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.23 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (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) ) 22.12/22.23 ( 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), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.23 ( 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), (one_one int) ) 22.12/22.23 ( 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), (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) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (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) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.12/22.23 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.12/22.23 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120643 $$unsorted) (BOUND_VARIABLE_120644 $$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_120643) BOUND_VARIABLE_120644)) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120644) BOUND_VARIABLE_120643))) (= (ti X_a BOUND_VARIABLE_120644) (ti X_a BOUND_VARIABLE_120643)))))) ) 22.12/22.23 ( int, pls, (zero_zero int) ) 22.12/22.23 ( int, (one_one int), (zero_zero int) ) 22.12/22.23 ( int, (one_one int), t ) 22.12/22.23 ( int, min, min ) 22.12/22.23 ( int, min, (zero_zero int) ) 22.12/22.23 ( int, (zero_zero int), pls ) 22.12/22.23 ( int, (zero_zero int), (one_one int) ) 22.12/22.23 ( int, (zero_zero int), min ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.12/22.23 ( int, t, (one_one int) ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.23 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.23 ( nat, (zero_zero nat), n ) 22.12/22.23 ( nat, (zero_zero nat), tn ) 22.12/22.23 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.12/22.23 ( nat, n, (zero_zero nat) ) 22.12/22.23 ( nat, tn, (zero_zero nat) ) 22.12/22.23 ( real, pi, (zero_zero real) ) 22.12/22.23 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( 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)) ) 22.12/22.23 ( 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)))) ) 22.12/22.23 ( 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))) ) 22.12/22.23 ( 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)))), (zero_zero real) ) 22.12/22.23 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( real, (zero_zero real), pi ) 22.12/22.23 ( 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)))) ) 22.12/22.23 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( 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))))) ) 22.12/22.23 ( real, (zero_zero real), skv_2 ) 22.12/22.23 ( real, (zero_zero real), skv_9 ) 22.12/22.23 ( real, (zero_zero real), skv_12 ) 22.12/22.23 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.12/22.23 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.23 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.12/22.23 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.23 ( 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) ) 22.12/22.23 ( 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 ) 22.12/22.23 ( real, skv_2, (zero_zero real) ) 22.12/22.23 ( real, skv_9, (zero_zero real) ) 22.12/22.23 ( real, skv_12, (zero_zero real) ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120697 $$unsorted) (BOUND_VARIABLE_120698 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_120698) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_120697)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120697) BOUND_VARIABLE_120698)))))) ) 22.12/22.23 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.12/22.23 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.12/22.23 ( 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) ) 22.12/22.23 ( 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) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.12/22.23 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.23 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.23 ( nat, (one_one nat), (one_one nat) ) 22.12/22.23 ) 22.12/22.23 (instantiation (forall ((M $$unsorted) (N $$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)))) (= _let_0 (hAPP int int _let_1 M))))) ) 22.12/22.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.12/22.23 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( (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 ) 22.12/22.23 ( (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))), m1 ) 22.12/22.23 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.12/22.23 ( (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_21 ) 22.12/22.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.12/22.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.12/22.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.12/22.23 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.12/22.23 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.12/22.23 ( y, v ) 22.12/22.23 ( y, w ) 22.12/22.23 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( sa, v ) 22.12/22.23 ( sa, w ) 22.12/22.23 ( x, v ) 22.12/22.23 ( x, w ) 22.12/22.23 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.23 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( r, v ) 22.12/22.23 ( r, w ) 22.12/22.23 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.12/22.23 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.12/22.23 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.12/22.23 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.12/22.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.12/22.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.23 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.12/22.23 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.23 ) 22.12/22.23 (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)))) ) 22.12/22.23 ( int ) 22.12/22.23 ( nat ) 22.12/22.23 ( bool ) 22.12/22.23 ( real ) 22.12/22.23 ( (filter nat) ) 22.12/22.23 ( (fun int bool) ) 22.12/22.23 ( (product_prod int int) ) 22.12/22.23 ( (fun nat bool) ) 22.12/22.23 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.12/22.23 ( (product_prod real real) ) 22.12/22.23 ( (filter real) ) 22.12/22.23 ( (product_prod nat nat) ) 22.12/22.23 ( (fun nat rat) ) 22.12/22.23 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.12/22.23 ) 22.12/22.24 (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)))))) ) 22.12/22.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( y ) 22.12/22.24 ( x ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.24 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.12/22.24 ( (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))) m1))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120805 $$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_120805) (ti X_a BOUND_VARIABLE_120805))) ) 22.12/22.24 ( int, pls ) 22.12/22.24 ( int, min ) 22.12/22.24 ( int, s ) 22.12/22.24 ( int, s1 ) 22.12/22.24 ( int, m ) 22.12/22.24 ( int, t ) 22.12/22.24 ( int, v ) 22.12/22.24 ( int, w ) 22.12/22.24 ( int, y ) 22.12/22.24 ( int, sa ) 22.12/22.24 ( int, x ) 22.12/22.24 ( int, r ) 22.12/22.24 ( int, m1 ) 22.12/22.24 ( int, skv_14 ) 22.12/22.24 ( int, skv_20 ) 22.12/22.24 ( (fun int int), bit1 ) 22.12/22.24 ( (fun int int), bit0 ) 22.12/22.24 ( (fun int int), succ ) 22.12/22.24 ( (fun int int), pred ) 22.12/22.24 ( (fun int int), (fact_fact int) ) 22.12/22.24 ( (fun int int), zfact ) 22.12/22.24 ( nat, n ) 22.12/22.24 ( nat, tn ) 22.12/22.24 ( bool, fTrue ) 22.12/22.24 ( bool, fFalse ) 22.12/22.24 ( real, pi ) 22.12/22.24 ( (fun nat real), (real_1 nat) ) 22.12/22.24 ( (fun nat real), cos_coeff ) 22.12/22.24 ( (fun nat real), sin_coeff ) 22.12/22.24 ( (fun real real), sin ) 22.12/22.24 ( (fun real real), cos ) 22.12/22.24 ( (fun real real), sqrt ) 22.12/22.24 ( (fun real real), tan ) 22.12/22.24 ( (fun real real), ln ) 22.12/22.24 ( (fun real real), arctan ) 22.12/22.24 ( (fun real real), arcsin ) 22.12/22.24 ( (fun real real), arccos ) 22.12/22.24 ( (fun nat nat), suc ) 22.12/22.24 ( (fun nat nat), (fact_fact nat) ) 22.12/22.24 ( (fun nat nat), nat_size ) 22.12/22.24 ( (fun nat nat), (size_size nat) ) 22.12/22.24 ( (fun nat nat), fact ) 22.12/22.24 ( (filter nat), sequentially ) 22.12/22.24 ( (fun int (fun int rat)), fract ) 22.12/22.24 ( complex, ii ) 22.12/22.24 ( (fun int bool), zOdd ) 22.12/22.24 ( (fun int bool), zprime ) 22.12/22.24 ( (fun int bool), zEven ) 22.12/22.24 ( (fun int bool), nat_neg ) 22.12/22.24 ( (fun int bool), nat_is_nat ) 22.12/22.24 ( (fun int bool), (even_odd_even int) ) 22.12/22.24 ( (fun int bool), twoSqu1091635170sum2sq ) 22.12/22.24 ( (fun int (fun int int)), legacy_zgcd ) 22.12/22.24 ( (fun int (fun int int)), (gcd_gcd int) ) 22.12/22.24 ( (fun int (fun int int)), inv ) 22.12/22.24 ( (fun int (fun int int)), multInv ) 22.12/22.24 ( (fun int (fun int int)), legendre ) 22.12/22.24 ( (fun int (fun int int)), standardRes ) 22.12/22.24 ( (fun int (fun int int)), nat_tsub ) 22.12/22.24 ( (fun int (fun int int)), z3div ) 22.12/22.24 ( (fun int (fun int int)), z3mod ) 22.12/22.24 ( (fun int (fun int int)), int_lcm ) 22.12/22.24 ( (fun int (fun int int)), int_gcd ) 22.12/22.24 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.12/22.24 ( (fun bool bool), fNot ) 22.12/22.24 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.12/22.24 ( (fun bool (fun bool bool)), fconj ) 22.12/22.24 ( (fun bool (fun bool bool)), fdisj ) 22.12/22.24 ( (fun bool (fun bool bool)), fimplies ) 22.12/22.24 ( (fun int (fun int bool)), quadRes ) 22.12/22.24 ( (fun int (fun int bool)), d22set ) 22.12/22.24 ( (fun int (fun int bool)), norRRset ) 22.12/22.24 ( (fun int (fun int bool)), sRStar ) 22.12/22.24 ( (fun int (fun int bool)), sr ) 22.12/22.24 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.12/22.24 ( (fun nat bool), (even_odd_even nat) ) 22.12/22.24 ( (fun nat bool), prime ) 22.12/22.24 ( (fun real complex), cis ) 22.12/22.24 ( (fun nat (fun nat bool)), coprime ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.12/22.24 ( (fun (product_prod int int) bool), frac_1 ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.12/22.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.12/22.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.12/22.24 ( (fun (fun int bool) bool), nat_nat_set ) 22.12/22.24 ( (fun nat (fun real real)), root ) 22.12/22.24 ( (fun real (fun real real)), log ) 22.12/22.24 ( (fun real (fun real real)), powr ) 22.12/22.24 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.12/22.24 ( (fun complex complex), cnj ) 22.12/22.24 ( (fun complex complex), expi ) 22.12/22.24 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.12/22.24 ( (fun nat (fun nat nat)), nat_gcd ) 22.12/22.24 ( (fun nat (fun nat nat)), nat_lcm ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.12/22.24 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.12/22.24 ( (fun int (fun (fun int bool) bool)), resSet ) 22.12/22.24 ( (fun int nat), nat_1 ) 22.12/22.24 ( (fun int nat), phi ) 22.12/22.24 ( (fun complex real), re ) 22.12/22.24 ( (fun complex real), im ) 22.12/22.24 ( (fun complex real), arg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.12/22.24 ( (fun (product_prod nat nat) bool), pred_nat ) 22.12/22.24 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.12/22.24 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.12/22.24 ( (fun (fun int bool) int), (the int) ) 22.12/22.24 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.12/22.24 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.12/22.24 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.12/22.24 ( (fun real (fun real complex)), rcis ) 22.12/22.24 ( (fun real (fun real complex)), complex_1 ) 22.12/22.24 ( (fun int (fun int (fun int bool))), zcong ) 22.12/22.24 ( (fun int (fun int (fun int bool))), wset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), noXRRset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), bnorRset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), zcongm ) 22.12/22.24 ( (fun real nat), natceiling ) 22.12/22.24 ( (fun real nat), natfloor ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.12/22.24 ( (fun int real), (real_1 int) ) 22.12/22.24 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.12/22.24 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.12/22.24 ( (fun complex nat), (size_size complex) ) 22.12/22.24 ( (fun complex nat), complex_size ) 22.12/22.24 ( (fun (fun nat rat) bool), vanishes ) 22.12/22.24 ( (fun (product_prod int int) rat), frct ) 22.12/22.24 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.12/22.24 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.12/22.24 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.12/22.24 ( (fun rat real), ratreal ) 22.12/22.24 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.12/22.24 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.12/22.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.12/22.24 ( (fun rat (product_prod int int)), quotient_of ) 22.12/22.24 ( (fun int (fun nat nat)), nat_aux ) 22.12/22.24 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.12/22.24 ( (fun int (list int)), quickc666637781d_zero ) 22.12/22.24 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.12/22.24 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.12/22.24 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.12/22.24 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.12/22.24 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.12/22.24 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.12/22.24 ( (fun code_code_numeral int), code_int_of ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) (hAPP nat nat suc N))))) ) 22.12/22.24 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP nat nat suc _let_0))) (= (= _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) Na)) (or (and (= _let_0 Na) (= _let_1 Ma)) (and (= _let_0 Ma) (= _let_1 Na)))))) ) 22.12/22.24 ( (one_one nat), (one_one nat) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120900 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_1 X_a)) (= (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_120900)) (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_120900))))) ) 22.12/22.24 ( real, pls ) 22.12/22.24 ( real, (one_one int) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (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))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real sin X)) _let_0)))))) ) 22.12/22.24 ( pi ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (zero_zero real) ) 22.12/22.24 ( (hAPP real 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))))) ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.12/22.24 ( (hAPP real real (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))))) ) 22.12/22.24 ( (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)))) ) 22.12/22.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((N $$unsorted)) (= (hAPP nat int (semiring_1_of_nat int) N) (hAPP real int (archimedean_ceiling real) (hAPP nat real (real_1 nat) N))) ) 22.12/22.24 ( (zero_zero nat) ) 22.12/22.24 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (one_one nat) ) 22.12/22.24 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.24 ( n ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real _let_0 X)) N) (hAPP int real _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)))) ) 22.12/22.24 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_120963 $$unsorted) (BOUND_VARIABLE_120964 $$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_120963) BOUND_VARIABLE_120964)) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_120963) BOUND_VARIABLE_120964)))))) ) 22.12/22.24 ( int, (one_one int), t ) 22.12/22.24 ( int, min, min ) 22.12/22.24 ( int, min, (zero_zero int) ) 22.12/22.24 ( int, (zero_zero int), pls ) 22.12/22.24 ( int, (zero_zero int), (one_one int) ) 22.12/22.24 ( int, (zero_zero int), min ) 22.12/22.24 ( 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))) ) 22.12/22.24 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( 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))) ) 22.12/22.24 ( 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) ) 22.12/22.24 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( 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))) ) 22.12/22.24 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.24 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.24 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.24 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.24 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.12/22.24 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.12/22.24 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.12/22.24 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.12/22.24 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.24 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.24 ( 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))) ) 22.12/22.24 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( nat, (zero_zero nat), n ) 22.12/22.24 ( nat, (zero_zero nat), tn ) 22.12/22.24 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.12/22.24 ( real, pi, (zero_zero real) ) 22.12/22.24 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( real, (hAPP real real (hAPP 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))) ) 22.12/22.24 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( real, (zero_zero real), pi ) 22.12/22.24 ( 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)))) ) 22.12/22.24 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( real, (zero_zero real), skv_2 ) 22.12/22.24 ( real, (zero_zero real), skv_9 ) 22.12/22.24 ( real, (zero_zero real), skv_12 ) 22.12/22.24 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.24 ( 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) ) 22.12/22.24 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.12/22.24 ( 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 ) 22.12/22.24 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (hAPP int _let_1 (ord_less_eq int) _let_3))) (or (not (hBOOL (hAPP int bool _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) B_5) Q_5)) R_4)))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 R_4) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 _let_3) B_5))) (hBOOL (hAPP int bool _let_4 Q_5)))))))) ) 22.12/22.24 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.12/22.24 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 22.12/22.24 ( x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.12/22.24 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 22.12/22.24 ( r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.24 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.12/22.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121016 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_121016) (ti X_a BOUND_VARIABLE_121016))) ) 22.12/22.24 ( int, pls ) 22.12/22.24 ( int, min ) 22.12/22.24 ( int, s ) 22.12/22.24 ( int, s1 ) 22.12/22.24 ( int, m ) 22.12/22.24 ( int, t ) 22.12/22.24 ( int, v ) 22.12/22.24 ( int, w ) 22.12/22.24 ( int, y ) 22.12/22.24 ( int, sa ) 22.12/22.24 ( int, x ) 22.12/22.24 ( int, r ) 22.12/22.24 ( int, m1 ) 22.12/22.24 ( int, skv_14 ) 22.12/22.24 ( int, skv_20 ) 22.12/22.24 ( (fun int int), bit1 ) 22.12/22.24 ( (fun int int), bit0 ) 22.12/22.24 ( (fun int int), succ ) 22.12/22.24 ( (fun int int), pred ) 22.12/22.24 ( (fun int int), (fact_fact int) ) 22.12/22.24 ( (fun int int), zfact ) 22.12/22.24 ( nat, n ) 22.12/22.24 ( nat, tn ) 22.12/22.24 ( bool, fTrue ) 22.12/22.24 ( bool, fFalse ) 22.12/22.24 ( real, pi ) 22.12/22.24 ( (fun nat real), (real_1 nat) ) 22.12/22.24 ( (fun nat real), cos_coeff ) 22.12/22.24 ( (fun nat real), sin_coeff ) 22.12/22.24 ( (fun real real), sin ) 22.12/22.24 ( (fun real real), cos ) 22.12/22.24 ( (fun real real), sqrt ) 22.12/22.24 ( (fun real real), tan ) 22.12/22.24 ( (fun real real), ln ) 22.12/22.24 ( (fun real real), arctan ) 22.12/22.24 ( (fun real real), arcsin ) 22.12/22.24 ( (fun real real), arccos ) 22.12/22.24 ( (fun nat nat), suc ) 22.12/22.24 ( (fun nat nat), (fact_fact nat) ) 22.12/22.24 ( (fun nat nat), nat_size ) 22.12/22.24 ( (fun nat nat), (size_size nat) ) 22.12/22.24 ( (fun nat nat), fact ) 22.12/22.24 ( (filter nat), sequentially ) 22.12/22.24 ( (fun int (fun int rat)), fract ) 22.12/22.24 ( complex, ii ) 22.12/22.24 ( (fun int bool), zOdd ) 22.12/22.24 ( (fun int bool), zprime ) 22.12/22.24 ( (fun int bool), zEven ) 22.12/22.24 ( (fun int bool), nat_neg ) 22.12/22.24 ( (fun int bool), nat_is_nat ) 22.12/22.24 ( (fun int bool), (even_odd_even int) ) 22.12/22.24 ( (fun int bool), twoSqu1091635170sum2sq ) 22.12/22.24 ( (fun int (fun int int)), legacy_zgcd ) 22.12/22.24 ( (fun int (fun int int)), (gcd_gcd int) ) 22.12/22.24 ( (fun int (fun int int)), inv ) 22.12/22.24 ( (fun int (fun int int)), multInv ) 22.12/22.24 ( (fun int (fun int int)), legendre ) 22.12/22.24 ( (fun int (fun int int)), standardRes ) 22.12/22.24 ( (fun int (fun int int)), nat_tsub ) 22.12/22.24 ( (fun int (fun int int)), z3div ) 22.12/22.24 ( (fun int (fun int int)), z3mod ) 22.12/22.24 ( (fun int (fun int int)), int_lcm ) 22.12/22.24 ( (fun int (fun int int)), int_gcd ) 22.12/22.24 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.12/22.24 ( (fun bool bool), fNot ) 22.12/22.24 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.12/22.24 ( (fun bool (fun bool bool)), fconj ) 22.12/22.24 ( (fun bool (fun bool bool)), fdisj ) 22.12/22.24 ( (fun bool (fun bool bool)), fimplies ) 22.12/22.24 ( (fun int (fun int bool)), quadRes ) 22.12/22.24 ( (fun int (fun int bool)), d22set ) 22.12/22.24 ( (fun int (fun int bool)), norRRset ) 22.12/22.24 ( (fun int (fun int bool)), sRStar ) 22.12/22.24 ( (fun int (fun int bool)), sr ) 22.12/22.24 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.12/22.24 ( (fun nat bool), (even_odd_even nat) ) 22.12/22.24 ( (fun nat bool), prime ) 22.12/22.24 ( (fun real complex), cis ) 22.12/22.24 ( (fun nat (fun nat bool)), coprime ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.12/22.24 ( (fun (product_prod int int) bool), frac_1 ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.12/22.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.12/22.24 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.12/22.24 ( (fun (fun int bool) bool), nat_nat_set ) 22.12/22.24 ( (fun nat (fun real real)), root ) 22.12/22.24 ( (fun real (fun real real)), log ) 22.12/22.24 ( (fun real (fun real real)), powr ) 22.12/22.24 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.12/22.24 ( (fun complex complex), cnj ) 22.12/22.24 ( (fun complex complex), expi ) 22.12/22.24 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.12/22.24 ( (fun nat (fun nat nat)), nat_gcd ) 22.12/22.24 ( (fun nat (fun nat nat)), nat_lcm ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.12/22.24 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.12/22.24 ( (fun int (fun (fun int bool) bool)), resSet ) 22.12/22.24 ( (fun int nat), nat_1 ) 22.12/22.24 ( (fun int nat), phi ) 22.12/22.24 ( (fun complex real), re ) 22.12/22.24 ( (fun complex real), im ) 22.12/22.24 ( (fun complex real), arg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.12/22.24 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.12/22.24 ( (fun (product_prod nat nat) bool), pred_nat ) 22.12/22.24 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.12/22.24 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.12/22.24 ( (fun (fun int bool) int), (the int) ) 22.12/22.24 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.12/22.24 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.12/22.24 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.12/22.24 ( (fun real (fun real complex)), rcis ) 22.12/22.24 ( (fun real (fun real complex)), complex_1 ) 22.12/22.24 ( (fun int (fun int (fun int bool))), zcong ) 22.12/22.24 ( (fun int (fun int (fun int bool))), wset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), noXRRset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), bnorRset ) 22.12/22.24 ( (fun int (fun int (fun int bool))), zcongm ) 22.12/22.24 ( (fun real nat), natceiling ) 22.12/22.24 ( (fun real nat), natfloor ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.12/22.24 ( (fun int real), (real_1 int) ) 22.12/22.24 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.12/22.24 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.12/22.24 ( (fun complex nat), (size_size complex) ) 22.12/22.24 ( (fun complex nat), complex_size ) 22.12/22.24 ( (fun (fun nat rat) bool), vanishes ) 22.12/22.24 ( (fun (product_prod int int) rat), frct ) 22.12/22.24 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.12/22.24 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.12/22.24 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.12/22.24 ( (fun rat real), ratreal ) 22.12/22.24 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.12/22.24 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.12/22.24 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.12/22.24 ( (fun rat (product_prod int int)), quotient_of ) 22.12/22.24 ( (fun int (fun nat nat)), nat_aux ) 22.12/22.24 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.12/22.24 ( (fun int (list int)), quickc666637781d_zero ) 22.12/22.24 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.12/22.24 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.12/22.24 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.12/22.24 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.12/22.24 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.12/22.24 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.12/22.24 ( (fun code_code_numeral int), code_int_of ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real (hAPP 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_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (uminus_uminus real) _let_0)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (= X (hAPP real real arcsin (hAPP real real sin X))))))) ) 22.12/22.24 ( pi ) 22.12/22.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (zero_zero real) ) 22.12/22.24 ( (hAPP real 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))))) ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.12/22.24 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (hAPP real real (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))))) ) 22.12/22.24 ( (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)))) ) 22.12/22.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.12/22.24 ( skv_10 ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (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)) A_1))) ) 22.12/22.24 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq X))) (not (hBOOL (hAPP int bool twoSqu1091635170sum2sq Y))) (hBOOL (hAPP int bool twoSqu1091635170sum2sq (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)))) ) 22.12/22.24 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.12/22.24 ( 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))) ) 22.12/22.24 ( v, y ) 22.12/22.24 ( v, sa ) 22.12/22.24 ( v, x ) 22.12/22.24 ( v, r ) 22.12/22.24 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.24 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.24 ( w, y ) 22.12/22.24 ( w, sa ) 22.12/22.24 ( w, x ) 22.12/22.24 ( w, r ) 22.12/22.24 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.24 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.24 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.12/22.24 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( skv_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))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((W $$unsorted)) (= (hAPP int complex (number_number_of complex) W) (hAPP int complex (ring_1_of_int complex) W)) ) 22.12/22.24 ( min ) 22.12/22.24 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$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)))) ) 22.12/22.24 ( rat ) 22.12/22.24 ( int ) 22.12/22.24 ( (fun int int) ) 22.12/22.24 ( nat ) 22.12/22.24 ( bool ) 22.12/22.24 ( real ) 22.12/22.24 ( (fun nat real) ) 22.12/22.24 ( (fun real real) ) 22.12/22.24 ( complex ) 22.12/22.24 ( (fun int bool) ) 22.12/22.24 ( (product_prod int int) ) 22.12/22.24 ( (fun (product_prod int int) int) ) 22.12/22.24 ( (fun int (fun int bool)) ) 22.12/22.24 ( (fun nat bool) ) 22.12/22.24 ( (fun (product_prod int int) bool) ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.12/22.24 ( (fun real bool) ) 22.12/22.24 ( quickcheck_code_int ) 22.12/22.24 ( code_code_numeral ) 22.12/22.24 ( (fun int (fun int (fun int bool))) ) 22.12/22.24 ( (fun int real) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((C $$unsorted) (D_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun int _let_0) zcong C))) (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_3) B_2) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 A_3)) Ma)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 B_2)) Ma))))))) ) 22.12/22.24 ( (hAPP nat int (hAPP 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 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))) ) 22.12/22.24 ( s1, sa, (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( (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) (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), 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))) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X))))))) ) 22.12/22.24 ( pi ) 22.12/22.24 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (zero_zero real) ) 22.12/22.24 ( (hAPP real 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))))) ) 22.12/22.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.12/22.24 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.24 ( (hAPP real real (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))))) ) 22.12/22.24 ( (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)))) ) 22.12/22.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.12/22.24 ( skv_10 ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (dvd_dvd X_a))) (or (not (dvd X_a)) (= _let_0 (ti (fun X_a (fun X_a bool)) _let_0)))) ) 22.12/22.24 ( rat ) 22.12/22.24 ( int ) 22.12/22.24 ( nat ) 22.12/22.24 ( bool ) 22.12/22.24 ( real ) 22.12/22.24 ( (filter nat) ) 22.12/22.24 ( complex ) 22.12/22.24 ( (fun int bool) ) 22.12/22.24 ( (product_prod int int) ) 22.12/22.24 ( (fun nat bool) ) 22.12/22.24 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.12/22.24 ( quickcheck_code_int ) 22.12/22.24 ( code_code_numeral ) 22.12/22.24 ( (product_prod real real) ) 22.12/22.24 ( (filter real) ) 22.12/22.24 ( (product_prod nat nat) ) 22.12/22.24 ( (fun nat rat) ) 22.12/22.24 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.12/22.24 ) 22.12/22.24 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) K_4))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (= (ti int K_4) (hAPP nat int (semiring_1_of_nat int) N_1)))) ))) ) 22.12/22.24 ( pls ) 22.12/22.24 ( (one_one int) ) 22.12/22.24 ( min ) 22.12/22.24 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.24 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.24 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121304 $$unsorted) (BOUND_VARIABLE_121305 $$unsorted) (BOUND_VARIABLE_121306 $$unsorted) (BOUND_VARIABLE_121307 $$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_121304))) (let ((_let_3 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121306) BOUND_VARIABLE_121307))) (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_121305)) _let_3) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121305) _let_3)))))))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121332 $$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_121332)) (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_121332) (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_121332)) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))))))))) ) 22.12/22.25 ( int, pls ) 22.12/22.25 ( int, min ) 22.12/22.25 ( int, s ) 22.12/22.25 ( int, s1 ) 22.12/22.25 ( int, m ) 22.12/22.25 ( int, t ) 22.12/22.25 ( int, v ) 22.12/22.25 ( int, w ) 22.12/22.25 ( int, y ) 22.12/22.25 ( int, sa ) 22.12/22.25 ( int, x ) 22.12/22.25 ( int, r ) 22.12/22.25 ( int, m1 ) 22.12/22.25 ( int, skv_14 ) 22.12/22.25 ( int, skv_20 ) 22.12/22.25 ( (fun int int), bit1 ) 22.12/22.25 ( (fun int int), bit0 ) 22.12/22.25 ( (fun int int), succ ) 22.12/22.25 ( (fun int int), pred ) 22.12/22.25 ( (fun int int), (fact_fact int) ) 22.12/22.25 ( (fun int int), zfact ) 22.12/22.25 ( nat, n ) 22.12/22.25 ( nat, tn ) 22.12/22.25 ( bool, fTrue ) 22.12/22.25 ( bool, fFalse ) 22.12/22.25 ( real, pi ) 22.12/22.25 ( real, (zero_zero real) ) 22.12/22.25 ( (fun nat real), (real_1 nat) ) 22.12/22.25 ( (fun nat real), cos_coeff ) 22.12/22.25 ( (fun nat real), sin_coeff ) 22.12/22.25 ( (fun real real), sin ) 22.12/22.25 ( (fun real real), cos ) 22.12/22.25 ( (fun real real), sqrt ) 22.12/22.25 ( (fun real real), tan ) 22.12/22.25 ( (fun real real), ln ) 22.12/22.25 ( (fun real real), arctan ) 22.12/22.25 ( (fun real real), arcsin ) 22.12/22.25 ( (fun real real), arccos ) 22.12/22.25 ( (fun nat nat), suc ) 22.12/22.25 ( (fun nat nat), (fact_fact nat) ) 22.12/22.25 ( (fun nat nat), nat_size ) 22.12/22.25 ( (fun nat nat), (size_size nat) ) 22.12/22.25 ( (fun nat nat), fact ) 22.12/22.25 ( (filter nat), sequentially ) 22.12/22.25 ( (fun int (fun int rat)), fract ) 22.12/22.25 ( complex, ii ) 22.12/22.25 ( (fun int bool), zOdd ) 22.12/22.25 ( (fun int bool), zprime ) 22.12/22.25 ( (fun int bool), zEven ) 22.12/22.25 ( (fun int bool), nat_neg ) 22.12/22.25 ( (fun int bool), nat_is_nat ) 22.12/22.25 ( (fun int bool), (even_odd_even int) ) 22.12/22.25 ( (fun int bool), twoSqu1091635170sum2sq ) 22.12/22.25 ( (fun int (fun int int)), legacy_zgcd ) 22.12/22.25 ( (fun int (fun int int)), (gcd_gcd int) ) 22.12/22.25 ( (fun int (fun int int)), inv ) 22.12/22.25 ( (fun int (fun int int)), multInv ) 22.12/22.25 ( (fun int (fun int int)), legendre ) 22.12/22.25 ( (fun int (fun int int)), standardRes ) 22.12/22.25 ( (fun int (fun int int)), nat_tsub ) 22.12/22.25 ( (fun int (fun int int)), z3div ) 22.12/22.25 ( (fun int (fun int int)), z3mod ) 22.12/22.25 ( (fun int (fun int int)), int_lcm ) 22.12/22.25 ( (fun int (fun int int)), int_gcd ) 22.12/22.25 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.12/22.25 ( (fun bool bool), fNot ) 22.12/22.25 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.12/22.25 ( (fun bool (fun bool bool)), fconj ) 22.12/22.25 ( (fun bool (fun bool bool)), fdisj ) 22.12/22.25 ( (fun bool (fun bool bool)), fimplies ) 22.12/22.25 ( (fun int (fun int bool)), quadRes ) 22.12/22.25 ( (fun int (fun int bool)), d22set ) 22.12/22.25 ( (fun int (fun int bool)), norRRset ) 22.12/22.25 ( (fun int (fun int bool)), sRStar ) 22.12/22.25 ( (fun int (fun int bool)), sr ) 22.12/22.25 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.12/22.25 ( (fun nat bool), (even_odd_even nat) ) 22.12/22.25 ( (fun nat bool), prime ) 22.12/22.25 ( (fun real complex), cis ) 22.12/22.25 ( (fun nat (fun nat bool)), coprime ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.12/22.25 ( (fun (product_prod int int) bool), frac_1 ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.12/22.25 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.12/22.25 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.12/22.25 ( (fun (fun int bool) bool), nat_nat_set ) 22.12/22.25 ( (fun nat (fun real real)), root ) 22.12/22.25 ( (fun real (fun real real)), log ) 22.12/22.25 ( (fun real (fun real real)), powr ) 22.12/22.25 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.12/22.25 ( (fun complex complex), cnj ) 22.12/22.25 ( (fun complex complex), expi ) 22.12/22.25 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.12/22.25 ( (fun nat (fun nat nat)), nat_gcd ) 22.12/22.25 ( (fun nat (fun nat nat)), nat_lcm ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.12/22.25 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.12/22.25 ( (fun int (fun (fun int bool) bool)), resSet ) 22.12/22.25 ( (fun int nat), nat_1 ) 22.12/22.25 ( (fun int nat), phi ) 22.12/22.25 ( (fun complex real), re ) 22.12/22.25 ( (fun complex real), im ) 22.12/22.25 ( (fun complex real), arg ) 22.12/22.25 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.12/22.25 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.12/22.25 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.12/22.25 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.12/22.25 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.12/22.25 ( (fun (product_prod nat nat) bool), pred_nat ) 22.12/22.25 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.12/22.25 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.12/22.25 ( (fun (fun int bool) int), (the int) ) 22.12/22.25 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.12/22.25 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.12/22.25 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.12/22.25 ( (fun real (fun real complex)), rcis ) 22.12/22.25 ( (fun real (fun real complex)), complex_1 ) 22.12/22.25 ( (fun int (fun int (fun int bool))), zcong ) 22.12/22.25 ( (fun int (fun int (fun int bool))), wset ) 22.12/22.25 ( (fun int (fun int (fun int bool))), noXRRset ) 22.12/22.25 ( (fun int (fun int (fun int bool))), bnorRset ) 22.12/22.25 ( (fun int (fun int (fun int bool))), zcongm ) 22.12/22.25 ( (fun real nat), natceiling ) 22.12/22.25 ( (fun real nat), natfloor ) 22.12/22.25 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.12/22.25 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.12/22.25 ( (fun int real), (real_1 int) ) 22.12/22.25 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.12/22.25 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.12/22.25 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.12/22.25 ( (fun complex nat), (size_size complex) ) 22.12/22.25 ( (fun complex nat), complex_size ) 22.12/22.25 ( (fun (fun nat rat) bool), vanishes ) 22.12/22.25 ( (fun (product_prod int int) rat), frct ) 22.12/22.25 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.12/22.25 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.12/22.25 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.12/22.25 ( (fun rat real), ratreal ) 22.12/22.25 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.12/22.25 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.12/22.25 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.12/22.25 ( (fun rat (product_prod int int)), quotient_of ) 22.12/22.25 ( (fun int (fun nat nat)), nat_aux ) 22.12/22.25 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.12/22.25 ( (fun int (list int)), quickc666637781d_zero ) 22.12/22.25 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.12/22.25 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.12/22.25 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.12/22.25 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.12/22.25 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.12/22.25 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.12/22.25 ( (fun code_code_numeral int), code_int_of ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP int int (fact_fact int) (hAPP nat int _let_0 X)) (hAPP nat int _let_0 (hAPP nat nat (fact_fact nat) X)))) ) 22.12/22.25 ( (zero_zero nat) ) 22.12/22.25 ( (one_one nat) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121362 $$unsorted) (BOUND_VARIABLE_121363 $$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_121362) BOUND_VARIABLE_121363)) (hAPP X_a real _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_121363) BOUND_VARIABLE_121362))))))) ) 22.12/22.25 ( 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) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.25 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.12/22.25 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.25 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.12/22.25 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.25 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.12/22.25 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.12/22.25 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 22.12/22.25 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.12/22.25 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.12/22.25 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.12/22.25 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.12/22.25 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((M $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) M))) (= (hAPP int int (hAPP int (fun int int) legacy_zgcd M) M) (ti int M))) ) 22.12/22.25 ( pls ) 22.12/22.25 ( (one_one int) ) 22.12/22.25 ( min ) 22.12/22.25 ( s ) 22.12/22.25 ( s1 ) 22.12/22.25 ( m ) 22.12/22.25 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( t ) 22.12/22.25 ( v ) 22.12/22.25 ( w ) 22.12/22.25 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.12/22.25 ( y ) 22.12/22.25 ( sa ) 22.12/22.25 ( x ) 22.12/22.25 ( r ) 22.12/22.25 ( m1 ) 22.12/22.25 ( skv_4 ) 22.12/22.25 ( skv_5 ) 22.12/22.25 ( skv_14 ) 22.12/22.25 ( skv_20 ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121410 $$unsorted) (BOUND_VARIABLE_121411 $$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_121411) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121410) _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_121411) BOUND_VARIABLE_121410))))))) ) 22.12/22.25 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.12/22.25 ( 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))) ) 22.12/22.25 ( int, v, y ) 22.12/22.25 ( int, v, sa ) 22.12/22.25 ( int, v, x ) 22.12/22.25 ( int, v, r ) 22.12/22.25 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.25 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.25 ( int, w, y ) 22.12/22.25 ( int, w, sa ) 22.12/22.25 ( int, w, x ) 22.12/22.25 ( int, w, r ) 22.12/22.25 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.12/22.25 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.12/22.25 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.12/22.25 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.12/22.25 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( int, skv_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))) ) 22.12/22.25 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( 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))))) ) 22.12/22.25 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( 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)))) ) 22.12/22.25 ( complex, ii, ii ) 22.12/22.25 ( 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)) ) 22.12/22.25 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121466 $$unsorted) (BOUND_VARIABLE_121467 $$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_121466)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_121467))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121467) BOUND_VARIABLE_121466))))))) ) 22.12/22.25 ( int, pls, pls ) 22.12/22.25 ( int, pls, (one_one int) ) 22.12/22.25 ( int, pls, min ) 22.12/22.25 ( int, pls, (zero_zero int) ) 22.12/22.25 ( int, (one_one int), pls ) 22.12/22.25 ( int, (one_one int), (one_one int) ) 22.12/22.25 ( int, (one_one int), (zero_zero int) ) 22.12/22.25 ( int, min, min ) 22.12/22.25 ( int, min, (zero_zero int) ) 22.12/22.25 ( int, s, (zero_zero int) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.12/22.25 ( int, t, (one_one int) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.12/22.25 ( int, skv_4, (zero_zero int) ) 22.12/22.25 ( int, skv_5, (zero_zero int) ) 22.12/22.25 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.12/22.25 ( real, pi, (zero_zero real) ) 22.12/22.25 ( 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)))) ) 22.12/22.25 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.12/22.25 ( real, (hAPP real real (hAPP 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) ) 22.12/22.25 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.12/22.25 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.12/22.25 ( real, skv_10, (zero_zero real) ) 22.12/22.25 ( real, skv_11, (zero_zero real) ) 22.12/22.25 ( real, skv_15, (zero_zero real) ) 22.12/22.25 ( real, skv_18, (zero_zero real) ) 22.12/22.25 ) 22.12/22.25 (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)))))) ) 22.12/22.25 ( (zero_zero nat) ) 22.12/22.25 ( (hAPP nat nat suc (zero_zero nat)) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (uminus_uminus _let_0))) (= (ti _let_0 A_2) (hAPP _let_0 _let_0 _let_1 (hAPP _let_0 _let_0 _let_1 A_2))))) ) 22.12/22.25 ( int, zOdd ) 22.12/22.25 ( int, zprime ) 22.12/22.25 ( int, zEven ) 22.12/22.25 ( int, nat_neg ) 22.12/22.25 ( int, nat_is_nat ) 22.12/22.25 ( int, (even_odd_even int) ) 22.12/22.25 ( int, twoSqu1091635170sum2sq ) 22.12/22.25 ( nat, (even_odd_even nat) ) 22.12/22.25 ( nat, prime ) 22.12/22.25 ( bool, fNot ) 22.12/22.25 ( (fun int bool), nat_nat_set ) 22.12/22.25 ( (product_prod int int), frac_1 ) 22.12/22.25 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 22.12/22.25 ( (product_prod nat nat), pred_nat ) 22.12/22.25 ( (fun nat rat), vanishes ) 22.12/22.25 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 22.12/22.25 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121540 $$unsorted) (BOUND_VARIABLE_121541 $$unsorted) (BOUND_VARIABLE_121542 $$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_121542))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_121540) BOUND_VARIABLE_121541))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121540) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_121542) BOUND_VARIABLE_121541)))))) ) 22.12/22.25 ( int, (zero_zero 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) ) 22.12/22.25 ( int, (zero_zero int), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.12/22.25 ( 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) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 22.12/22.25 ( 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) ) 22.12/22.25 ( int, m1, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.12/22.25 ( 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) ) 22.12/22.25 ( int, skv_5, (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) ) 22.12/22.25 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_2)) (= (zero_zero nat) (hAPP _let_0 nat (finite_card X_a) A_2)))) ) 22.12/22.25 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_0 (isCont X_a X_b))) (or (not (topological_space X_b)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun X_a X_b) (fun X_a bool)) _let_0)))) ) 22.12/22.25 ( int, int ) 22.12/22.25 ( int, (product_prod int int) ) 22.12/22.25 ( bool, int ) 22.12/22.25 ( bool, nat ) 22.12/22.25 ( bool, real ) 22.12/22.25 ( bool, (product_prod int int) ) 22.12/22.25 ( real, int ) 22.12/22.25 ( real, nat ) 22.12/22.25 ( (fun int bool), int ) 22.12/22.25 ( (fun int bool), real ) 22.12/22.25 ( (fun nat bool), int ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121631 $$unsorted) (BOUND_VARIABLE_121632 $$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_121631) BOUND_VARIABLE_121632))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_121631)) (hAPP X_a real _let_0 BOUND_VARIABLE_121632)))))) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.12/22.25 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.12/22.25 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.12/22.25 ( int, y, v ) 22.12/22.25 ( int, y, w ) 22.12/22.25 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, sa, v ) 22.12/22.25 ( int, sa, w ) 22.12/22.25 ( int, x, v ) 22.12/22.25 ( int, x, w ) 22.12/22.25 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.12/22.25 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, r, v ) 22.12/22.25 ( int, r, w ) 22.12/22.25 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.12/22.25 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.12/22.25 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.12/22.25 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.12/22.25 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.12/22.25 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.12/22.25 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.12/22.25 ( 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)))))) ) 22.12/22.25 ( 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 ) 22.12/22.25 ( complex, ii, ii ) 22.12/22.25 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.12/22.25 ( 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 ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted) (Ya $$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) Na) (hAPP int int (hAPP int _let_0 (minus_minus int) Xa) Ya))) (= (hAPP int int (hAPP int _let_0 _let_1 Xa) Na) (hAPP int int (hAPP int _let_0 _let_1 Ya) Na))))) ) 22.12/22.25 ( (hAPP nat int (hAPP 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) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121754 $$unsorted) (BOUND_VARIABLE_121755 $$unsorted) (BOUND_VARIABLE_121756 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_121754) BOUND_VARIABLE_121755)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_121756) BOUND_VARIABLE_121755)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_121756))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121754) BOUND_VARIABLE_121756))))))) ) 22.12/22.25 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) N) (hAPP nat nat suc N)) ) 22.12/22.25 ( (zero_zero nat) ) 22.12/22.25 ( (one_one nat) ) 22.12/22.25 ( (hAPP nat nat suc (zero_zero nat)) ) 22.12/22.25 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((X_a $$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)))) ) 22.12/22.25 ( rat ) 22.12/22.25 ( int ) 22.12/22.25 ( nat ) 22.12/22.25 ( real ) 22.12/22.25 ( complex ) 22.12/22.25 ( quickcheck_code_int ) 22.12/22.25 ( code_code_numeral ) 22.12/22.25 ) 22.12/22.25 (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))) ) 22.12/22.25 ( int, int ) 22.12/22.25 ( int, (product_prod int int) ) 22.12/22.25 ( nat, nat ) 22.12/22.25 ( real, real ) 22.12/22.25 ( (product_prod int int), (product_prod int int) ) 22.12/22.25 ( quickcheck_code_int, quickcheck_code_int ) 22.12/22.25 ( code_code_numeral, code_code_numeral ) 22.12/22.25 ( (product_prod nat nat), (product_prod nat nat) ) 22.12/22.25 ) 22.12/22.25 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun complex complex))) (= (hAPP complex complex (hAPP complex _let_0 (times_times complex) (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real im Z_1)))) ii) (hAPP complex complex (hAPP complex _let_0 (minus_minus complex) Z_1) (hAPP complex complex cnj Z_1)))) ) 22.12/22.25 ( (zero_zero complex) ) 22.12/22.25 ( ii ) 22.12/22.25 ( (one_one complex) ) 22.12/22.25 ) 22.21/22.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121801 $$unsorted) (BOUND_VARIABLE_121802 $$unsorted) (BOUND_VARIABLE_121803 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (times_times X_a))) (or (not (comm_monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121801) BOUND_VARIABLE_121803)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121802) BOUND_VARIABLE_121803)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_121801) BOUND_VARIABLE_121802)) BOUND_VARIABLE_121803))))))) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.29 ) 22.21/22.29 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B_2) A_3)) (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_3) B_2))))))) ) 22.21/22.29 ( pls, (zero_zero int) ) 22.21/22.29 ( (one_one int), (one_one int) ) 22.21/22.29 ( (one_one int), (zero_zero int) ) 22.21/22.29 ( min, min ) 22.21/22.29 ( min, (zero_zero int) ) 22.21/22.29 ( (zero_zero int), (one_one int) ) 22.21/22.29 ( (zero_zero int), min ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.29 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.21/22.29 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.21/22.29 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.29 ( t, (one_one int) ) 22.21/22.29 ) 22.21/22.29 (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 (hAPP real _let_0 _let_1 (hAPP real real _let_2 Z2)) Z3) (hAPP real real _let_2 (hAPP real real (hAPP real _let_0 _let_1 Z2) Z3)))))) ) 22.21/22.29 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.29 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.29 ) 22.21/22.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121835 $$unsorted) (BOUND_VARIABLE_121836 $$unsorted) (BOUND_VARIABLE_121837 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fact_fact nat))) (let ((_let_3 (fun nat bool))) (let ((_let_4 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)))) (let ((_let_5 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)))) (let ((_let_6 (fun nat X_a))) (let ((_let_7 (fun X_a X_a))) (let ((_let_8 (fun nat _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (combs nat X_a X_a))) (let ((_let_11 (hAPP (fun real _let_7) (fun _let_0 _let_8) (combb real _let_7 nat) (scaleR_scaleR X_a)))) (let ((_let_12 (power_power X_a))) (let ((_let_13 (hAPP nat _let_1 (minus_minus nat) BOUND_VARIABLE_121835))) (or (not (real_field X_a)) (= (hAPP X_a X_a (hAPP real _let_7 (scaleR_scaleR X_a) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat _let_2 BOUND_VARIABLE_121835)))) (hAPP nat X_a (hAPP X_a _let_6 _let_12 (hAPP X_a X_a (hAPP X_a _let_7 (plus_plus X_a) BOUND_VARIABLE_121836) BOUND_VARIABLE_121837)) BOUND_VARIABLE_121835)) (hAPP _let_3 X_a (hAPP _let_6 (fun _let_3 X_a) (big_co1399186613setsum nat X_a) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 _let_10 (hAPP _let_6 _let_8 (hAPP (fun X_a _let_7) (fun _let_6 _let_8) (combb X_a _let_7 nat) (times_times X_a)) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 _let_10 (hAPP _let_0 _let_8 _let_11 (hAPP _let_0 _let_0 _let_5 (hAPP _let_1 _let_0 _let_4 _let_2)))) (hAPP X_a _let_6 _let_12 BOUND_VARIABLE_121836)))) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 _let_10 (hAPP _let_0 _let_8 _let_11 (hAPP _let_0 _let_0 _let_5 (hAPP _let_1 _let_0 _let_4 (hAPP _let_1 _let_1 (hAPP _let_1 (fun _let_1 _let_1) (combb nat nat nat) _let_2) _let_13))))) (hAPP _let_1 _let_6 (hAPP _let_6 (fun _let_1 _let_6) (combb nat X_a nat) (hAPP X_a _let_6 _let_12 BOUND_VARIABLE_121837)) _let_13)))) (hAPP nat _let_3 (hAPP nat (fun nat _let_3) (ord_atLeastAtMost nat) (zero_zero nat)) BOUND_VARIABLE_121835)))))))))))))))))) ) 22.21/22.29 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.21/22.29 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.21/22.29 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.21/22.29 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.29 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.21/22.29 ) 22.21/22.29 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_121879 $$unsorted) (BOUND_VARIABLE_121880 $$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_121880))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_121879) _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_121879) BOUND_VARIABLE_121880)) _let_2)))))) ) 22.21/22.29 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.21/22.29 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.29 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.21/22.29 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.21/22.29 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.21/22.29 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.21/22.29 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.21/22.29 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.21/22.29 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.29 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.21/22.29 ( int, y, v ) 22.21/22.29 ( int, y, w ) 22.21/22.29 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( int, sa, v ) 22.21/22.29 ( int, sa, w ) 22.21/22.29 ( int, x, v ) 22.21/22.29 ( int, x, w ) 22.21/22.29 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.29 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( int, r, v ) 22.21/22.29 ( int, r, w ) 22.21/22.29 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.21/22.29 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.21/22.29 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.21/22.29 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.21/22.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.21/22.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.21/22.29 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.21/22.29 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.29 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.30 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.30 ( 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)))))) ) 22.21/22.30 ( 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 ) 22.21/22.30 ( complex, ii, ii ) 22.21/22.30 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.21/22.30 ( 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 ) 22.21/22.30 ) 22.21/22.30 (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)))) ) 22.21/22.30 ( rat ) 22.21/22.30 ( int ) 22.21/22.30 ( (fun int int) ) 22.21/22.30 ( nat ) 22.21/22.30 ( bool ) 22.21/22.30 ( real ) 22.21/22.30 ( (fun nat real) ) 22.21/22.30 ( (fun real real) ) 22.21/22.30 ( complex ) 22.21/22.30 ( (fun int bool) ) 22.21/22.30 ( (product_prod int int) ) 22.21/22.30 ( (fun (product_prod int int) int) ) 22.21/22.30 ( (fun int (fun int bool)) ) 22.21/22.30 ( (fun nat bool) ) 22.21/22.30 ( (fun (product_prod int int) bool) ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.21/22.30 ( (fun real bool) ) 22.21/22.30 ( quickcheck_code_int ) 22.21/22.30 ( code_code_numeral ) 22.21/22.30 ( (fun int (fun int (fun int bool))) ) 22.21/22.30 ( (fun int real) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP real real (hAPP real (fun real real) (minus_minus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X)) _let_2))))) ) 22.21/22.30 ( pi ) 22.21/22.30 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.30 ( (zero_zero real) ) 22.21/22.30 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.21/22.30 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.21/22.30 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.21/22.30 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.21/22.30 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 22.21/22.30 ( skv_10 ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) pls) K_4)) ) 22.21/22.30 ( pls ) 22.21/22.30 ( min ) 22.21/22.30 ( s ) 22.21/22.30 ( s1 ) 22.21/22.30 ( m ) 22.21/22.30 ( t ) 22.21/22.30 ( v ) 22.21/22.30 ( w ) 22.21/22.30 ( y ) 22.21/22.30 ( sa ) 22.21/22.30 ( x ) 22.21/22.30 ( r ) 22.21/22.30 ( m1 ) 22.21/22.30 ( skv_14 ) 22.21/22.30 ( skv_20 ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((F $$unsorted) (L $$unsorted) (C $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP (fun real real) (fun real _let_1) (tendsto real real) F) L) (hAPP real _let_0 (at real) C)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) L))) (not (forall ((R_1 $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= C X_1) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (abs_abs real) (hAPP real real (hAPP real (fun real real) (minus_minus real) C) X_1))) R_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real F X_1)))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1)))) ))))) ) 22.21/22.30 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (= (and (= (one_one real) A_3) (= (zero_zero real) B_2)) (= (one_one complex) (hAPP real complex (hAPP real (fun real complex) complex_1 A_3) B_2))) ) 22.21/22.30 ( (one_one real), (zero_zero real) ) 22.21/22.30 ( (zero_zero real), (one_one real) ) 22.21/22.30 ( (zero_zero real), (zero_zero real) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_1))) (= (hAPP real real ln Xa) (hAPP _let_1 real (the real) (hAPP real _let_1 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 real) (fequal real)) (exp real))) Xa)))))) ) 22.21/22.30 ( (one_one real) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122081 $$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_122081) (one_one X_a)) (ti X_a BOUND_VARIABLE_122081))) ) 22.21/22.30 ( int, pls ) 22.21/22.30 ( int, min ) 22.21/22.30 ( int, s ) 22.21/22.30 ( int, s1 ) 22.21/22.30 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.30 ( int, m ) 22.21/22.30 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.30 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.30 ( int, t ) 22.21/22.30 ( int, v ) 22.21/22.30 ( int, w ) 22.21/22.30 ( int, y ) 22.21/22.30 ( int, sa ) 22.21/22.30 ( int, x ) 22.21/22.30 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.21/22.30 ( int, r ) 22.21/22.30 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.30 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.30 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.30 ( int, m1 ) 22.21/22.30 ( int, skv_13 ) 22.21/22.30 ( int, skv_14 ) 22.21/22.30 ( int, skv_19 ) 22.21/22.30 ( int, skv_20 ) 22.21/22.30 ( (fun int int), bit1 ) 22.21/22.30 ( (fun int int), bit0 ) 22.21/22.30 ( (fun int int), succ ) 22.21/22.30 ( (fun int int), pred ) 22.21/22.30 ( (fun int int), (fact_fact int) ) 22.21/22.30 ( (fun int int), zfact ) 22.21/22.30 ( nat, n ) 22.21/22.30 ( nat, tn ) 22.21/22.30 ( bool, fTrue ) 22.21/22.30 ( bool, fFalse ) 22.21/22.30 ( real, pi ) 22.21/22.30 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.30 ( 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))))) ) 22.21/22.30 ( (fun nat real), (real_1 nat) ) 22.21/22.30 ( (fun nat real), cos_coeff ) 22.21/22.30 ( (fun nat real), sin_coeff ) 22.21/22.30 ( (fun real real), sin ) 22.21/22.30 ( (fun real real), cos ) 22.21/22.30 ( (fun real real), sqrt ) 22.21/22.30 ( (fun real real), tan ) 22.21/22.30 ( (fun real real), ln ) 22.21/22.30 ( (fun real real), arctan ) 22.21/22.30 ( (fun real real), arcsin ) 22.21/22.30 ( (fun real real), arccos ) 22.21/22.30 ( (fun nat nat), suc ) 22.21/22.30 ( (fun nat nat), (fact_fact nat) ) 22.21/22.30 ( (fun nat nat), nat_size ) 22.21/22.30 ( (fun nat nat), (size_size nat) ) 22.21/22.30 ( (fun nat nat), fact ) 22.21/22.30 ( (filter nat), sequentially ) 22.21/22.30 ( (fun int (fun int rat)), fract ) 22.21/22.30 ( complex, ii ) 22.21/22.30 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( 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)) ) 22.21/22.30 ( (fun int bool), zOdd ) 22.21/22.30 ( (fun int bool), zprime ) 22.21/22.30 ( (fun int bool), zEven ) 22.21/22.30 ( (fun int bool), nat_neg ) 22.21/22.30 ( (fun int bool), nat_is_nat ) 22.21/22.30 ( (fun int bool), (even_odd_even int) ) 22.21/22.30 ( (fun int bool), twoSqu1091635170sum2sq ) 22.21/22.30 ( (fun int (fun int int)), legacy_zgcd ) 22.21/22.30 ( (fun int (fun int int)), (gcd_gcd int) ) 22.21/22.30 ( (fun int (fun int int)), inv ) 22.21/22.30 ( (fun int (fun int int)), multInv ) 22.21/22.30 ( (fun int (fun int int)), legendre ) 22.21/22.30 ( (fun int (fun int int)), standardRes ) 22.21/22.30 ( (fun int (fun int int)), nat_tsub ) 22.21/22.30 ( (fun int (fun int int)), z3div ) 22.21/22.30 ( (fun int (fun int int)), z3mod ) 22.21/22.30 ( (fun int (fun int int)), int_lcm ) 22.21/22.30 ( (fun int (fun int int)), int_gcd ) 22.21/22.30 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.21/22.30 ( (fun bool bool), fNot ) 22.21/22.30 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.21/22.30 ( (fun bool (fun bool bool)), fconj ) 22.21/22.30 ( (fun bool (fun bool bool)), fdisj ) 22.21/22.30 ( (fun bool (fun bool bool)), fimplies ) 22.21/22.30 ( (fun int (fun int bool)), quadRes ) 22.21/22.30 ( (fun int (fun int bool)), d22set ) 22.21/22.30 ( (fun int (fun int bool)), norRRset ) 22.21/22.30 ( (fun int (fun int bool)), sRStar ) 22.21/22.30 ( (fun int (fun int bool)), sr ) 22.21/22.30 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.21/22.30 ( (fun nat bool), (even_odd_even nat) ) 22.21/22.30 ( (fun nat bool), prime ) 22.21/22.30 ( (fun real complex), cis ) 22.21/22.30 ( (fun nat (fun nat bool)), coprime ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.21/22.30 ( (fun (product_prod int int) bool), frac_1 ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.21/22.30 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.21/22.30 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.21/22.30 ( (fun (fun int bool) bool), nat_nat_set ) 22.21/22.30 ( (fun nat (fun real real)), root ) 22.21/22.30 ( (fun real (fun real real)), log ) 22.21/22.30 ( (fun real (fun real real)), powr ) 22.21/22.30 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.21/22.30 ( (fun complex complex), cnj ) 22.21/22.30 ( (fun complex complex), expi ) 22.21/22.30 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.21/22.30 ( (fun nat (fun nat nat)), nat_gcd ) 22.21/22.30 ( (fun nat (fun nat nat)), nat_lcm ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.21/22.30 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.21/22.30 ( (fun int (fun (fun int bool) bool)), resSet ) 22.21/22.30 ( (fun int nat), nat_1 ) 22.21/22.30 ( (fun int nat), phi ) 22.21/22.30 ( (fun complex real), re ) 22.21/22.30 ( (fun complex real), im ) 22.21/22.30 ( (fun complex real), arg ) 22.21/22.30 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.21/22.30 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.21/22.30 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.21/22.30 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.21/22.30 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.21/22.30 ( (fun (product_prod nat nat) bool), pred_nat ) 22.21/22.30 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.21/22.30 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.21/22.30 ( (fun (fun int bool) int), (the int) ) 22.21/22.30 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.21/22.30 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.21/22.30 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.21/22.30 ( (fun real (fun real complex)), rcis ) 22.21/22.30 ( (fun real (fun real complex)), complex_1 ) 22.21/22.30 ( (fun int (fun int (fun int bool))), zcong ) 22.21/22.30 ( (fun int (fun int (fun int bool))), wset ) 22.21/22.30 ( (fun int (fun int (fun int bool))), noXRRset ) 22.21/22.30 ( (fun int (fun int (fun int bool))), bnorRset ) 22.21/22.30 ( (fun int (fun int (fun int bool))), zcongm ) 22.21/22.30 ( (fun real nat), natceiling ) 22.21/22.30 ( (fun real nat), natfloor ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.21/22.30 ( (fun int real), (real_1 int) ) 22.21/22.30 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.21/22.30 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.21/22.30 ( (fun complex nat), (size_size complex) ) 22.21/22.30 ( (fun complex nat), complex_size ) 22.21/22.30 ( (fun (fun nat rat) bool), vanishes ) 22.21/22.30 ( (fun (product_prod int int) rat), frct ) 22.21/22.30 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.21/22.30 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.21/22.30 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.21/22.30 ( (fun rat real), ratreal ) 22.21/22.30 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.21/22.30 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.21/22.30 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.21/22.30 ( (fun rat (product_prod int int)), quotient_of ) 22.21/22.30 ( (fun int (fun nat nat)), nat_aux ) 22.21/22.30 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.21/22.30 ( (fun int (list int)), quickc666637781d_zero ) 22.21/22.30 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.21/22.30 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.21/22.30 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.21/22.30 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.21/22.30 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.21/22.30 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.21/22.30 ( (fun code_code_numeral int), code_int_of ) 22.21/22.30 ) 22.21/22.30 (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)))))) ) 22.21/22.30 ( pls, min ) 22.21/22.30 ( pls, (zero_zero int) ) 22.21/22.30 ( (one_one int), (zero_zero int) ) 22.21/22.30 ( min, min ) 22.21/22.30 ( min, (zero_zero int) ) 22.21/22.30 ( s, (zero_zero int) ) 22.21/22.30 ( (hAPP nat int (hAPP 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) ) 22.21/22.30 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.21/22.30 ( t, (one_one int) ) 22.21/22.30 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.21/22.30 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.30 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.30 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.30 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.21/22.30 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.30 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.30 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.30 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.30 ( skv_4, (zero_zero int) ) 22.21/22.30 ( skv_5, (zero_zero int) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (tendsto nat real))) (let ((_let_6 (fun nat bool))) (let ((_let_7 (fun nat _let_6))) (let ((_let_8 (fun _let_6 real))) (let ((_let_9 (fun nat _let_1))) (let ((_let_10 (fun nat _let_2))) (let ((_let_11 (hAPP _let_0 _let_0 (hAPP _let_9 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_9 (hAPP (fun real _let_1) (fun _let_0 _let_9) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 A_3) (zero_zero real)) sequentially))) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_3 N_1))) )) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_3 (hAPP nat nat suc N_1))) (hAPP nat real A_3 N_1))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 (hAPP _let_7 _let_0 (hAPP _let_8 (fun _let_7 _let_0) (combb _let_6 real nat) (hAPP _let_0 _let_8 (big_co1399186613setsum nat real) _let_11)) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb nat _let_6 nat) (hAPP nat _let_7 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (hAPP _let_10 _let_10 (combc nat nat nat) (hAPP _let_2 _let_10 (hAPP _let_10 (fun _let_2 _let_10) (combb nat _let_2 nat) (plus_plus nat)) (hAPP nat _let_2 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat))))) (hAPP _let_0 real (suminf real) _let_11)) sequentially))))))))))))))) ) 22.21/22.30 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) X))))) ) 22.21/22.30 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((Va $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int (hAPP int (fun int int) (plus_plus int) Va) (hAPP int int (uminus_uminus int) V_1))))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V_1) pls)) (= (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) (hAPP int nat _let_1 Va)) (hAPP int nat _let_1 V_1)) (hAPP nat nat (hAPP nat _let_0 (hAPP bool (fun nat _let_0) (if nat) (hAPP int bool nat_neg _let_2)) (zero_zero nat)) (hAPP int nat nat_1 _let_2))))))) ) 22.21/22.30 ( (one_one int), pls ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (finite_finite T_2)) (not (finite_finite T_1)) (finite_finite (fun T_2 T_1))) ) 22.21/22.30 ( rat, real ) 22.21/22.30 ( rat, (product_prod int int) ) 22.21/22.30 ( int, rat ) 22.21/22.30 ( int, int ) 22.21/22.30 ( int, (fun int int) ) 22.21/22.30 ( int, nat ) 22.21/22.30 ( int, bool ) 22.21/22.30 ( int, real ) 22.21/22.30 ( int, (fun nat real) ) 22.21/22.30 ( int, (fun real real) ) 22.21/22.30 ( int, (fun nat nat) ) 22.21/22.30 ( int, (fun int rat) ) 22.21/22.30 ( int, (fun int bool) ) 22.21/22.30 ( int, (product_prod int int) ) 22.21/22.30 ( int, (fun (product_prod int int) int) ) 22.21/22.30 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.21/22.30 ( int, (fun nat int) ) 22.21/22.30 ( int, (fun bool bool) ) 22.21/22.30 ( int, (fun int (fun bool bool)) ) 22.21/22.30 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( int, (fun int (fun int bool)) ) 22.21/22.30 ( int, (fun nat bool) ) 22.21/22.30 ( int, (fun (product_prod int int) bool) ) 22.21/22.30 ( int, (fun int (fun (product_prod int int) bool)) ) 22.21/22.30 ( int, quickcheck_code_int ) 22.21/22.30 ( int, (fun (fun int bool) bool) ) 22.21/22.30 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.21/22.30 ( int, (product_prod int (product_prod int int)) ) 22.21/22.30 ( int, (fun int (product_prod int (product_prod int int))) ) 22.21/22.30 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 22.21/22.30 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.21/22.30 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.21/22.30 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.21/22.30 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.21/22.30 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.21/22.30 ( int, (fun nat (fun bool bool)) ) 22.21/22.30 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( int, (fun int (product_prod int int)) ) 22.21/22.30 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.21/22.30 ( int, (fun int (fun (fun int bool) bool)) ) 22.21/22.30 ( int, (fun (fun int int) (fun int bool)) ) 22.21/22.30 ( int, (list int) ) 22.21/22.30 ( int, (fun int (fun int (fun int bool))) ) 22.21/22.30 ( int, (fun int real) ) 22.21/22.30 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun int int), (fun int int) ) 22.21/22.30 ( (fun int int), (fun int bool) ) 22.21/22.30 ( (fun int int), (fun int (fun int int)) ) 22.21/22.30 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun int int), (fun int (fun int bool)) ) 22.21/22.30 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.21/22.30 ( nat, rat ) 22.21/22.30 ( nat, int ) 22.21/22.30 ( nat, (fun int int) ) 22.21/22.30 ( nat, nat ) 22.21/22.30 ( nat, bool ) 22.21/22.30 ( nat, real ) 22.21/22.30 ( nat, (fun real real) ) 22.21/22.30 ( nat, (fun nat nat) ) 22.21/22.30 ( nat, complex ) 22.21/22.30 ( nat, (product_prod int int) ) 22.21/22.30 ( nat, (fun bool bool) ) 22.21/22.30 ( nat, (fun nat bool) ) 22.21/22.30 ( nat, (fun nat (fun nat bool)) ) 22.21/22.30 ( nat, (fun nat (product_prod int int)) ) 22.21/22.30 ( nat, (product_prod real real) ) 22.21/22.30 ( nat, (product_prod nat nat) ) 22.21/22.30 ( nat, (fun (product_prod nat nat) bool) ) 22.21/22.30 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 22.21/22.30 ( nat, (fun nat (product_prod nat nat)) ) 22.21/22.30 ( bool, bool ) 22.21/22.30 ( bool, (fun bool bool) ) 22.21/22.30 ( real, nat ) 22.21/22.30 ( real, bool ) 22.21/22.30 ( real, real ) 22.21/22.30 ( real, (fun nat real) ) 22.21/22.30 ( real, (fun real real) ) 22.21/22.30 ( real, (fun (filter nat) bool) ) 22.21/22.30 ( real, complex ) 22.21/22.30 ( real, (fun int bool) ) 22.21/22.30 ( real, (fun bool bool) ) 22.21/22.30 ( real, (fun int (fun int bool)) ) 22.21/22.30 ( real, (fun real complex) ) 22.21/22.30 ( real, (fun real bool) ) 22.21/22.30 ( real, (fun nat (product_prod real real)) ) 22.21/22.30 ( real, (fun real (fun nat (product_prod real real))) ) 22.21/22.30 ( real, (fun (filter real) bool) ) 22.21/22.30 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 22.21/22.30 ( real, (fun int (fun int (fun bool bool))) ) 22.21/22.30 ( real, (fun int (fun nat bool)) ) 22.21/22.30 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 22.21/22.30 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( real, (fun int (fun nat (fun bool bool))) ) 22.21/22.30 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.21/22.30 ( real, (fun (fun nat real) (fun nat bool)) ) 22.21/22.30 ( real, (fun (fun int real) (fun int bool)) ) 22.21/22.30 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.21/22.30 ( (fun nat real), (fun nat real) ) 22.21/22.30 ( (fun nat real), (fun nat bool) ) 22.21/22.30 ( (fun nat real), (fun nat (fun real real)) ) 22.21/22.30 ( (fun nat real), (fun int (fun nat real)) ) 22.21/22.30 ( (fun real real), (fun real real) ) 22.21/22.30 ( (fun real real), (fun real (fun real bool)) ) 22.21/22.30 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun real real), (fun real (fun real real)) ) 22.21/22.30 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun nat nat), (fun nat real) ) 22.21/22.30 ( (fun nat nat), (fun nat (fun nat bool)) ) 22.21/22.30 ( (fun nat nat), (fun nat (fun nat nat)) ) 22.21/22.30 ( (filter nat), bool ) 22.21/22.30 ( complex, nat ) 22.21/22.30 ( complex, real ) 22.21/22.30 ( complex, complex ) 22.21/22.30 ( (fun int bool), int ) 22.21/22.30 ( (fun int bool), bool ) 22.21/22.30 ( (fun int bool), (fun int bool) ) 22.21/22.30 ( (fun int bool), (fun int (fun int int)) ) 22.21/22.30 ( (fun int bool), (fun int (fun bool bool)) ) 22.21/22.30 ( (fun int bool), (fun int (fun int bool)) ) 22.21/22.30 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 22.21/22.30 ( (fun int bool), (fun real (fun int (fun int bool))) ) 22.21/22.30 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 22.21/22.30 ( (product_prod int int), rat ) 22.21/22.30 ( (product_prod int int), int ) 22.21/22.30 ( (product_prod int int), (fun int int) ) 22.21/22.30 ( (product_prod int int), bool ) 22.21/22.30 ( (product_prod int int), (fun int bool) ) 22.21/22.30 ( (product_prod int int), (product_prod int int) ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) int) ) 22.21/22.30 ( (product_prod int int), (fun bool bool) ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.21/22.30 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 22.21/22.30 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.21/22.30 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 22.21/22.30 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 22.21/22.30 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 22.21/22.30 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 22.21/22.30 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 22.21/22.30 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (fun int (fun int bool)), (fun int bool) ) 22.21/22.30 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 22.21/22.30 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 22.21/22.30 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 22.21/22.30 ( (fun nat bool), bool ) 22.21/22.30 ( (fun nat bool), (fun nat bool) ) 22.21/22.30 ( (fun nat bool), (fun nat (fun bool bool)) ) 22.21/22.30 ( (fun nat bool), (fun int (fun nat bool)) ) 22.21/22.30 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 22.21/22.30 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 22.21/22.30 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (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)))) ) 22.21/22.30 ( (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)))) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (fun real bool), real ) 22.21/22.30 ( (fun real bool), (fun real bool) ) 22.21/22.30 ( (fun real bool), (fun real (fun bool bool)) ) 22.21/22.30 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 22.21/22.30 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 22.21/22.30 ( quickcheck_code_int, int ) 22.21/22.30 ( quickcheck_code_int, nat ) 22.21/22.30 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 22.21/22.30 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 22.21/22.30 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 22.21/22.30 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 22.21/22.30 ( code_code_numeral, int ) 22.21/22.30 ( code_code_numeral, nat ) 22.21/22.30 ( code_code_numeral, (fun nat nat) ) 22.21/22.30 ( code_code_numeral, code_code_numeral ) 22.21/22.30 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 22.21/22.30 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.21/22.30 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.21/22.30 ( (product_prod real real), bool ) 22.21/22.30 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 22.21/22.30 ( (filter real), bool ) 22.21/22.30 ( (product_prod nat nat), bool ) 22.21/22.30 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 22.21/22.30 ( (fun nat rat), bool ) 22.21/22.30 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 22.21/22.30 ( (fun int real), (fun int bool) ) 22.21/22.30 ( (fun int real), (fun int real) ) 22.21/22.30 ( (fun int real), (fun int (fun real real)) ) 22.21/22.30 ( (fun int real), (fun int (fun int real)) ) 22.21/22.30 ( (fun real (fun int bool)), (fun real bool) ) 22.21/22.30 ( (fun int (fun nat bool)), (fun int bool) ) 22.21/22.30 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 22.21/22.30 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 22.21/22.30 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 22.21/22.30 ( (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))) ) 22.21/22.30 ( (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)))) ) 22.21/22.30 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.21/22.30 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 22.21/22.30 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 22.21/22.30 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.21/22.30 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 22.21/22.30 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 22.21/22.30 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.21/22.30 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 22.21/22.30 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 22.21/22.30 ( (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)))) ) 22.21/22.30 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.21/22.30 ( (fun int (fun int real)), (fun int (fun int bool)) ) 22.21/22.30 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 22.21/22.30 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) X))) (= _let_0 (hAPP real real (abs_abs real) _let_0))) ) 22.21/22.30 ( (zero_zero nat) ) 22.21/22.30 ( (one_one nat) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (fun int int))) (or (not (= (hAPP int int (hAPP int _let_0 (minus_minus int) A_1) B) (ti int C_1))) (= (ti int A_1) (hAPP int int (hAPP int _let_0 (plus_plus int) C_1) B)))) ) 22.21/22.30 ( (hAPP nat int (hAPP 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), t ) 22.21/22.30 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), s1 ) 22.21/22.30 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.21/22.30 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), sa ) 22.21/22.30 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), pls ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v), v ) 22.21/22.30 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), r ) 22.21/22.30 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), min ) 22.21/22.30 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), m ) 22.21/22.30 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), s ) 22.21/22.30 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), m1 ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun X_a X_b))) (or (not (forall ((X_1 $$unsorted)) (= (hAPP X_a X_b F X_1) (hAPP X_a X_b G X_1)) )) (= (ti _let_0 G) (ti _let_0 F)))) ) 22.21/22.30 ( rat, real, ratreal, ratreal ) 22.21/22.30 ( rat, (product_prod int int), quotient_of, quotient_of ) 22.21/22.30 ( int, int, bit1, (fact_fact int) ) 22.21/22.30 ( int, int, bit0, bit1 ) 22.21/22.30 ( int, int, bit0, bit0 ) 22.21/22.30 ( int, int, bit0, (fact_fact int) ) 22.21/22.30 ( int, int, succ, succ ) 22.21/22.30 ( int, int, succ, pred ) 22.21/22.30 ( int, int, succ, zfact ) 22.21/22.30 ( int, int, pred, zfact ) 22.21/22.30 ( int, int, (fact_fact int), bit0 ) 22.21/22.30 ( int, int, zfact, succ ) 22.21/22.30 ( int, (fun int int), legacy_zgcd, legacy_zgcd ) 22.21/22.30 ( int, (fun int int), legacy_zgcd, nat_tsub ) 22.21/22.30 ( int, (fun int int), (gcd_gcd int), (gcd_gcd int) ) 22.21/22.30 ( int, (fun int int), (gcd_gcd int), multInv ) 22.21/22.30 ( int, (fun int int), (gcd_gcd int), standardRes ) 22.21/22.30 ( int, (fun int int), inv, int_gcd ) 22.21/22.30 ( int, (fun int int), multInv, (gcd_gcd int) ) 22.21/22.30 ( int, (fun int int), legendre, int_lcm ) 22.21/22.30 ( int, (fun int int), standardRes, multInv ) 22.21/22.30 ( int, (fun int int), nat_tsub, legacy_zgcd ) 22.21/22.30 ( int, (fun int int), z3div, inv ) 22.21/22.30 ( int, (fun int int), z3mod, legendre ) 22.21/22.30 ( int, (fun int int), int_lcm, legendre ) 22.21/22.30 ( int, (fun int int), int_lcm, z3mod ) 22.21/22.30 ( int, (fun int int), int_lcm, int_lcm ) 22.21/22.30 ( int, (fun int int), int_gcd, inv ) 22.21/22.30 ( int, (fun int int), int_gcd, z3div ) 22.21/22.30 ( int, (fun int int), int_gcd, int_gcd ) 22.21/22.30 ( int, nat, nat_1, phi ) 22.21/22.30 ( int, nat, phi, nat_1 ) 22.21/22.30 ( int, nat, phi, phi ) 22.21/22.30 ( int, bool, zOdd, zOdd ) 22.21/22.30 ( int, bool, zOdd, zprime ) 22.21/22.30 ( int, bool, zOdd, nat_is_nat ) 22.21/22.30 ( int, bool, zprime, zOdd ) 22.21/22.30 ( int, bool, zEven, nat_neg ) 22.21/22.30 ( int, bool, nat_neg, twoSqu1091635170sum2sq ) 22.21/22.30 ( int, bool, nat_is_nat, zprime ) 22.21/22.30 ( int, bool, (even_odd_even int), (even_odd_even int) ) 22.21/22.30 ( int, bool, twoSqu1091635170sum2sq, zEven ) 22.21/22.30 ( int, bool, twoSqu1091635170sum2sq, nat_neg ) 22.21/22.30 ( int, bool, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.21/22.30 ( int, real, (real_1 int), (real_1 int) ) 22.21/22.30 ( int, (fun nat nat), nat_aux, nat_aux ) 22.21/22.30 ( int, (fun int rat), fract, fract ) 22.21/22.30 ( int, (fun int bool), quadRes, sRStar ) 22.21/22.30 ( int, (fun int bool), d22set, quickc1265749348ro_rel ) 22.21/22.30 ( int, (fun int bool), norRRset, quadRes ) 22.21/22.30 ( int, (fun int bool), norRRset, norRRset ) 22.21/22.30 ( int, (fun int bool), norRRset, sRStar ) 22.21/22.30 ( int, (fun int bool), sRStar, norRRset ) 22.21/22.30 ( int, (fun int bool), sr, d22set ) 22.21/22.30 ( int, (fun int bool), sr, sr ) 22.21/22.30 ( int, (fun int bool), sr, quickc1265749348ro_rel ) 22.21/22.30 ( int, (fun int bool), quickc1265749348ro_rel, sr ) 22.21/22.30 ( int, (fun int (fun int bool)), zcong, zcong ) 22.21/22.30 ( int, (fun int (fun int bool)), zcong, noXRRset ) 22.21/22.30 ( int, (fun int (fun int bool)), wset, wset ) 22.21/22.30 ( int, (fun int (fun int bool)), wset, bnorRset ) 22.21/22.30 ( int, (fun int (fun int bool)), wset, zcongm ) 22.21/22.30 ( int, (fun int (fun int bool)), noXRRset, zcong ) 22.21/22.30 ( int, (fun int (fun int bool)), bnorRset, wset ) 22.21/22.30 ( int, (fun int (fun int bool)), zcongm, bnorRset ) 22.21/22.30 ( int, (fun (product_prod int int) bool), int_ge_less_than2, int_ge_less_than2 ) 22.21/22.30 ( int, (fun (product_prod int int) bool), int_ge_less_than2, int_ge_less_than ) 22.21/22.30 ( int, (fun (product_prod int int) bool), int_ge_less_than, int_ge_less_than2 ) 22.21/22.30 ( int, (fun int (fun (product_prod int int) bool)), divmod_int_rel, divmod_int_rel ) 22.21/22.30 ( int, quickcheck_code_int, quickcheck_of_int, quickcheck_of_int ) 22.21/22.30 ( int, (fun (fun int bool) bool), rsetR, rsetR ) 22.21/22.30 ( int, (fun (fun int bool) bool), rsetR, resSet ) 22.21/22.30 ( int, (fun (fun int bool) bool), resSet, rsetR ) 22.21/22.30 ( int, (fun int (product_prod int (product_prod int int))), xzgcd, xzgcd ) 22.21/22.30 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))), xzgcda, xzgcda ) 22.21/22.30 ( int, (fun int (product_prod int int)), divmod_int, divmod_int ) 22.21/22.30 ( int, (fun int (product_prod int int)), divmod_int, negDivAlg ) 22.21/22.30 ( int, (fun int (product_prod int int)), divmod_int, pdivmod ) 22.21/22.30 ( int, (fun int (product_prod int int)), posDivAlg, norm_frac ) 22.21/22.30 ( int, (fun int (product_prod int int)), negDivAlg, pdivmod ) 22.21/22.30 ( int, (fun int (product_prod int int)), pdivmod, divmod_int ) 22.21/22.30 ( int, (fun int (product_prod int int)), norm_frac, posDivAlg ) 22.21/22.30 ( int, (fun int (product_prod int int)), norm_frac, norm_frac ) 22.21/22.30 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), adjust, adjust ) 22.21/22.30 ( int, (fun int (fun (fun int bool) bool)), setS, setS ) 22.21/22.30 ( int, (list int), quickc666637781d_zero, quickc666637781d_zero ) 22.21/22.30 ( int, (fun int (fun int (fun int bool))), multInvPair, multInvPair ) 22.21/22.30 ( nat, nat, suc, (size_size nat) ) 22.21/22.30 ( nat, nat, (fact_fact nat), fact ) 22.21/22.30 ( nat, nat, nat_size, suc ) 22.21/22.30 ( nat, nat, nat_size, nat_size ) 22.21/22.30 ( nat, nat, nat_size, (size_size nat) ) 22.21/22.30 ( nat, nat, (size_size nat), nat_size ) 22.21/22.30 ( nat, nat, fact, (fact_fact nat) ) 22.21/22.30 ( nat, nat, fact, fact ) 22.21/22.30 ( nat, bool, (even_odd_even nat), (even_odd_even nat) ) 22.21/22.30 ( nat, bool, (even_odd_even nat), prime ) 22.21/22.30 ( nat, bool, prime, (even_odd_even nat) ) 22.21/22.30 ( nat, real, (real_1 nat), cos_coeff ) 22.21/22.30 ( nat, real, cos_coeff, sin_coeff ) 22.21/22.30 ( nat, real, sin_coeff, (real_1 nat) ) 22.21/22.30 ( nat, real, sin_coeff, cos_coeff ) 22.21/22.30 ( nat, real, sin_coeff, sin_coeff ) 22.21/22.30 ( nat, (fun real real), root, root ) 22.21/22.30 ( nat, (fun nat nat), (gcd_gcd nat), nat_lcm ) 22.21/22.30 ( nat, (fun nat nat), nat_gcd, (gcd_gcd nat) ) 22.21/22.30 ( nat, (fun nat nat), nat_gcd, nat_gcd ) 22.21/22.30 ( nat, (fun nat nat), nat_gcd, nat_lcm ) 22.21/22.30 ( nat, (fun nat nat), nat_lcm, nat_gcd ) 22.21/22.30 ( nat, (fun nat bool), coprime, coprime ) 22.21/22.30 ( nat, (fun nat (fun nat bool)), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.21/22.30 ( nat, (fun nat (product_prod int int)), bezw, bezw ) 22.21/22.30 ( nat, (fun nat (fun (product_prod nat nat) bool)), divmod_nat_rel, divmod_nat_rel ) 22.21/22.30 ( nat, (fun nat (product_prod nat nat)), divmod_nat, divmod_nat ) 22.21/22.30 ( bool, bool, fNot, fNot ) 22.21/22.30 ( bool, (fun bool bool), fconj, fdisj ) 22.21/22.30 ( bool, (fun bool bool), fdisj, fconj ) 22.21/22.30 ( bool, (fun bool bool), fdisj, fdisj ) 22.21/22.30 ( bool, (fun bool bool), fdisj, fimplies ) 22.21/22.30 ( bool, (fun bool bool), fimplies, fconj ) 22.21/22.30 ( real, nat, natceiling, natceiling ) 22.21/22.30 ( real, nat, natceiling, natfloor ) 22.21/22.30 ( real, nat, natfloor, natceiling ) 22.21/22.30 ( real, real, sin, sin ) 22.21/22.30 ( real, real, sin, ln ) 22.21/22.30 ( real, real, sin, arctan ) 22.21/22.30 ( real, real, cos, tan ) 22.21/22.30 ( real, real, sqrt, arcsin ) 22.21/22.30 ( real, real, tan, cos ) 22.21/22.30 ( real, real, tan, tan ) 22.21/22.30 ( real, real, tan, arccos ) 22.21/22.30 ( real, real, ln, sin ) 22.21/22.30 ( real, real, arctan, ln ) 22.21/22.30 ( real, real, arcsin, sqrt ) 22.21/22.30 ( real, real, arcsin, arcsin ) 22.21/22.30 ( real, real, arccos, cos ) 22.21/22.30 ( real, (fun real real), log, powr ) 22.21/22.30 ( real, (fun real real), powr, log ) 22.21/22.30 ( real, (fun real real), powr, powr ) 22.21/22.30 ( real, complex, cis, cis ) 22.21/22.30 ( real, (fun real complex), rcis, rcis ) 22.21/22.30 ( real, (fun real complex), rcis, complex_1 ) 22.21/22.30 ( real, (fun real complex), complex_1, rcis ) 22.21/22.30 ( complex, nat, (size_size complex), (size_size complex) ) 22.21/22.30 ( complex, nat, (size_size complex), complex_size ) 22.21/22.30 ( complex, nat, complex_size, (size_size complex) ) 22.21/22.30 ( complex, real, re, arg ) 22.21/22.30 ( complex, real, im, re ) 22.21/22.30 ( complex, real, arg, re ) 22.21/22.30 ( complex, real, arg, im ) 22.21/22.30 ( complex, real, arg, arg ) 22.21/22.30 ( complex, complex, cnj, expi ) 22.21/22.30 ( complex, complex, expi, cnj ) 22.21/22.30 ( complex, complex, expi, expi ) 22.21/22.30 ( (fun int bool), int, (the int), (the int) ) 22.21/22.30 ( (fun int bool), bool, nat_nat_set, nat_nat_set ) 22.21/22.30 ( (fun int bool), (fun int bool), is_RRset, is_RRset ) 22.21/22.30 ( (fun int bool), (fun int (fun int int)), rRset2norRR, rRset2norRR ) 22.21/22.30 ( (product_prod int int), rat, frct, frct ) 22.21/22.30 ( (product_prod int int), int, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.21/22.30 ( (product_prod int int), bool, frac_1, frac_1 ) 22.21/22.30 ( (product_prod int int), (product_prod int int), normalize, normalize ) 22.21/22.30 ( (product_prod int int), (product_prod int int), normalize, negateSnd ) 22.21/22.30 ( (product_prod int int), (product_prod int int), negateSnd, normalize ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, upto_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, posDivAlg_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), upto_rel, norm_frac_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), posDivAlg_rel, upto_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), negDivAlg_rel, lazy_small_lazy_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), lazy_small_lazy_rel, negDivAlg_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.21/22.30 ( (product_prod int int), (fun (product_prod int int) bool), norm_frac_rel, posDivAlg_rel ) 22.21/22.30 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool, ratrel, ratrel ) 22.21/22.30 ( (fun real bool), real, (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.21/22.30 ( quickcheck_code_int, int, quickcheck_int_of, quickcheck_int_of ) 22.21/22.30 ( quickcheck_code_int, nat, quickcheck_nat_of, quickcheck_nat_of ) 22.21/22.30 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)), quickc495462417de_int, quickc495462417de_int ) 22.21/22.30 ( code_code_numeral, int, code_int_of, code_int_of ) 22.21/22.30 ( code_code_numeral, nat, code_c271388182l_size, code_c271388182l_size ) 22.21/22.30 ( code_code_numeral, nat, code_c271388182l_size, (size_size code_code_numeral) ) 22.21/22.30 ( code_code_numeral, nat, (size_size code_code_numeral), code_c271388182l_size ) 22.21/22.30 ( code_code_numeral, (fun nat nat), code_nat_of_aux, code_nat_of_aux ) 22.21/22.30 ( code_code_numeral, code_code_numeral, code_S1047413653umeral, code_S1047413653umeral ) 22.21/22.30 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)), code_d418564891umeral, code_d418564891umeral ) 22.21/22.30 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))), bolzano_bisect, bolzano_bisect ) 22.21/22.30 ( (product_prod nat nat), bool, pred_nat, pred_nat ) 22.21/22.30 ( (product_prod nat nat), (fun (product_prod nat nat) bool), nat_gcd_rel, nat_gcd_rel ) 22.21/22.30 ( (fun nat rat), bool, vanishes, vanishes ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_less, pair_leq ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_leq, pair_less ) 22.21/22.30 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool, pair_leq, pair_leq ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((I_1 $$unsorted) (N $$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)) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (hAPP nat nat suc I_1))) N))))) ) 22.21/22.30 ( (zero_zero nat), (hAPP int nat nat_1 t) ) 22.21/22.30 ) 22.21/22.30 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122263 $$unsorted) (BOUND_VARIABLE_122264 $$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_122263) BOUND_VARIABLE_122264)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_122263)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_122264))))))) ) 22.21/22.30 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.21/22.30 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.30 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.21/22.31 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.21/22.31 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.21/22.31 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.21/22.31 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.21/22.31 ( int, y, v ) 22.21/22.31 ( int, y, w ) 22.21/22.31 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( int, sa, v ) 22.21/22.31 ( int, sa, w ) 22.21/22.31 ( int, x, v ) 22.21/22.31 ( int, x, w ) 22.21/22.31 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.31 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( int, r, v ) 22.21/22.31 ( int, r, w ) 22.21/22.31 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.21/22.31 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.21/22.31 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.21/22.31 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.21/22.31 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.31 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.31 ( 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)))))) ) 22.21/22.31 ( 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 ) 22.21/22.31 ( complex, ii, ii ) 22.21/22.31 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.21/22.31 ( 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 ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122283 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (of_real X_a))) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) _let_2) (hAPP real X_a _let_2 BOUND_VARIABLE_122283)) (hAPP real _let_0 (at real) BOUND_VARIABLE_122283))))))) ) 22.21/22.31 ( complex, (hAPP int real (number_number_of real) min) ) 22.21/22.31 ( complex, pi ) 22.21/22.31 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ring_1_Ints X_a))) (or (not (ring_1 X_a)) (= _let_0 (ti (fun X_a bool) _let_0)))) ) 22.21/22.31 ( rat ) 22.21/22.31 ( int ) 22.21/22.31 ( nat ) 22.21/22.31 ( bool ) 22.21/22.31 ( real ) 22.21/22.31 ( (filter nat) ) 22.21/22.31 ( complex ) 22.21/22.31 ( (fun int bool) ) 22.21/22.31 ( (product_prod int int) ) 22.21/22.31 ( (fun nat bool) ) 22.21/22.31 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.21/22.31 ( (product_prod real real) ) 22.21/22.31 ( (filter real) ) 22.21/22.31 ( (product_prod nat nat) ) 22.21/22.31 ( (fun nat rat) ) 22.21/22.31 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_idom X_a)) (not (number_ring X_a)) (= (hAPP X_a X_a (abs_abs X_a) (hAPP int X_a (number_number_of X_a) min)) (one_one X_a))) ) 22.21/22.31 ( rat ) 22.21/22.31 ( int ) 22.21/22.31 ( nat ) 22.21/22.31 ( real ) 22.21/22.31 ( complex ) 22.21/22.31 ( quickcheck_code_int ) 22.21/22.31 ( code_code_numeral ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (number_number_of int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_2 V)) (hAPP int int _let_2 W)) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 V) W)))))) ) 22.21/22.31 ( (hAPP int int bit1 pls), pls ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$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)))) ) 22.21/22.31 ( rat ) 22.21/22.31 ( int ) 22.21/22.31 ( nat ) 22.21/22.31 ( real ) 22.21/22.31 ( complex ) 22.21/22.31 ( quickcheck_code_int ) 22.21/22.31 ( code_code_numeral ) 22.21/22.31 ) 22.21/22.31 (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))) ) 22.21/22.31 ( (one_one rat), (zero_zero rat) ) 22.21/22.31 ( (zero_zero rat), (one_one rat) ) 22.21/22.31 ( (zero_zero rat), (zero_zero rat) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP nat int _let_0 (hAPP nat nat suc M)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int _let_0 M)))) ) 22.21/22.31 ( (zero_zero nat) ) 22.21/22.31 ( (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.31 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.21/22.31 ( n ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int bit1 K_4)) (hAPP int int bit1 L_4)) (hAPP int int bit0 (hAPP int int (hAPP int _let_0 _let_1 K_4) (hAPP int int succ L_4)))))) ) 22.21/22.31 ( (one_one int), min ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122456 $$unsorted) (BOUND_VARIABLE_122457 $$unsorted) (BOUND_VARIABLE_122458 $$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_122458))) (let ((_let_4 (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_122457)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122457) (zero_zero X_a))))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_3) BOUND_VARIABLE_122457))) (or (not (linord1117847801e_zero X_a)) (not (number 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_122456) BOUND_VARIABLE_122457)) _let_3)) (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_122456))) (or _let_5 (hBOOL (hAPP X_a bool _let_2 _let_3))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122456) _let_6))))))))))))) ) 22.21/22.31 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( int, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 22.21/22.31 ( 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)) ) 22.21/22.31 ( real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.31 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.31 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122502 $$unsorted) (BOUND_VARIABLE_122503 $$unsorted)) (or (not (group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_122502) (ti X_a BOUND_VARIABLE_122503)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_122502) BOUND_VARIABLE_122503)))) ) 22.21/22.31 ( 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) ) 22.21/22.31 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.31 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.31 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.31 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.31 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.31 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.31 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.21/22.31 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.21/22.31 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_mod nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc (hAPP nat nat suc M))) _let_1) (hAPP nat nat (hAPP nat _let_0 _let_2 M) _let_1))))) ) 22.21/22.31 ( (zero_zero nat) ) 22.21/22.31 ( (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP int bool _let_0 Y))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat nat_1 X)) (hAPP int nat nat_1 Y))))) ) 22.21/22.31 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.21/22.31 ( 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))) ) 22.21/22.31 ( v, y ) 22.21/22.31 ( v, sa ) 22.21/22.31 ( v, x ) 22.21/22.31 ( v, r ) 22.21/22.31 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.31 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.31 ( w, y ) 22.21/22.31 ( w, sa ) 22.21/22.31 ( w, x ) 22.21/22.31 ( w, r ) 22.21/22.31 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.31 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.31 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.21/22.31 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.31 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( skv_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))) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Wa) Z)) (not (forall ((N_1 $$unsorted)) (not (= (ti int Z) (hAPP int int (hAPP int (fun int int) (plus_plus int) Wa) (hAPP nat int (semiring_1_of_nat int) N_1)))) ))) ) 22.21/22.31 ( (one_one int), t ) 22.21/22.31 ( min, pls ) 22.21/22.31 ( min, min ) 22.21/22.31 ( (zero_zero int), pls ) 22.21/22.31 ( (zero_zero int), (one_one int) ) 22.21/22.31 ( (zero_zero int), min ) 22.21/22.31 ( (zero_zero int), s ) 22.21/22.31 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (zero_zero int), skv_4 ) 22.21/22.31 ( (zero_zero int), skv_5 ) 22.21/22.31 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 bool))) (or (= _let_0 (ti int B)) (hBOOL (hAPP _let_1 bool (hAPP int _let_2 (hAPP int (fun int _let_2) divmod_int_rel _let_0) B) (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) _let_0))))))) ) 22.21/22.31 ( min ) 22.21/22.31 ( s ) 22.21/22.31 ( s1 ) 22.21/22.31 ( m ) 22.21/22.31 ( t ) 22.21/22.31 ( v ) 22.21/22.31 ( w ) 22.21/22.31 ( y ) 22.21/22.31 ( sa ) 22.21/22.31 ( x ) 22.21/22.31 ( r ) 22.21/22.31 ( m1 ) 22.21/22.31 ( skv_14 ) 22.21/22.31 ( skv_20 ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((A_1 $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int rat))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (times_times int))) (or (= _let_2 (ti int B)) (= _let_2 (ti int D_3)) (= (hAPP int rat (hAPP int _let_1 fract (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 A_1) D_3)) (hAPP int int (hAPP int _let_0 _let_3 C_1) B))) (hAPP int int (hAPP int _let_0 _let_3 B) D_3)) (hAPP rat rat (hAPP rat (fun rat rat) (minus_minus rat) (hAPP int rat (hAPP int _let_1 fract A_1) B)) (hAPP int rat (hAPP int _let_1 fract C_1) D_3)))))))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.31 ( x, y, w, v ) 22.21/22.31 ( r, sa, w, v ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w, v ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M) N)))) ) 22.21/22.31 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (zero_zero nat), n ) 22.21/22.31 ( (zero_zero nat), tn ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122719 $$unsorted) (BOUND_VARIABLE_122720 $$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_122719) suc)) BOUND_VARIABLE_122720))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_122719) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_122720) (hAPP nat X_a BOUND_VARIABLE_122719 (zero_zero nat)))))))))) ) 22.21/22.31 ( int, (semiring_1_of_nat int), (one_one int) ) 22.21/22.31 ( nat, fact, (one_one nat) ) 22.21/22.31 ( 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) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122759 $$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 (archimedean_ceiling X_a) BOUND_VARIABLE_122759))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_122759)))) ) 22.21/22.31 ( int, pls ) 22.21/22.31 ( int, (one_one int) ) 22.21/22.31 ( int, min ) 22.21/22.31 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.31 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( nat, n ) 22.21/22.31 ( nat, tn ) 22.21/22.31 ( real, pi ) 22.21/22.31 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.31 ( real, skv_2 ) 22.21/22.31 ( real, skv_9 ) 22.21/22.31 ( real, skv_12 ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (ord_less int))) (let ((_let_1 (hAPP int (fun int bool) _let_0 (zero_zero int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool _let_1 Na))) (= (hAPP (fun int bool) nat (finite_card int) (hAPP (fun int bool) (fun int bool) (collect int) (hAPP (fun int bool) (fun int bool) (hAPP _let_3 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_3 (hAPP (fun bool _let_2) (fun (fun int bool) _let_3) (combb bool _let_2 int) fconj) _let_1)) (hAPP int (fun int bool) (hAPP _let_4 _let_4 (combc int int bool) _let_0) Na)))) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 Na)) (one_one nat))))))))) ) 22.21/22.31 ( pls ) 22.21/22.31 ( (one_one int) ) 22.21/22.31 ( min ) 22.21/22.31 ( (zero_zero int) ) 22.21/22.31 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.31 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.31 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( t ) 22.21/22.31 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_122832 $$unsorted) (BOUND_VARIABLE_122833 $$unsorted) (BOUND_VARIABLE_122834 $$unsorted) (BOUND_VARIABLE_122835 $$unsorted) (BOUND_VARIABLE_122836 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_122836))) (or (not (metric_space X_c)) (not (metric_space X_b)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_122834) BOUND_VARIABLE_122835) _let_2))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_122836)) (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_122832 X_1)) BOUND_VARIABLE_122833)) (hAPP X_b real (hAPP X_b (fun X_b real) (dist_dist X_b) (hAPP X_a X_b BOUND_VARIABLE_122834 X_1)) BOUND_VARIABLE_122835)))) )) (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_122832) BOUND_VARIABLE_122833) _let_2)))))) ) 22.21/22.31 ( 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)))) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122880 $$unsorted) (BOUND_VARIABLE_122881 $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_122880)) (hAPP int int (number_number_of int) BOUND_VARIABLE_122881)) (hAPP X_a int _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_122880) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_122881)))))) ) 22.21/22.31 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min ) 22.21/22.31 ( nat, (hAPP int nat nat_1 t), (hAPP int int bit1 pls) ) 22.21/22.31 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 22.21/22.31 ) 22.21/22.31 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (hBOOL (hAPP int bool nat_is_nat (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)))) ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.21/22.31 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.21/22.32 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.21/22.32 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.21/22.32 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.21/22.32 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.21/22.32 ( (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.21/22.32 ( (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.21/22.32 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.21/22.32 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong X) _let_2) M))))))) ) 22.21/22.32 ( pls, (zero_zero int) ) 22.21/22.32 ( (one_one int), (zero_zero int) ) 22.21/22.32 ( min, min ) 22.21/22.32 ( min, (zero_zero int) ) 22.21/22.32 ( (zero_zero int), min ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.32 ( t, (one_one int) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_122936 $$unsorted) (BOUND_VARIABLE_122937 $$unsorted) (BOUND_VARIABLE_122938 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (dense_linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_122937) BOUND_VARIABLE_122938))) (not (forall ((W_1 $$unsorted)) (let ((_let_1 (ord_less X_a))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_122937) W_1))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 W_1) BOUND_VARIABLE_122938))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) W_1) BOUND_VARIABLE_122936)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_122938) BOUND_VARIABLE_122936)))) ) 22.21/22.32 ( int, pls, (zero_zero int), pls ) 22.21/22.32 ( int, pls, (zero_zero int), min ) 22.21/22.32 ( int, (one_one int), min, (zero_zero int) ) 22.21/22.32 ( int, min, min, min ) 22.21/22.32 ( int, t, (zero_zero int), (one_one int) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( 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) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( real, (hAPP real real (hAPP 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, (zero_zero real) ) 22.21/22.32 ( 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) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_122979 $$unsorted) (BOUND_VARIABLE_122980 $$unsorted) (BOUND_VARIABLE_122981 $$unsorted) (BOUND_VARIABLE_122982 $$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_122980))) (or (not (t2_space X_b)) (hBOOL (hAPP (filter X_a) bool (trivial_limit X_a) BOUND_VARIABLE_122982)) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_122981) BOUND_VARIABLE_122982))) (not (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_122979) BOUND_VARIABLE_122982))) (= (ti X_b BOUND_VARIABLE_122981) (ti X_b BOUND_VARIABLE_122979))))) ) 22.21/22.32 ( nat, real, (zero_zero real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya)) zEven)))))) ) 22.21/22.32 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.21/22.32 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.21/22.32 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.21/22.32 ) 22.21/22.32 (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)))) ) 22.21/22.32 ( bool, (ord_less real), pi, (zero_zero real) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( bool, (ord_less real), (zero_zero real), pi ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( bool, (ord_less real), (zero_zero real), skv_2 ) 22.21/22.32 ( bool, (ord_less real), (zero_zero real), skv_9 ) 22.21/22.32 ( bool, (ord_less real), (zero_zero real), skv_12 ) 22.21/22.32 ( 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) ) 22.21/22.32 ( 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) ) 22.21/22.32 ( 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 ) 22.21/22.32 ( bool, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( bool, (ord_less_eq real), (zero_zero real), pi ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( bool, (ord_less_eq real), (zero_zero real), skv_10 ) 22.21/22.32 ( bool, (ord_less_eq real), (zero_zero real), skv_11 ) 22.21/22.32 ( bool, (ord_less_eq real), (zero_zero real), skv_15 ) 22.21/22.32 ( bool, (ord_less_eq real), (zero_zero real), skv_18 ) 22.21/22.32 ( 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) ) 22.21/22.32 ( bool, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( real, (inverse_divide real), pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.32 ( real, (inverse_divide real), (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( 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))))))))) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.32 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.32 ( 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)))))) ) 22.21/22.32 ( 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 ) 22.21/22.32 ( real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.21/22.32 ( complex, complex_1, (one_one real), (zero_zero real) ) 22.21/22.32 ( complex, complex_1, (zero_zero real), (one_one real) ) 22.21/22.32 ( complex, complex_1, (zero_zero real), (zero_zero real) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123017 $$unsorted) (BOUND_VARIABLE_123018 $$unsorted) (BOUND_VARIABLE_123019 $$unsorted) (BOUND_VARIABLE_123020 $$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_123017))) (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_123019)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123018) BOUND_VARIABLE_123020)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_123018)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123019) BOUND_VARIABLE_123020))))))) ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), m1 ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.21/22.32 ) 22.21/22.32 (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)))) ) 22.21/22.32 ( (zero_zero nat) ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( (one_one nat) ) 22.21/22.32 ( (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.32 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.32 ( n ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_123061 $$unsorted) (BOUND_VARIABLE_123062 $$unsorted) (BOUND_VARIABLE_123063 $$unsorted) (BOUND_VARIABLE_123064 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_123062))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool _let_0 (hAPP X_b X_a BOUND_VARIABLE_123063 BOUND_VARIABLE_123064)))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_123064) BOUND_VARIABLE_123061))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) X_1) Y_1))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_123063 X_1)) (hAPP X_b X_a BOUND_VARIABLE_123063 Y_1)))) )) (hBOOL (hAPP X_a bool _let_0 (hAPP X_b X_a BOUND_VARIABLE_123063 BOUND_VARIABLE_123061))))) ) 22.21/22.32 ( int, int, pls, (one_one int), (number_number_of int), min ) 22.21/22.32 ( int, int, pls, m1, pred, pls ) 22.21/22.32 ( int, int, (one_one int), (zero_zero int), bit1, pls ) 22.21/22.32 ( int, int, min, min, (uminus_uminus int), min ) 22.21/22.32 ( int, int, min, s, succ, pls ) 22.21/22.32 ( int, int, s, skv_4, (uminus_uminus int), pls ) 22.21/22.32 ( int, int, t, 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) ) 22.21/22.32 ( int, int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (number_number_of int), pls ) 22.21/22.32 ( int, int, skv_4, skv_5, (fact_fact int), (zero_zero int) ) 22.21/22.32 ( nat, int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat), nat_1, (zero_zero int) ) 22.21/22.32 ( real, real, pi, pi, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( 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))))), arctan, (zero_zero real) ) 22.21/22.32 ( real, real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.32 ( 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)))), (one_one real), tan, (zero_zero real) ) 22.21/22.32 ( 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 (hAPP 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, (zero_zero real) ) 22.21/22.32 ( real, real, skv_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)), cos, (zero_zero real) ) 22.21/22.32 ( real, real, skv_11, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sqrt, (zero_zero real) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123094 $$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_123094))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_123094)))) ) 22.21/22.32 ( int, t ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123139 $$unsorted) (BOUND_VARIABLE_123140 $$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_123139)) (hAPP X_a int _let_0 BOUND_VARIABLE_123140)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_123139) BOUND_VARIABLE_123140)))) ) 22.21/22.32 ( int, (one_one int), t ) 22.21/22.32 ( int, min, min ) 22.21/22.32 ( int, min, (zero_zero int) ) 22.21/22.32 ( int, (zero_zero int), pls ) 22.21/22.32 ( int, (zero_zero int), (one_one int) ) 22.21/22.32 ( int, (zero_zero int), min ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( 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))) ) 22.21/22.32 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.32 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.32 ( nat, (zero_zero nat), n ) 22.21/22.32 ( nat, (zero_zero nat), tn ) 22.21/22.32 ( real, pi, (zero_zero real) ) 22.21/22.32 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.32 ( real, (hAPP real real (hAPP 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))) ) 22.21/22.32 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.32 ( real, (zero_zero real), pi ) 22.21/22.32 ( 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)))) ) 22.21/22.32 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.32 ( real, (zero_zero real), skv_2 ) 22.21/22.32 ( real, (zero_zero real), skv_9 ) 22.21/22.32 ( real, (zero_zero real), skv_12 ) 22.21/22.32 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.21/22.32 ( 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) ) 22.21/22.32 ( 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 ) 22.21/22.32 ) 22.21/22.32 (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)))) ) 22.21/22.32 ( rat ) 22.21/22.32 ( int ) 22.21/22.32 ( (fun int int) ) 22.21/22.32 ( nat ) 22.21/22.32 ( bool ) 22.21/22.32 ( real ) 22.21/22.32 ( (fun nat real) ) 22.21/22.32 ( (fun real real) ) 22.21/22.32 ( complex ) 22.21/22.32 ( (fun int bool) ) 22.21/22.32 ( (product_prod int int) ) 22.21/22.32 ( (fun (product_prod int int) int) ) 22.21/22.32 ( (fun int (fun int bool)) ) 22.21/22.32 ( (fun nat bool) ) 22.21/22.32 ( (fun (product_prod int int) bool) ) 22.21/22.32 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.21/22.32 ( (fun real bool) ) 22.21/22.32 ( quickcheck_code_int ) 22.21/22.32 ( code_code_numeral ) 22.21/22.32 ( (fun int (fun int (fun int bool))) ) 22.21/22.32 ( (fun int real) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((F $$unsorted)) (let ((_let_0 (fun nat real))) (or (not (hBOOL (hAPP _let_0 bool (summable real) F))) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real F N_1))) )) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP _let_0 real (suminf real) F))))) ) 22.21/22.32 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (and (= (hAPP complex real re Xa) (hAPP complex real re Ya)) (= (hAPP complex real im Ya) (hAPP complex real im Xa))) (= Xa Ya)) ) 22.21/22.32 ( (zero_zero complex), ii ) 22.21/22.32 ( (zero_zero complex), (one_one complex) ) 22.21/22.32 ( ii, (one_one complex) ) 22.21/22.32 ( (one_one complex), (zero_zero complex) ) 22.21/22.32 ( (one_one complex), (one_one complex) ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((I_1 $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I_1) (zero_zero int))) (= (ti int I_1) (hAPP int int (abs_abs int) I_1))) ) 22.21/22.32 ( pls ) 22.21/22.32 ( (one_one int) ) 22.21/22.32 ( min ) 22.21/22.32 ( (zero_zero int) ) 22.21/22.32 ( s ) 22.21/22.32 ( s1 ) 22.21/22.32 ( m ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( t ) 22.21/22.32 ( v ) 22.21/22.32 ( w ) 22.21/22.32 ( y ) 22.21/22.32 ( sa ) 22.21/22.32 ( x ) 22.21/22.32 ( r ) 22.21/22.32 ( m1 ) 22.21/22.32 ( skv_4 ) 22.21/22.32 ( skv_5 ) 22.21/22.32 ( skv_14 ) 22.21/22.32 ( skv_20 ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((I_1 $$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))) ) 22.21/22.32 ( pls ) 22.21/22.32 ( (one_one int) ) 22.21/22.32 ( min ) 22.21/22.32 ( (zero_zero int) ) 22.21/22.32 ( s ) 22.21/22.32 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( t ) 22.21/22.32 ( v ) 22.21/22.32 ( w ) 22.21/22.32 ( m1 ) 22.21/22.32 ( skv_4 ) 22.21/22.32 ( skv_5 ) 22.21/22.32 ( skv_14 ) 22.21/22.32 ( skv_20 ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123271 $$unsorted) (BOUND_VARIABLE_123272 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_123271) (ti X_a BOUND_VARIABLE_123272)) (= (ti X_a BOUND_VARIABLE_123271) (hAPP X_a X_a _let_0 BOUND_VARIABLE_123272))))) ) 22.21/22.32 ( int, pls, r ) 22.21/22.32 ( int, (one_one int), v ) 22.21/22.32 ( int, min, s1 ) 22.21/22.32 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.21/22.32 ( complex, (one_one complex), ii ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123302 $$unsorted) (BOUND_VARIABLE_123303 $$unsorted) (BOUND_VARIABLE_123304 $$unsorted) (BOUND_VARIABLE_123305 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123302) BOUND_VARIABLE_123304)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123303) BOUND_VARIABLE_123305))) (let ((_let_6 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_123304))) (or (not (real_normed_algebra 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_3 (hAPP X_a X_a _let_4 _let_5)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_123305))) (hAPP X_a X_a _let_6 _let_5)) (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_123302) BOUND_VARIABLE_123303)) (hAPP X_a X_a _let_6 BOUND_VARIABLE_123305))))))))))) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.32 ( int, x, w, y, v ) 22.21/22.32 ( int, r, w, sa, v ) 22.21/22.32 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123335 $$unsorted) (BOUND_VARIABLE_123336 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_123335))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_123336))) (or (not (ab_sem1668676832m_mult X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))))) ) 22.21/22.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.21/22.32 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.21/22.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.21/22.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.21/22.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.21/22.32 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.21/22.32 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.21/22.32 ( int, y, v ) 22.21/22.32 ( int, y, w ) 22.21/22.32 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( int, sa, v ) 22.21/22.32 ( int, sa, w ) 22.21/22.32 ( int, x, v ) 22.21/22.32 ( int, x, w ) 22.21/22.32 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.32 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( int, r, v ) 22.21/22.32 ( int, r, w ) 22.21/22.32 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.21/22.32 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.21/22.32 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.21/22.32 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.21/22.32 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.21/22.32 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.32 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.32 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.32 ( 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)))))) ) 22.21/22.32 ( 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 ) 22.21/22.32 ( complex, ii, ii ) 22.21/22.32 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.21/22.32 ( 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 ) 22.21/22.32 ) 22.21/22.32 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (= (or (not (forall ((J_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) J_1) Na))) (not (= Ma (hAPP nat nat suc J_1)))) )) (= (zero_zero nat) Ma)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) (hAPP nat nat suc Na)))) ) 22.21/22.32 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.32 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123361 $$unsorted) (BOUND_VARIABLE_123362 $$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_123361) BOUND_VARIABLE_123362)) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123361) BOUND_VARIABLE_123362)))))) ) 22.21/22.33 ( int, (one_one int), t ) 22.21/22.33 ( int, min, pls ) 22.21/22.33 ( int, min, min ) 22.21/22.33 ( int, (zero_zero int), pls ) 22.21/22.33 ( int, (zero_zero int), (one_one int) ) 22.21/22.33 ( int, (zero_zero int), min ) 22.21/22.33 ( int, (zero_zero int), s ) 22.21/22.33 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ( int, (zero_zero int), skv_4 ) 22.21/22.33 ( int, (zero_zero int), skv_5 ) 22.21/22.33 ( 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) ) 22.21/22.33 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.33 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.33 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.33 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.21/22.33 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.33 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.33 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.21/22.33 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.33 ( real, (hAPP real real (hAPP 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))) ) 22.21/22.33 ( real, (zero_zero real), pi ) 22.21/22.33 ( 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)))) ) 22.21/22.33 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( real, (zero_zero real), skv_10 ) 22.21/22.33 ( real, (zero_zero real), skv_11 ) 22.21/22.33 ( real, (zero_zero real), skv_15 ) 22.21/22.33 ( real, (zero_zero real), skv_18 ) 22.21/22.33 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.21/22.33 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.21/22.33 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (= (= (ti int B_2) (ti int A_3)) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_3) B_2) (zero_zero int))))) ) 22.21/22.33 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 22.21/22.33 ( s1, s ) 22.21/22.33 ( s1, skv_4 ) 22.21/22.33 ( s1, skv_5 ) 22.21/22.33 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 22.21/22.33 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (hAPP int int (fact_fact int) X)))) ) 22.21/22.33 ( (one_one int) ) 22.21/22.33 ( (zero_zero int) ) 22.21/22.33 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (uminus_uminus real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (zero_zero real)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 pi)) X))) (= (hAPP real real _let_2 X) (hAPP real real arccos (hAPP real real cos X))))))) ) 22.21/22.33 ( pi ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (one_one real) ) 22.21/22.33 ( (zero_zero real) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.21/22.33 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 22.21/22.33 ( skv_10 ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123490 $$unsorted) (BOUND_VARIABLE_123491 $$unsorted) (BOUND_VARIABLE_123502 $$unsorted) (BOUND_VARIABLE_123503 $$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 (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_123491))) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_123490) BOUND_VARIABLE_123491) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_123490)) BOUND_VARIABLE_123491))) (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_123503)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_123502)) BOUND_VARIABLE_123503) (hAPP X_a X_a _let_3 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_123502) BOUND_VARIABLE_123503)))))))))) ) 22.21/22.33 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one int), (one_one nat) ) 22.21/22.33 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), min, (zero_zero nat) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((N $$unsorted)) (= N (hAPP real nat natceiling (hAPP nat real (real_1 nat) N))) ) 22.21/22.33 ( (zero_zero nat) ) 22.21/22.33 ( (one_one nat) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_3 (ord_less_eq real) _let_2) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_3 (ord_less real) Xa) (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) Xa)) _let_2) sequentially))))))) ) 22.21/22.33 ( (hAPP int real (number_number_of real) min) ) 22.21/22.33 ( pi ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (one_one real) ) 22.21/22.33 ( (zero_zero real) ) 22.21/22.33 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (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))))) ) 22.21/22.33 ( (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)))) ) 22.21/22.33 ( (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)) ) 22.21/22.33 ( skv_10 ) 22.21/22.33 ( skv_11 ) 22.21/22.33 ( skv_15 ) 22.21/22.33 ( skv_18 ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123562 $$unsorted) (BOUND_VARIABLE_123563 $$unsorted) (BOUND_VARIABLE_123564 $$unsorted) (BOUND_VARIABLE_123565 $$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_123565)) (= _let_3 (ti X_a BOUND_VARIABLE_123564)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123562) BOUND_VARIABLE_123564) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_123563) BOUND_VARIABLE_123565)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_123563) BOUND_VARIABLE_123564) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_123562) BOUND_VARIABLE_123565)))))))) ) 22.21/22.33 ( 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)))), s1, s1 ) 22.21/22.33 ( 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 ) 22.21/22.33 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1, m1 ) 22.21/22.33 ( 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))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), m1, m1 ) 22.21/22.33 ( 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)))), v, v ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), pls, pls ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, pls ) 22.21/22.33 ( int, y, y, min, min ) 22.21/22.33 ( int, y, x, min, min ) 22.21/22.33 ( int, sa, sa, r, r ) 22.21/22.33 ( int, sa, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), r, r ) 22.21/22.33 ( int, x, y, s, s ) 22.21/22.33 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), sa, m, m ) 22.21/22.33 ( int, r, r, t, t ) 22.21/22.33 ( int, r, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), t, t ) 22.21/22.33 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), r, y, y ) 22.21/22.33 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), sa, sa ) 22.21/22.33 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w, w ) 22.21/22.33 ( int, skv_13, skv_13, x, x ) 22.21/22.33 ( int, skv_13, skv_19, x, x ) 22.21/22.33 ( int, skv_19, skv_13, skv_14, skv_14 ) 22.21/22.33 ( 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 ) 22.21/22.33 ( 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))))), pi, pi ) 22.21/22.33 ( complex, ii, ii, ii, ii ) 22.21/22.33 ( complex, ii, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), ii, ii ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123597 $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_123597)) (zero_zero X_a))))) ) 22.21/22.33 ( int, (zero_zero nat) ) 22.21/22.33 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( int, (one_one nat) ) 22.21/22.33 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ( int, n ) 22.21/22.33 ( real, (zero_zero nat) ) 22.21/22.33 ( real, (one_one nat) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$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 A_3) B_2))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) (zero_zero real)))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) Y_1)))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F B_2)) (hAPP real real F A_3)))))) ) 22.21/22.33 ( cos, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (ord_atLeastLessThan int))) (= (hAPP _let_1 _let_1 (hAPP _let_0 (fun _let_1 _let_1) (image int int) (hAPP int _let_0 (hAPP _let_2 _let_2 (combc int int int) (plus_plus int)) L)) (hAPP int _let_1 (hAPP int _let_3 _let_4 (zero_zero int)) (hAPP int int (hAPP int _let_0 (minus_minus int) U) L))) (hAPP int _let_1 (hAPP int _let_3 _let_4 L) U))))))) ) 22.21/22.33 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.21/22.33 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.21/22.33 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.21/22.33 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.21/22.33 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123663 $$unsorted) (BOUND_VARIABLE_123664 $$unsorted) (BOUND_VARIABLE_123665 $$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_123664) BOUND_VARIABLE_123665) sequentially))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_123663))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (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_123664 N_1)) BOUND_VARIABLE_123665)) BOUND_VARIABLE_123663))) )) )))) ) 22.21/22.33 ( real, pi, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP real real sqrt (hAPP complex real re (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) Z_1) (hAPP complex complex cnj Z_1)))) (hAPP complex real (norm_norm complex) Z_1)) ) 22.21/22.33 ( (zero_zero complex) ) 22.21/22.33 ( ii ) 22.21/22.33 ( (one_one complex) ) 22.21/22.33 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_123714 $$unsorted) (BOUND_VARIABLE_123715 $$unsorted) (BOUND_VARIABLE_123716 $$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_123714) BOUND_VARIABLE_123715) BOUND_VARIABLE_123716))) (= (zero_zero X_b) (ti X_b BOUND_VARIABLE_123715)) (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_123714)) (hAPP X_b X_b _let_4 BOUND_VARIABLE_123715)) BOUND_VARIABLE_123716)))))))) ) 22.21/22.33 ( nat, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real), sequentially ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP real bool _let_1 Y))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln X)) (hAPP real real ln Y)) (hAPP real real ln (hAPP real real (hAPP real _let_0 (inverse_divide real) X) Y)))))) ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.21/22.33 ( (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)))) ) 22.21/22.33 ( (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))) ) 22.21/22.33 ( (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)))) ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.21/22.33 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.21/22.33 ( (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) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_2 (div_div nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 X) _let_1) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc X)) _let_1)))))) ) 22.21/22.33 ( (zero_zero nat) ) 22.21/22.33 ( (one_one nat) ) 22.21/22.33 ( (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.33 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M) N))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc M)) N)))) ) 22.21/22.33 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (zero_zero nat), n ) 22.21/22.33 ( (zero_zero nat), tn ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (C $$unsorted) (P_1 $$unsorted) (BOUND_VARIABLE_123765 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 BOUND_VARIABLE_123765))) (not (= (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1) (ti X_a C))) (hBOOL (hAPP X_a bool P_1 C))) ) 22.21/22.33 ( int, pls, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( int, min, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( int, s, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 22.21/22.33 ( int, s1, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.33 ( int, m, (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))) ) 22.21/22.33 ( int, t, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 22.21/22.33 ( int, v, (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) ) 22.21/22.33 ( int, w, (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))) ) 22.21/22.33 ( int, y, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ( int, sa, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.33 ( int, x, nat_neg, (one_one int) ) 22.21/22.33 ( int, r, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 22.21/22.33 ( int, m1, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 22.21/22.33 ( int, skv_14, (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))) ) 22.21/22.33 ( int, skv_20, (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.33 ( nat, n, (even_odd_even nat), (zero_zero nat) ) 22.21/22.33 ( nat, tn, prime, (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.33 ( real, pi, (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)))) ) 22.21/22.33 ( (filter nat), sequentially, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 22.21/22.33 ( (fun int bool), zOdd, (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)) ) 22.21/22.33 ( (fun int bool), zprime, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 22.21/22.33 ( (fun nat bool), (even_odd_even nat), (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) ) 22.21/22.33 ( (fun nat bool), prime, (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_0))) (let ((_let_3 (hAPP real real cos Xa))) (or (= (zero_zero real) _let_3) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (deriv 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) (inverse_divide real)) sin)) cos)) Xa) (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)))))))))))) ) 22.21/22.33 ( pi ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (zero_zero real) ) 22.21/22.33 ( (hAPP real 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))))) ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.21/22.33 ( (hAPP real real (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))))) ) 22.21/22.33 ( (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)))) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (number_number_of int))) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 N)))) (and (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 (hAPP int int bit1 N)))) (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 (hAPP int int bit0 N)))))))) ) 22.21/22.33 ( pls ) 22.21/22.33 ( (hAPP int int bit1 pls) ) 22.21/22.33 ( min ) 22.21/22.33 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.33 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.21/22.33 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.21/22.33 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 22.21/22.33 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (real_1 nat))) (= (= Na Ma) (= (hAPP nat real _let_0 Na) (hAPP nat real _let_0 Ma)))) ) 22.21/22.33 ( (zero_zero nat), (one_one nat) ) 22.21/22.33 ( (one_one nat), (zero_zero nat) ) 22.21/22.33 ( (one_one nat), (one_one nat) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((U_1 $$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)) U_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (hAPP real (fun real real) (inverse_divide real) U_1) (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) U_1))))) ) 22.21/22.33 ( pi ) 22.21/22.33 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (one_one real) ) 22.21/22.33 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.33 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.21/22.33 ( skv_2 ) 22.21/22.33 ( skv_9 ) 22.21/22.33 ( skv_12 ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_123885 $$unsorted) (BOUND_VARIABLE_123886 $$unsorted) (BOUND_VARIABLE_123887 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (minus_minus X_b))) (let ((_let_2 (hAPP X_b _let_0 (times_times X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_123885)))) (or (not (ring X_b)) (not (number X_b)) (= (hAPP X_b X_b (hAPP X_b _let_0 _let_1 (hAPP X_b X_b _let_2 BOUND_VARIABLE_123886)) (hAPP X_b X_b _let_2 BOUND_VARIABLE_123887)) (hAPP X_b X_b _let_2 (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_123886) BOUND_VARIABLE_123887))))))) ) 22.21/22.33 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.33 ) 22.21/22.33 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_123922 $$unsorted) (BOUND_VARIABLE_123923 $$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_123922) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_123923) _let_0))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_123922))) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_123923))) (= (ti X_a BOUND_VARIABLE_123923) (ti X_a BOUND_VARIABLE_123922))))))) ) 22.21/22.33 ( int, s, s1 ) 22.21/22.33 ( int, s1, s ) 22.21/22.33 ( int, s1, s1 ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.33 ( int, v, w ) 22.21/22.33 ( int, w, v ) 22.21/22.33 ( int, w, w ) 22.21/22.33 ( int, y, y ) 22.21/22.33 ( int, y, x ) 22.21/22.33 ( int, x, y ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), skv_7 ) 22.21/22.33 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.33 ( int, skv_6, skv_6 ) 22.21/22.33 ( int, skv_6, skv_16 ) 22.21/22.34 ( int, skv_7, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.21/22.34 ( int, skv_16, skv_6 ) 22.21/22.34 ( int, skv_23, skv_24 ) 22.21/22.34 ( int, skv_24, skv_23 ) 22.21/22.34 ( int, skv_24, skv_24 ) 22.21/22.34 ( real, (hAPP int real (number_number_of real) min), (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)))) ) 22.21/22.34 ( 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) ) 22.21/22.34 ( 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)))) ) 22.21/22.34 ( complex, ii, ii ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((P_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun nat bool))) (let ((_let_4 (fun int nat))) (= (hAPP _let_3 _let_3 (collect nat) P_1) (hAPP _let_0 _let_3 (hAPP _let_4 (fun _let_0 _let_3) (image int nat) nat_1) (hAPP _let_0 _let_0 (collect int) (hAPP _let_0 _let_0 (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_eq int) (zero_zero int)))) (hAPP _let_4 _let_0 (hAPP _let_3 (fun _let_4 _let_0) (combb nat bool int) P_1) nat_1)))))))))) ) 22.21/22.34 ( prime ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_124009 $$unsorted) (BOUND_VARIABLE_124010 $$unsorted)) (let ((_let_0 (fun X_a X_b))) (or (not (uminus X_b)) (= (hAPP X_a X_b (hAPP _let_0 _let_0 (uminus_uminus _let_0) BOUND_VARIABLE_124009) BOUND_VARIABLE_124010) (hAPP X_b X_b (uminus_uminus X_b) (hAPP X_a X_b BOUND_VARIABLE_124009 BOUND_VARIABLE_124010))))) ) 22.21/22.34 ( int, int, bit1, min ) 22.21/22.34 ( int, int, bit0, pls ) 22.21/22.34 ( int, int, (fact_fact int), (zero_zero int) ) 22.21/22.34 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.21/22.34 ( real, complex, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 22.21/22.34 ( complex, real, im, ii ) 22.21/22.34 ( 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))) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) (hAPP real real (exp real) X)))))) ) 22.21/22.34 ( pi ) 22.21/22.34 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( skv_2 ) 22.21/22.34 ( skv_9 ) 22.21/22.34 ( skv_12 ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) M_2) N_1))) (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_1) S))))) )) ) (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S)))) ) 22.21/22.34 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124056 $$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) BOUND_VARIABLE_124056)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_124056)) _let_2))))))) ) 22.21/22.34 ( int, pls ) 22.21/22.34 ( int, (one_one int) ) 22.21/22.34 ( int, min ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( nat, n ) 22.21/22.34 ( nat, tn ) 22.21/22.34 ( real, pi ) 22.21/22.34 ( 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)))) ) 22.21/22.34 ( real, (one_one real) ) 22.21/22.34 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( 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) ) 22.21/22.34 ( real, skv_2 ) 22.21/22.34 ( real, skv_9 ) 22.21/22.34 ( real, skv_12 ) 22.21/22.34 ( complex, ii ) 22.21/22.34 ( complex, (one_one complex) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X)) (hBOOL (hAPP int bool _let_0 Y)) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y))))) ) 22.21/22.34 ( (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)))) ) 22.21/22.34 ( (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) ) 22.21/22.34 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.21/22.34 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.21/22.34 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.34 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.21/22.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.21/22.34 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.21/22.34 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.21/22.34 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.21/22.34 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.34 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.21/22.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted)) (or (not (number_semiring X_a)) (= (zero_zero X_a) (hAPP int X_a (number_number_of X_a) pls))) ) 22.21/22.34 ( rat ) 22.21/22.34 ( int ) 22.21/22.34 ( nat ) 22.21/22.34 ( real ) 22.21/22.34 ( complex ) 22.21/22.34 ( quickcheck_code_int ) 22.21/22.34 ( code_code_numeral ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124088 $$unsorted) (BOUND_VARIABLE_124089 $$unsorted) (BOUND_VARIABLE_124090 $$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 (times_times X_a))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124089) BOUND_VARIABLE_124090))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124088) (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 _let_3 BOUND_VARIABLE_124090) BOUND_VARIABLE_124088)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124089) BOUND_VARIABLE_124088)))))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124156 $$unsorted) (BOUND_VARIABLE_124157 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_124157)) (= (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_124157) BOUND_VARIABLE_124156)) BOUND_VARIABLE_124157) (ti X_a BOUND_VARIABLE_124156)))) ) 22.21/22.34 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.21/22.34 ( 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))) ) 22.21/22.34 ( int, v, y ) 22.21/22.34 ( int, v, sa ) 22.21/22.34 ( int, v, x ) 22.21/22.34 ( int, v, r ) 22.21/22.34 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.34 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.34 ( int, w, y ) 22.21/22.34 ( int, w, sa ) 22.21/22.34 ( int, w, x ) 22.21/22.34 ( int, w, r ) 22.21/22.34 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.34 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.34 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.21/22.34 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.34 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( int, skv_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))) ) 22.21/22.34 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( 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))))) ) 22.21/22.34 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ( 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)))) ) 22.21/22.34 ( complex, ii, ii ) 22.21/22.34 ( 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)) ) 22.21/22.34 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124242 $$unsorted) (BOUND_VARIABLE_124243 $$unsorted) (BOUND_VARIABLE_124244 $$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_124244)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_124243) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124242) BOUND_VARIABLE_124244)) (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_124242) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_124244) BOUND_VARIABLE_124243))) BOUND_VARIABLE_124244)))))) ) 22.21/22.34 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w, y ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w, sa ) 22.21/22.34 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun code_code_numeral X_a))) (let ((_let_1 (code_c600343653l_case X_a))) (= _let_1 (ti (fun X_a (fun _let_0 _let_0)) _let_1)))) ) 22.21/22.34 ( int ) 22.21/22.34 ( nat ) 22.21/22.34 ( (fun nat nat) ) 22.21/22.34 ( code_code_numeral ) 22.21/22.34 ( (product_prod code_code_numeral code_code_numeral) ) 22.21/22.34 ( (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124322 $$unsorted) (BOUND_VARIABLE_124323 $$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_124322) _let_1)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124323) _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_124322)) BOUND_VARIABLE_124323)) (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_124322) BOUND_VARIABLE_124323)) _let_1)))))))))) ) 22.21/22.34 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.21/22.34 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.21/22.34 ( 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)))), (one_one int) ) 22.21/22.34 ( 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) ) 22.21/22.34 ( int, v, w ) 22.21/22.34 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.21/22.34 ( int, x, y ) 22.21/22.34 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.21/22.34 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.21/22.34 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.21/22.34 ( int, skv_6, skv_7 ) 22.21/22.34 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, skv_23, skv_24 ) 22.21/22.34 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( nat, (one_one nat), (one_one nat) ) 22.21/22.34 ( complex, (hAPP real complex (of_real complex) pi), ii ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124346 $$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 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_124346)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124346) _let_2))))))) ) 22.21/22.34 ( real, (zero_zero real) ) 22.21/22.34 ( complex, ii ) 22.21/22.34 ) 22.21/22.34 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124368 $$unsorted) (BOUND_VARIABLE_124369 $$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_124369))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_124368))) (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_124369) BOUND_VARIABLE_124368))))) ) 22.21/22.34 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.21/22.34 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.21/22.34 ( 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))) ) 22.21/22.34 ( int, v, y ) 22.21/22.34 ( int, v, sa ) 22.21/22.34 ( int, v, x ) 22.21/22.34 ( int, v, r ) 22.21/22.34 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.35 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.35 ( int, w, y ) 22.21/22.35 ( int, w, sa ) 22.21/22.35 ( int, w, x ) 22.21/22.35 ( int, w, r ) 22.21/22.35 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.21/22.35 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.21/22.35 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.21/22.35 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.35 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.21/22.35 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.35 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, skv_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))) ) 22.21/22.35 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( complex, ii, ii ) 22.21/22.35 ( 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)) ) 22.21/22.35 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) _let_0) X))) (one_one real))))))) ) 22.21/22.35 ( pi ) 22.21/22.35 ( (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)))) ) 22.21/22.35 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.21/22.35 ( skv_2 ) 22.21/22.35 ( skv_9 ) 22.21/22.35 ( skv_12 ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((B $$unsorted) (Q_3 $$unsorted) (R_3 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (ord_less int))) (let ((_let_4 (zero_zero int))) (let ((_let_5 (times_times int))) (let ((_let_6 (ord_less_eq int))) (let ((_let_7 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_5 B_5) Q_5)) R_4))) (or (not (= _let_7 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_5 B) Q_3)) R_3))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 _let_7) _let_4))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 R_3) B))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_6 _let_4) R_4))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 _let_4) B_5))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_6 B_5) B))) (hBOOL (hAPP int bool (hAPP int _let_2 _let_6 Q_5) Q_3))))))))))) ) 22.21/22.35 ( (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) ) 22.21/22.35 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.21/22.35 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 22.21/22.35 ( x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.21/22.35 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 22.21/22.35 ( r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.21/22.35 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.21/22.35 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124528 $$unsorted)) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_124528)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_124528) BOUND_VARIABLE_124528))) ) 22.21/22.35 ( int, pls ) 22.21/22.35 ( int, min ) 22.21/22.35 ( int, s ) 22.21/22.35 ( int, s1 ) 22.21/22.35 ( int, m ) 22.21/22.35 ( int, t ) 22.21/22.35 ( int, v ) 22.21/22.35 ( int, w ) 22.21/22.35 ( int, y ) 22.21/22.35 ( int, sa ) 22.21/22.35 ( int, x ) 22.21/22.35 ( int, r ) 22.21/22.35 ( int, m1 ) 22.21/22.35 ( int, skv_14 ) 22.21/22.35 ( int, skv_20 ) 22.21/22.35 ( (fun int int), bit1 ) 22.21/22.35 ( (fun int int), bit0 ) 22.21/22.35 ( (fun int int), succ ) 22.21/22.35 ( (fun int int), pred ) 22.21/22.35 ( (fun int int), (fact_fact int) ) 22.21/22.35 ( (fun int int), zfact ) 22.21/22.35 ( nat, n ) 22.21/22.35 ( nat, tn ) 22.21/22.35 ( bool, fTrue ) 22.21/22.35 ( bool, fFalse ) 22.21/22.35 ( real, pi ) 22.21/22.35 ( (fun nat real), (real_1 nat) ) 22.21/22.35 ( (fun nat real), cos_coeff ) 22.21/22.35 ( (fun nat real), sin_coeff ) 22.21/22.35 ( (fun real real), sin ) 22.21/22.35 ( (fun real real), cos ) 22.21/22.35 ( (fun real real), sqrt ) 22.21/22.35 ( (fun real real), tan ) 22.21/22.35 ( (fun real real), ln ) 22.21/22.35 ( (fun real real), arctan ) 22.21/22.35 ( (fun real real), arcsin ) 22.21/22.35 ( (fun real real), arccos ) 22.21/22.35 ( (fun nat nat), suc ) 22.21/22.35 ( (fun nat nat), (fact_fact nat) ) 22.21/22.35 ( (fun nat nat), nat_size ) 22.21/22.35 ( (fun nat nat), (size_size nat) ) 22.21/22.35 ( (fun nat nat), fact ) 22.21/22.35 ( (filter nat), sequentially ) 22.21/22.35 ( (fun int (fun int rat)), fract ) 22.21/22.35 ( complex, ii ) 22.21/22.35 ( (fun int bool), zOdd ) 22.21/22.35 ( (fun int bool), zprime ) 22.21/22.35 ( (fun int bool), zEven ) 22.21/22.35 ( (fun int bool), nat_neg ) 22.21/22.35 ( (fun int bool), nat_is_nat ) 22.21/22.35 ( (fun int bool), (even_odd_even int) ) 22.21/22.35 ( (fun int bool), twoSqu1091635170sum2sq ) 22.21/22.35 ( (fun int (fun int int)), legacy_zgcd ) 22.21/22.35 ( (fun int (fun int int)), (gcd_gcd int) ) 22.21/22.35 ( (fun int (fun int int)), inv ) 22.21/22.35 ( (fun int (fun int int)), multInv ) 22.21/22.35 ( (fun int (fun int int)), legendre ) 22.21/22.35 ( (fun int (fun int int)), standardRes ) 22.21/22.35 ( (fun int (fun int int)), nat_tsub ) 22.21/22.35 ( (fun int (fun int int)), z3div ) 22.21/22.35 ( (fun int (fun int int)), z3mod ) 22.21/22.35 ( (fun int (fun int int)), int_lcm ) 22.21/22.35 ( (fun int (fun int int)), int_gcd ) 22.21/22.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.21/22.35 ( (fun bool bool), fNot ) 22.21/22.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.21/22.35 ( (fun bool (fun bool bool)), fconj ) 22.21/22.35 ( (fun bool (fun bool bool)), fdisj ) 22.21/22.35 ( (fun bool (fun bool bool)), fimplies ) 22.21/22.35 ( (fun int (fun int bool)), quadRes ) 22.21/22.35 ( (fun int (fun int bool)), d22set ) 22.21/22.35 ( (fun int (fun int bool)), norRRset ) 22.21/22.35 ( (fun int (fun int bool)), sRStar ) 22.21/22.35 ( (fun int (fun int bool)), sr ) 22.21/22.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.21/22.35 ( (fun nat bool), (even_odd_even nat) ) 22.21/22.35 ( (fun nat bool), prime ) 22.21/22.35 ( (fun real complex), cis ) 22.21/22.35 ( (fun nat (fun nat bool)), coprime ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.21/22.35 ( (fun (product_prod int int) bool), frac_1 ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.21/22.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.21/22.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.21/22.35 ( (fun (fun int bool) bool), nat_nat_set ) 22.21/22.35 ( (fun nat (fun real real)), root ) 22.21/22.35 ( (fun real (fun real real)), log ) 22.21/22.35 ( (fun real (fun real real)), powr ) 22.21/22.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.21/22.35 ( (fun complex complex), cnj ) 22.21/22.35 ( (fun complex complex), expi ) 22.21/22.35 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.21/22.35 ( (fun nat (fun nat nat)), nat_gcd ) 22.21/22.35 ( (fun nat (fun nat nat)), nat_lcm ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.21/22.35 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.21/22.35 ( (fun int (fun (fun int bool) bool)), resSet ) 22.21/22.35 ( (fun int nat), nat_1 ) 22.21/22.35 ( (fun int nat), phi ) 22.21/22.35 ( (fun complex real), re ) 22.21/22.35 ( (fun complex real), im ) 22.21/22.35 ( (fun complex real), arg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.21/22.35 ( (fun (product_prod nat nat) bool), pred_nat ) 22.21/22.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.21/22.35 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.21/22.35 ( (fun (fun int bool) int), (the int) ) 22.21/22.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.21/22.35 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.21/22.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.21/22.35 ( (fun real (fun real complex)), rcis ) 22.21/22.35 ( (fun real (fun real complex)), complex_1 ) 22.21/22.35 ( (fun int (fun int (fun int bool))), zcong ) 22.21/22.35 ( (fun int (fun int (fun int bool))), wset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), noXRRset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), bnorRset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), zcongm ) 22.21/22.35 ( (fun real nat), natceiling ) 22.21/22.35 ( (fun real nat), natfloor ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.21/22.35 ( (fun int real), (real_1 int) ) 22.21/22.35 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.21/22.35 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.21/22.35 ( (fun complex nat), (size_size complex) ) 22.21/22.35 ( (fun complex nat), complex_size ) 22.21/22.35 ( (fun (fun nat rat) bool), vanishes ) 22.21/22.35 ( (fun (product_prod int int) rat), frct ) 22.21/22.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.21/22.35 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.21/22.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.21/22.35 ( (fun rat real), ratreal ) 22.21/22.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.21/22.35 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.21/22.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.21/22.35 ( (fun rat (product_prod int int)), quotient_of ) 22.21/22.35 ( (fun int (fun nat nat)), nat_aux ) 22.21/22.35 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.21/22.35 ( (fun int (list int)), quickc666637781d_zero ) 22.21/22.35 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.21/22.35 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.21/22.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.21/22.35 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.21/22.35 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.21/22.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.21/22.35 ( (fun code_code_numeral int), code_int_of ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124551 $$unsorted) (BOUND_VARIABLE_124552 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (div_div X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ring_div X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_124551) BOUND_VARIABLE_124552))) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124552) BOUND_VARIABLE_124551)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_124552)) BOUND_VARIABLE_124551)))))) ) 22.21/22.35 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)) ) 22.21/22.35 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124577 $$unsorted)) (or (not (real_vector X_a)) (= (ti X_a BOUND_VARIABLE_124577) (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (one_one real)) BOUND_VARIABLE_124577))) ) 22.21/22.35 ( int, pls ) 22.21/22.35 ( int, min ) 22.21/22.35 ( int, s ) 22.21/22.35 ( int, s1 ) 22.21/22.35 ( int, m ) 22.21/22.35 ( int, t ) 22.21/22.35 ( int, v ) 22.21/22.35 ( int, w ) 22.21/22.35 ( int, y ) 22.21/22.35 ( int, sa ) 22.21/22.35 ( int, x ) 22.21/22.35 ( int, r ) 22.21/22.35 ( int, m1 ) 22.21/22.35 ( int, skv_14 ) 22.21/22.35 ( int, skv_20 ) 22.21/22.35 ( (fun int int), bit1 ) 22.21/22.35 ( (fun int int), bit0 ) 22.21/22.35 ( (fun int int), succ ) 22.21/22.35 ( (fun int int), pred ) 22.21/22.35 ( (fun int int), (fact_fact int) ) 22.21/22.35 ( (fun int int), zfact ) 22.21/22.35 ( nat, n ) 22.21/22.35 ( nat, tn ) 22.21/22.35 ( bool, fTrue ) 22.21/22.35 ( bool, fFalse ) 22.21/22.35 ( real, pi ) 22.21/22.35 ( (fun nat real), (real_1 nat) ) 22.21/22.35 ( (fun nat real), cos_coeff ) 22.21/22.35 ( (fun nat real), sin_coeff ) 22.21/22.35 ( (fun real real), sin ) 22.21/22.35 ( (fun real real), cos ) 22.21/22.35 ( (fun real real), sqrt ) 22.21/22.35 ( (fun real real), tan ) 22.21/22.35 ( (fun real real), ln ) 22.21/22.35 ( (fun real real), arctan ) 22.21/22.35 ( (fun real real), arcsin ) 22.21/22.35 ( (fun real real), arccos ) 22.21/22.35 ( (fun nat nat), suc ) 22.21/22.35 ( (fun nat nat), (fact_fact nat) ) 22.21/22.35 ( (fun nat nat), nat_size ) 22.21/22.35 ( (fun nat nat), (size_size nat) ) 22.21/22.35 ( (fun nat nat), fact ) 22.21/22.35 ( (filter nat), sequentially ) 22.21/22.35 ( (fun int (fun int rat)), fract ) 22.21/22.35 ( complex, ii ) 22.21/22.35 ( (fun int bool), zOdd ) 22.21/22.35 ( (fun int bool), zprime ) 22.21/22.35 ( (fun int bool), zEven ) 22.21/22.35 ( (fun int bool), nat_neg ) 22.21/22.35 ( (fun int bool), nat_is_nat ) 22.21/22.35 ( (fun int bool), (even_odd_even int) ) 22.21/22.35 ( (fun int bool), twoSqu1091635170sum2sq ) 22.21/22.35 ( (fun int (fun int int)), legacy_zgcd ) 22.21/22.35 ( (fun int (fun int int)), (gcd_gcd int) ) 22.21/22.35 ( (fun int (fun int int)), inv ) 22.21/22.35 ( (fun int (fun int int)), multInv ) 22.21/22.35 ( (fun int (fun int int)), legendre ) 22.21/22.35 ( (fun int (fun int int)), standardRes ) 22.21/22.35 ( (fun int (fun int int)), nat_tsub ) 22.21/22.35 ( (fun int (fun int int)), z3div ) 22.21/22.35 ( (fun int (fun int int)), z3mod ) 22.21/22.35 ( (fun int (fun int int)), int_lcm ) 22.21/22.35 ( (fun int (fun int int)), int_gcd ) 22.21/22.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.21/22.35 ( (fun bool bool), fNot ) 22.21/22.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.21/22.35 ( (fun bool (fun bool bool)), fconj ) 22.21/22.35 ( (fun bool (fun bool bool)), fdisj ) 22.21/22.35 ( (fun bool (fun bool bool)), fimplies ) 22.21/22.35 ( (fun int (fun int bool)), quadRes ) 22.21/22.35 ( (fun int (fun int bool)), d22set ) 22.21/22.35 ( (fun int (fun int bool)), norRRset ) 22.21/22.35 ( (fun int (fun int bool)), sRStar ) 22.21/22.35 ( (fun int (fun int bool)), sr ) 22.21/22.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.21/22.35 ( (fun nat bool), (even_odd_even nat) ) 22.21/22.35 ( (fun nat bool), prime ) 22.21/22.35 ( (fun real complex), cis ) 22.21/22.35 ( (fun nat (fun nat bool)), coprime ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.21/22.35 ( (fun (product_prod int int) bool), frac_1 ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.21/22.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.21/22.35 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.21/22.35 ( (fun (fun int bool) bool), nat_nat_set ) 22.21/22.35 ( (fun nat (fun real real)), root ) 22.21/22.35 ( (fun real (fun real real)), log ) 22.21/22.35 ( (fun real (fun real real)), powr ) 22.21/22.35 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.21/22.35 ( (fun complex complex), cnj ) 22.21/22.35 ( (fun complex complex), expi ) 22.21/22.35 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.21/22.35 ( (fun nat (fun nat nat)), nat_gcd ) 22.21/22.35 ( (fun nat (fun nat nat)), nat_lcm ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.21/22.35 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.21/22.35 ( (fun int (fun (fun int bool) bool)), resSet ) 22.21/22.35 ( (fun int nat), nat_1 ) 22.21/22.35 ( (fun int nat), phi ) 22.21/22.35 ( (fun complex real), re ) 22.21/22.35 ( (fun complex real), im ) 22.21/22.35 ( (fun complex real), arg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.21/22.35 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.21/22.35 ( (fun (product_prod nat nat) bool), pred_nat ) 22.21/22.35 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.21/22.35 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.21/22.35 ( (fun (fun int bool) int), (the int) ) 22.21/22.35 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.21/22.35 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.21/22.35 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.21/22.35 ( (fun real (fun real complex)), rcis ) 22.21/22.35 ( (fun real (fun real complex)), complex_1 ) 22.21/22.35 ( (fun int (fun int (fun int bool))), zcong ) 22.21/22.35 ( (fun int (fun int (fun int bool))), wset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), noXRRset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), bnorRset ) 22.21/22.35 ( (fun int (fun int (fun int bool))), zcongm ) 22.21/22.35 ( (fun real nat), natceiling ) 22.21/22.35 ( (fun real nat), natfloor ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.21/22.35 ( (fun int real), (real_1 int) ) 22.21/22.35 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.21/22.35 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.21/22.35 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.21/22.35 ( (fun complex nat), (size_size complex) ) 22.21/22.35 ( (fun complex nat), complex_size ) 22.21/22.35 ( (fun (fun nat rat) bool), vanishes ) 22.21/22.35 ( (fun (product_prod int int) rat), frct ) 22.21/22.35 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.21/22.35 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.21/22.35 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.21/22.35 ( (fun rat real), ratreal ) 22.21/22.35 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.21/22.35 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.21/22.35 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.21/22.35 ( (fun rat (product_prod int int)), quotient_of ) 22.21/22.35 ( (fun int (fun nat nat)), nat_aux ) 22.21/22.35 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.21/22.35 ( (fun int (list int)), quickc666637781d_zero ) 22.21/22.35 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.21/22.35 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.21/22.35 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.21/22.35 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.21/22.35 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.21/22.35 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.21/22.35 ( (fun code_code_numeral int), code_int_of ) 22.21/22.35 ) 22.21/22.35 (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 (ti (fun X_a X_c) B_1_1) B_2_1)) ) 22.21/22.35 ( rat, real, ratreal, (one_one rat) ) 22.21/22.35 ( rat, real, ratreal, (zero_zero rat) ) 22.21/22.35 ( rat, (product_prod int int), quotient_of, (one_one rat) ) 22.21/22.35 ( rat, (product_prod int int), quotient_of, (zero_zero rat) ) 22.21/22.35 ( int, int, bit1, pls ) 22.21/22.35 ( int, int, bit1, (hAPP int int bit1 pls) ) 22.21/22.35 ( int, int, bit1, min ) 22.21/22.35 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.35 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.21/22.35 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.21/22.35 ( 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)))))) ) 22.21/22.35 ( 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))))))) ) 22.21/22.35 ( int, int, bit0, pls ) 22.21/22.35 ( int, int, bit0, (hAPP int int bit1 pls) ) 22.21/22.35 ( int, int, bit0, min ) 22.21/22.35 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.21/22.35 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.21/22.35 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, int, succ, pls ) 22.21/22.35 ( int, int, succ, min ) 22.21/22.35 ( int, int, pred, pls ) 22.21/22.35 ( int, int, pred, min ) 22.21/22.35 ( int, int, (fact_fact int), (one_one int) ) 22.21/22.35 ( int, int, (fact_fact int), (zero_zero int) ) 22.21/22.35 ( int, (fun int int), legendre, (hAPP int int (number_number_of int) min) ) 22.21/22.35 ( int, nat, nat_1, (one_one int) ) 22.21/22.35 ( int, nat, nat_1, (zero_zero int) ) 22.21/22.35 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, nat, nat_1, t ) 22.21/22.35 ( int, nat, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.35 ( 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))) ) 22.21/22.35 ( int, bool, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, bool, nat_neg, (one_one int) ) 22.21/22.35 ( int, bool, nat_neg, (zero_zero int) ) 22.21/22.35 ( int, bool, nat_neg, (hAPP int int (number_number_of int) min) ) 22.21/22.35 ( int, bool, nat_is_nat, (one_one int) ) 22.21/22.35 ( int, bool, nat_is_nat, (zero_zero int) ) 22.21/22.35 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, bool, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.35 ( int, bool, (even_odd_even int), (one_one int) ) 22.21/22.35 ( int, bool, (even_odd_even int), (zero_zero int) ) 22.21/22.35 ( int, bool, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 22.21/22.35 ( 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))) ) 22.21/22.35 ( int, bool, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 22.21/22.35 ( int, real, (real_1 int), (one_one int) ) 22.21/22.35 ( int, real, (real_1 int), (zero_zero int) ) 22.21/22.35 ( int, (fun int rat), fract, (one_one int) ) 22.21/22.35 ( int, (fun int rat), fract, (zero_zero int) ) 22.21/22.35 ( 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))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( int, (fun int (fun int bool)), zcong, s1 ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( int, (fun int (fun int bool)), zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.35 ( int, quickcheck_code_int, quickcheck_of_int, pls ) 22.21/22.35 ( int, quickcheck_code_int, quickcheck_of_int, (hAPP int int bit1 pls) ) 22.21/22.35 ( int, quickcheck_code_int, quickcheck_of_int, (one_one int) ) 22.21/22.35 ( nat, nat, suc, (zero_zero nat) ) 22.21/22.35 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.35 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.21/22.35 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 22.21/22.35 ( nat, nat, (fact_fact nat), (one_one nat) ) 22.21/22.35 ( nat, nat, nat_size, (zero_zero nat) ) 22.21/22.35 ( nat, nat, (size_size nat), (zero_zero nat) ) 22.21/22.35 ( nat, nat, fact, (zero_zero nat) ) 22.21/22.35 ( nat, bool, (even_odd_even nat), (zero_zero nat) ) 22.21/22.35 ( nat, bool, (even_odd_even nat), (one_one nat) ) 22.21/22.35 ( nat, bool, prime, (zero_zero nat) ) 22.21/22.35 ( nat, bool, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( nat, bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 22.21/22.35 ( nat, real, (real_1 nat), (zero_zero nat) ) 22.21/22.35 ( nat, real, (real_1 nat), (one_one nat) ) 22.21/22.35 ( nat, (fun real real), root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( real, nat, natceiling, (one_one real) ) 22.21/22.35 ( real, nat, natceiling, (zero_zero real) ) 22.21/22.35 ( real, nat, natfloor, (one_one real) ) 22.21/22.35 ( real, nat, natfloor, (zero_zero real) ) 22.21/22.35 ( real, real, sin, pi ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( real, real, sin, (zero_zero real) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.21/22.35 ( real, real, cos, pi ) 22.21/22.35 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( real, real, cos, (zero_zero real) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.21/22.35 ( real, real, cos, skv_10 ) 22.21/22.35 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.21/22.35 ( real, real, sqrt, (one_one real) ) 22.21/22.35 ( real, real, sqrt, (zero_zero real) ) 22.21/22.35 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.21/22.35 ( real, real, tan, pi ) 22.21/22.35 ( real, real, tan, (zero_zero real) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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)))) ) 22.21/22.35 ( real, real, ln, (one_one real) ) 22.21/22.35 ( real, real, arctan, (one_one real) ) 22.21/22.35 ( real, real, arctan, (zero_zero real) ) 22.21/22.35 ( 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))))) ) 22.21/22.35 ( 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)))))))))) ) 22.21/22.35 ( real, complex, cis, (zero_zero real) ) 22.21/22.35 ( real, (fun real complex), complex_1, (one_one real) ) 22.21/22.35 ( real, (fun real complex), complex_1, (zero_zero real) ) 22.21/22.35 ( complex, real, re, (zero_zero complex) ) 22.21/22.35 ( complex, real, re, ii ) 22.21/22.35 ( complex, real, re, (one_one complex) ) 22.21/22.35 ( complex, real, im, (zero_zero complex) ) 22.21/22.35 ( complex, real, im, ii ) 22.21/22.35 ( complex, real, im, (one_one complex) ) 22.21/22.35 ( complex, complex, cnj, (zero_zero complex) ) 22.21/22.35 ( complex, complex, cnj, ii ) 22.21/22.35 ( complex, complex, cnj, (one_one complex) ) 22.21/22.35 ( complex, complex, expi, (zero_zero complex) ) 22.21/22.35 ( 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))) ) 22.21/22.35 ( (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))) ) 22.21/22.35 ( (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))) ) 22.21/22.35 ( quickcheck_code_int, int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 22.21/22.35 ( code_code_numeral, int, code_int_of, (zero_zero code_code_numeral) ) 22.21/22.35 ( code_code_numeral, nat, code_c271388182l_size, (zero_zero code_code_numeral) ) 22.21/22.35 ( code_code_numeral, nat, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 22.21/22.35 ) 22.21/22.35 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124647 $$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_124647)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_124647)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_124647)))))) ) 22.21/22.35 ( int, pls ) 22.21/22.35 ( int, min ) 22.21/22.35 ( int, s ) 22.21/22.35 ( int, s1 ) 22.21/22.35 ( int, m ) 22.21/22.35 ( int, t ) 22.21/22.35 ( int, v ) 22.21/22.35 ( int, w ) 22.21/22.35 ( int, y ) 22.21/22.35 ( int, sa ) 22.21/22.35 ( int, x ) 22.21/22.35 ( int, r ) 22.21/22.35 ( int, m1 ) 22.21/22.35 ( int, skv_14 ) 22.21/22.35 ( int, skv_20 ) 22.21/22.35 ( (fun int int), bit1 ) 22.21/22.35 ( (fun int int), bit0 ) 22.21/22.35 ( (fun int int), succ ) 22.21/22.35 ( (fun int int), pred ) 22.21/22.35 ( (fun int int), (fact_fact int) ) 22.21/22.35 ( (fun int int), zfact ) 22.21/22.35 ( nat, n ) 22.21/22.35 ( nat, tn ) 22.21/22.35 ( bool, fTrue ) 22.21/22.35 ( bool, fFalse ) 22.21/22.35 ( real, pi ) 22.21/22.35 ( real, (zero_zero real) ) 22.21/22.35 ( (fun nat real), (real_1 nat) ) 22.21/22.35 ( (fun nat real), cos_coeff ) 22.21/22.35 ( (fun nat real), sin_coeff ) 22.21/22.35 ( (fun real real), sin ) 22.21/22.35 ( (fun real real), cos ) 22.21/22.35 ( (fun real real), sqrt ) 22.21/22.35 ( (fun real real), tan ) 22.21/22.35 ( (fun real real), ln ) 22.21/22.35 ( (fun real real), arctan ) 22.21/22.35 ( (fun real real), arcsin ) 22.21/22.35 ( (fun real real), arccos ) 22.21/22.35 ( (fun nat nat), suc ) 22.21/22.35 ( (fun nat nat), (fact_fact nat) ) 22.21/22.35 ( (fun nat nat), nat_size ) 22.21/22.35 ( (fun nat nat), (size_size nat) ) 22.21/22.35 ( (fun nat nat), fact ) 22.21/22.35 ( (filter nat), sequentially ) 22.21/22.35 ( (fun int (fun int rat)), fract ) 22.21/22.35 ( complex, ii ) 22.21/22.35 ( (fun int bool), zOdd ) 22.21/22.35 ( (fun int bool), zprime ) 22.21/22.35 ( (fun int bool), zEven ) 22.21/22.35 ( (fun int bool), nat_neg ) 22.21/22.35 ( (fun int bool), nat_is_nat ) 22.21/22.35 ( (fun int bool), (even_odd_even int) ) 22.21/22.35 ( (fun int bool), twoSqu1091635170sum2sq ) 22.21/22.35 ( (fun int (fun int int)), legacy_zgcd ) 22.21/22.35 ( (fun int (fun int int)), (gcd_gcd int) ) 22.21/22.35 ( (fun int (fun int int)), inv ) 22.21/22.35 ( (fun int (fun int int)), multInv ) 22.21/22.35 ( (fun int (fun int int)), legendre ) 22.21/22.35 ( (fun int (fun int int)), standardRes ) 22.21/22.35 ( (fun int (fun int int)), nat_tsub ) 22.21/22.35 ( (fun int (fun int int)), z3div ) 22.21/22.35 ( (fun int (fun int int)), z3mod ) 22.21/22.35 ( (fun int (fun int int)), int_lcm ) 22.21/22.35 ( (fun int (fun int int)), int_gcd ) 22.21/22.35 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.21/22.35 ( (fun bool bool), fNot ) 22.21/22.35 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.21/22.35 ( (fun bool (fun bool bool)), fconj ) 22.21/22.35 ( (fun bool (fun bool bool)), fdisj ) 22.21/22.35 ( (fun bool (fun bool bool)), fimplies ) 22.21/22.35 ( (fun int (fun int bool)), quadRes ) 22.21/22.35 ( (fun int (fun int bool)), d22set ) 22.21/22.35 ( (fun int (fun int bool)), norRRset ) 22.21/22.35 ( (fun int (fun int bool)), sRStar ) 22.21/22.35 ( (fun int (fun int bool)), sr ) 22.21/22.35 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.21/22.35 ( (fun nat bool), (even_odd_even nat) ) 22.21/22.35 ( (fun nat bool), prime ) 22.21/22.35 ( (fun real complex), cis ) 22.21/22.35 ( (fun nat (fun nat bool)), coprime ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.21/22.35 ( (fun (product_prod int int) bool), frac_1 ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.21/22.35 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.21/22.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.21/22.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.21/22.39 ( (fun (fun int bool) bool), nat_nat_set ) 22.21/22.39 ( (fun nat (fun real real)), root ) 22.21/22.39 ( (fun real (fun real real)), log ) 22.21/22.39 ( (fun real (fun real real)), powr ) 22.21/22.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.21/22.39 ( (fun complex complex), cnj ) 22.21/22.39 ( (fun complex complex), expi ) 22.21/22.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.21/22.39 ( (fun nat (fun nat nat)), nat_gcd ) 22.21/22.39 ( (fun nat (fun nat nat)), nat_lcm ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.21/22.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.21/22.39 ( (fun int (fun (fun int bool) bool)), resSet ) 22.21/22.39 ( (fun int nat), nat_1 ) 22.21/22.39 ( (fun int nat), phi ) 22.21/22.39 ( (fun complex real), re ) 22.21/22.39 ( (fun complex real), im ) 22.21/22.39 ( (fun complex real), arg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.21/22.39 ( (fun (product_prod nat nat) bool), pred_nat ) 22.21/22.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.21/22.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.21/22.39 ( (fun (fun int bool) int), (the int) ) 22.21/22.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.21/22.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.21/22.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.21/22.39 ( (fun real (fun real complex)), rcis ) 22.21/22.39 ( (fun real (fun real complex)), complex_1 ) 22.21/22.39 ( (fun int (fun int (fun int bool))), zcong ) 22.21/22.39 ( (fun int (fun int (fun int bool))), wset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), noXRRset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), bnorRset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), zcongm ) 22.21/22.39 ( (fun real nat), natceiling ) 22.21/22.39 ( (fun real nat), natfloor ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.21/22.39 ( (fun int real), (real_1 int) ) 22.21/22.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.21/22.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.21/22.39 ( (fun complex nat), (size_size complex) ) 22.21/22.39 ( (fun complex nat), complex_size ) 22.21/22.39 ( (fun (fun nat rat) bool), vanishes ) 22.21/22.39 ( (fun (product_prod int int) rat), frct ) 22.21/22.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.21/22.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.21/22.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.21/22.39 ( (fun rat real), ratreal ) 22.21/22.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.21/22.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.21/22.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.21/22.39 ( (fun rat (product_prod int int)), quotient_of ) 22.21/22.39 ( (fun int (fun nat nat)), nat_aux ) 22.21/22.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.21/22.39 ( (fun int (list int)), quickc666637781d_zero ) 22.21/22.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.21/22.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.21/22.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.21/22.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.21/22.39 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.21/22.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.21/22.39 ( (fun code_code_numeral int), code_int_of ) 22.21/22.39 ) 22.21/22.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124677 $$unsorted) (BOUND_VARIABLE_124678 $$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 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (= _let_3 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_124677) _let_0)) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_124678) _let_0))) (and (= _let_3 (ti X_a BOUND_VARIABLE_124677)) (= _let_3 (ti X_a BOUND_VARIABLE_124678))))))))) ) 22.21/22.39 ( int, v, w ) 22.21/22.39 ( int, x, y ) 22.21/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.21/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.21/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.21/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.21/22.39 ( int, skv_6, skv_7 ) 22.21/22.39 ( int, skv_23, skv_24 ) 22.21/22.39 ) 22.21/22.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124713 $$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_124713)) _let_2))) (= _let_2 (ti X_a BOUND_VARIABLE_124713)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124713) _let_2)))))) ) 22.21/22.39 ( int, pls ) 22.21/22.39 ( int, min ) 22.21/22.39 ( int, s ) 22.21/22.39 ( int, s1 ) 22.21/22.39 ( int, m ) 22.21/22.39 ( int, t ) 22.21/22.39 ( int, v ) 22.21/22.39 ( int, w ) 22.21/22.39 ( int, y ) 22.21/22.39 ( int, sa ) 22.21/22.39 ( int, x ) 22.21/22.39 ( int, r ) 22.21/22.39 ( int, m1 ) 22.21/22.39 ( int, skv_14 ) 22.21/22.39 ( int, skv_20 ) 22.21/22.39 ( (fun int int), bit1 ) 22.21/22.39 ( (fun int int), bit0 ) 22.21/22.39 ( (fun int int), succ ) 22.21/22.39 ( (fun int int), pred ) 22.21/22.39 ( (fun int int), (fact_fact int) ) 22.21/22.39 ( (fun int int), zfact ) 22.21/22.39 ( nat, n ) 22.21/22.39 ( nat, tn ) 22.21/22.39 ( bool, fTrue ) 22.21/22.39 ( bool, fFalse ) 22.21/22.39 ( real, pi ) 22.21/22.39 ( real, (zero_zero real) ) 22.21/22.39 ( (fun nat real), (real_1 nat) ) 22.21/22.39 ( (fun nat real), cos_coeff ) 22.21/22.39 ( (fun nat real), sin_coeff ) 22.21/22.39 ( (fun real real), sin ) 22.21/22.39 ( (fun real real), cos ) 22.21/22.39 ( (fun real real), sqrt ) 22.21/22.39 ( (fun real real), tan ) 22.21/22.39 ( (fun real real), ln ) 22.21/22.39 ( (fun real real), arctan ) 22.21/22.39 ( (fun real real), arcsin ) 22.21/22.39 ( (fun real real), arccos ) 22.21/22.39 ( (fun nat nat), suc ) 22.21/22.39 ( (fun nat nat), (fact_fact nat) ) 22.21/22.39 ( (fun nat nat), nat_size ) 22.21/22.39 ( (fun nat nat), (size_size nat) ) 22.21/22.39 ( (fun nat nat), fact ) 22.21/22.39 ( (filter nat), sequentially ) 22.21/22.39 ( (fun int (fun int rat)), fract ) 22.21/22.39 ( complex, ii ) 22.21/22.39 ( (fun int bool), zOdd ) 22.21/22.39 ( (fun int bool), zprime ) 22.21/22.39 ( (fun int bool), zEven ) 22.21/22.39 ( (fun int bool), nat_neg ) 22.21/22.39 ( (fun int bool), nat_is_nat ) 22.21/22.39 ( (fun int bool), (even_odd_even int) ) 22.21/22.39 ( (fun int bool), twoSqu1091635170sum2sq ) 22.21/22.39 ( (fun int (fun int int)), legacy_zgcd ) 22.21/22.39 ( (fun int (fun int int)), (gcd_gcd int) ) 22.21/22.39 ( (fun int (fun int int)), inv ) 22.21/22.39 ( (fun int (fun int int)), multInv ) 22.21/22.39 ( (fun int (fun int int)), legendre ) 22.21/22.39 ( (fun int (fun int int)), standardRes ) 22.21/22.39 ( (fun int (fun int int)), nat_tsub ) 22.21/22.39 ( (fun int (fun int int)), z3div ) 22.21/22.39 ( (fun int (fun int int)), z3mod ) 22.21/22.39 ( (fun int (fun int int)), int_lcm ) 22.21/22.39 ( (fun int (fun int int)), int_gcd ) 22.21/22.39 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.21/22.39 ( (fun bool bool), fNot ) 22.21/22.39 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.21/22.39 ( (fun bool (fun bool bool)), fconj ) 22.21/22.39 ( (fun bool (fun bool bool)), fdisj ) 22.21/22.39 ( (fun bool (fun bool bool)), fimplies ) 22.21/22.39 ( (fun int (fun int bool)), quadRes ) 22.21/22.39 ( (fun int (fun int bool)), d22set ) 22.21/22.39 ( (fun int (fun int bool)), norRRset ) 22.21/22.39 ( (fun int (fun int bool)), sRStar ) 22.21/22.39 ( (fun int (fun int bool)), sr ) 22.21/22.39 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.21/22.39 ( (fun nat bool), (even_odd_even nat) ) 22.21/22.39 ( (fun nat bool), prime ) 22.21/22.39 ( (fun real complex), cis ) 22.21/22.39 ( (fun nat (fun nat bool)), coprime ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.21/22.39 ( (fun (product_prod int int) bool), frac_1 ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.21/22.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.21/22.39 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.21/22.39 ( (fun (fun int bool) bool), nat_nat_set ) 22.21/22.39 ( (fun nat (fun real real)), root ) 22.21/22.39 ( (fun real (fun real real)), log ) 22.21/22.39 ( (fun real (fun real real)), powr ) 22.21/22.39 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.21/22.39 ( (fun complex complex), cnj ) 22.21/22.39 ( (fun complex complex), expi ) 22.21/22.39 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.21/22.39 ( (fun nat (fun nat nat)), nat_gcd ) 22.21/22.39 ( (fun nat (fun nat nat)), nat_lcm ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.21/22.39 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.21/22.39 ( (fun int (fun (fun int bool) bool)), resSet ) 22.21/22.39 ( (fun int nat), nat_1 ) 22.21/22.39 ( (fun int nat), phi ) 22.21/22.39 ( (fun complex real), re ) 22.21/22.39 ( (fun complex real), im ) 22.21/22.39 ( (fun complex real), arg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.21/22.39 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.21/22.39 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.21/22.39 ( (fun (product_prod nat nat) bool), pred_nat ) 22.21/22.39 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.21/22.39 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.21/22.39 ( (fun (fun int bool) int), (the int) ) 22.21/22.39 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.21/22.39 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.21/22.39 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.21/22.39 ( (fun real (fun real complex)), rcis ) 22.21/22.39 ( (fun real (fun real complex)), complex_1 ) 22.21/22.39 ( (fun int (fun int (fun int bool))), zcong ) 22.21/22.39 ( (fun int (fun int (fun int bool))), wset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), noXRRset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), bnorRset ) 22.21/22.39 ( (fun int (fun int (fun int bool))), zcongm ) 22.21/22.39 ( (fun real nat), natceiling ) 22.21/22.39 ( (fun real nat), natfloor ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.21/22.39 ( (fun int real), (real_1 int) ) 22.21/22.39 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.21/22.39 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.21/22.39 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.21/22.39 ( (fun complex nat), (size_size complex) ) 22.21/22.39 ( (fun complex nat), complex_size ) 22.21/22.39 ( (fun (fun nat rat) bool), vanishes ) 22.21/22.39 ( (fun (product_prod int int) rat), frct ) 22.21/22.39 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.21/22.39 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.21/22.39 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.21/22.39 ( (fun rat real), ratreal ) 22.21/22.39 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.21/22.39 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.21/22.39 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.21/22.39 ( (fun rat (product_prod int int)), quotient_of ) 22.21/22.39 ( (fun int (fun nat nat)), nat_aux ) 22.21/22.39 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.21/22.39 ( (fun int (list int)), quickc666637781d_zero ) 22.21/22.39 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.21/22.39 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.21/22.39 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.21/22.39 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.21/22.39 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.21/22.39 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.21/22.39 ( (fun code_code_numeral int), code_int_of ) 22.21/22.39 ) 22.21/22.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124776 $$unsorted) (BOUND_VARIABLE_124777 $$unsorted) (BOUND_VARIABLE_124778 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_124776))) (or (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_124777) BOUND_VARIABLE_124778))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_124777))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_124778)))) ) 22.21/22.39 ( int, (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))) ) 22.21/22.39 ( int, min, (zero_zero int), (one_one int) ) 22.21/22.39 ( int, (zero_zero 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))) ) 22.21/22.39 ( int, s, (one_one int), t ) 22.21/22.39 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), min, (zero_zero int) ) 22.21/22.39 ( int, t, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.39 ( int, m1, min, min ) 22.21/22.39 ( int, skv_4, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.21/22.39 ( int, skv_5, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.21/22.39 ( nat, (zero_zero nat), (zero_zero nat), n ) 22.21/22.39 ( real, pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.21/22.39 ( 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 real real (hAPP 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))) ) 22.21/22.39 ( real, (one_one 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) ) 22.21/22.39 ( real, (zero_zero real), (zero_zero real), pi ) 22.21/22.39 ( real, (hAPP real real cos (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 ) 22.33/22.39 ( 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), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.39 ( 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)), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.39 ) 22.33/22.39 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124804 $$unsorted) (BOUND_VARIABLE_124805 $$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_124804) BOUND_VARIABLE_124805)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_124804)) BOUND_VARIABLE_124805)))))) ) 22.33/22.39 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.39 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124855 $$unsorted) (BOUND_VARIABLE_124856 $$unsorted)) (or (not (linorder X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_124855) BOUND_VARIABLE_124856)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_124855) BOUND_VARIABLE_124856) (ti X_a BOUND_VARIABLE_124855)))) ) 22.33/22.40 ( int, (one_one int), t ) 22.33/22.40 ( int, min, pls ) 22.33/22.40 ( int, min, min ) 22.33/22.40 ( int, (zero_zero int), pls ) 22.33/22.40 ( int, (zero_zero int), (one_one int) ) 22.33/22.40 ( int, (zero_zero int), min ) 22.33/22.40 ( int, (zero_zero int), s ) 22.33/22.40 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, (zero_zero int), skv_4 ) 22.33/22.40 ( int, (zero_zero int), skv_5 ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.33/22.40 ( 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))) ) 22.33/22.40 ( real, (zero_zero real), pi ) 22.33/22.40 ( 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)))) ) 22.33/22.40 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( real, (zero_zero real), skv_10 ) 22.33/22.40 ( real, (zero_zero real), skv_11 ) 22.33/22.40 ( real, (zero_zero real), skv_15 ) 22.33/22.40 ( real, (zero_zero real), skv_18 ) 22.33/22.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.33/22.40 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_124883 $$unsorted) (BOUND_VARIABLE_124884 $$unsorted) (BOUND_VARIABLE_124885 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_124884) BOUND_VARIABLE_124885))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_124884))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_124883))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124884) BOUND_VARIABLE_124883)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_124885) BOUND_VARIABLE_124883)))))))) ) 22.33/22.40 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (one_one real))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) (one_one nat)))) ) 22.33/22.40 ( pi ) 22.33/22.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (one_one real) ) 22.33/22.40 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( skv_10 ) 22.33/22.40 ( skv_11 ) 22.33/22.40 ( skv_15 ) 22.33/22.40 ( skv_18 ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125049 $$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_125049))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125049) _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_125049))))))) ) 22.33/22.40 ( int, pls ) 22.33/22.40 ( int, (one_one int) ) 22.33/22.40 ( int, min ) 22.33/22.40 ( int, (zero_zero int) ) 22.33/22.40 ( 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))) ) 22.33/22.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.33/22.40 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.33/22.40 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( nat, n ) 22.33/22.40 ( nat, tn ) 22.33/22.40 ( real, pi ) 22.33/22.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( 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)))) ) 22.33/22.40 ( real, (zero_zero real) ) 22.33/22.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( real, skv_2 ) 22.33/22.40 ( real, skv_9 ) 22.33/22.40 ( real, skv_10 ) 22.33/22.40 ( real, skv_12 ) 22.33/22.40 ( complex, ii ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP _let_0 nat (finite_card nat) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastLessThan nat) L) U)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) U) L))) ) 22.33/22.40 ( (one_one nat), (hAPP int nat nat_1 t) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (if X_a))) (= _let_0 (ti (fun bool (fun X_a (fun X_a X_a))) _let_0))) ) 22.33/22.40 ( int ) 22.33/22.40 ( (fun int int) ) 22.33/22.40 ( nat ) 22.33/22.40 ( bool ) 22.33/22.40 ( real ) 22.33/22.40 ( (fun nat real) ) 22.33/22.40 ( (fun real real) ) 22.33/22.40 ( complex ) 22.33/22.40 ( (fun int bool) ) 22.33/22.40 ( (product_prod int int) ) 22.33/22.40 ( (fun (product_prod int int) int) ) 22.33/22.40 ( (fun int (fun int bool)) ) 22.33/22.40 ( (fun nat bool) ) 22.33/22.40 ( (fun (product_prod int int) bool) ) 22.33/22.40 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.33/22.40 ( (fun real bool) ) 22.33/22.40 ( code_code_numeral ) 22.33/22.40 ( (fun int (fun int (fun int bool))) ) 22.33/22.40 ( (fun int real) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125163 $$unsorted) (BOUND_VARIABLE_125164 $$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_125164))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_125164) (hAPP nat nat suc BOUND_VARIABLE_125163)))))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), v ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), w ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), y ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), x ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_6 ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_7 ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_16 ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_23 ) 22.33/22.40 ( int, (hAPP nat nat suc (zero_zero nat)), skv_24 ) 22.33/22.40 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125197 $$unsorted) (BOUND_VARIABLE_125198 $$unsorted) (BOUND_VARIABLE_125199 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_125198))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_125199))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_125199) BOUND_VARIABLE_125197))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_125197))))) ) 22.33/22.40 ( int, pls, (zero_zero int), pls ) 22.33/22.40 ( int, pls, (zero_zero int), min ) 22.33/22.40 ( int, (one_one int), min, (zero_zero int) ) 22.33/22.40 ( int, min, min, min ) 22.33/22.40 ( int, t, (zero_zero int), (one_one int) ) 22.33/22.40 ( real, pi, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( real, pi, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.33/22.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, (zero_zero real) ) 22.33/22.40 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP int rat (number_number_of rat) K_4) (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))))) ) 22.33/22.40 ( pls ) 22.33/22.40 ( (hAPP int int bit1 pls) ) 22.33/22.40 ( min ) 22.33/22.40 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.33/22.40 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (hAPP nat _let_1 root Na))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) Na))) (not (hBOOL (hAPP real bool (hAPP real _let_2 (ord_less real) (zero_zero real)) Xa))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (deriv real) _let_3) Xa) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP nat real (real_1 nat) Na)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 Xa)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) (hAPP nat nat suc _let_0)))))))))))) ) 22.33/22.40 ( (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))) ) 22.33/22.40 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( (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))) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex real re (hAPP complex complex (sgn_sgn complex) Z_1)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP complex real re Z_1)) (hAPP complex real (norm_norm complex) Z_1))) ) 22.33/22.40 ( (one_one complex) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) M))) (= (hAPP nat nat suc (hAPP nat nat _let_0 N)) (hAPP nat nat _let_0 (hAPP nat nat suc N)))) ) 22.33/22.40 ( (one_one nat), (zero_zero nat) ) 22.33/22.40 ( (one_one nat), (one_one nat) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((R_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_3) (zero_zero real)))) (= (hAPP real real (uminus_uminus real) R_3) (hAPP real real (abs_abs real) R_3))) ) 22.33/22.40 ( pi ) 22.33/22.40 ( (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)))) ) 22.33/22.40 ( (one_one real) ) 22.33/22.40 ( (zero_zero real) ) 22.33/22.40 ( (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) ) 22.33/22.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (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))))) ) 22.33/22.40 ( (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)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((R_3 $$unsorted)) (or (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_3) (zero_zero real))) (= R_3 (hAPP real real (abs_abs real) R_3))) ) 22.33/22.40 ( pi ) 22.33/22.40 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (one_one real) ) 22.33/22.40 ( (zero_zero real) ) 22.33/22.40 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.33/22.40 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125352 $$unsorted) (BOUND_VARIABLE_125353 $$unsorted) (BOUND_VARIABLE_125354 $$unsorted) (BOUND_VARIABLE_125355 $$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_125352) BOUND_VARIABLE_125353) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_125354) BOUND_VARIABLE_125355))) (= (= (ti X_a BOUND_VARIABLE_125354) (ti X_a BOUND_VARIABLE_125355)) (= (ti X_a BOUND_VARIABLE_125352) (ti X_a BOUND_VARIABLE_125353)))))) ) 22.33/22.40 ( 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), (hAPP nat int (hAPP 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) ) 22.33/22.40 ( 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), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.33/22.40 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.33/22.40 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.33/22.40 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP nat int (hAPP 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) ) 22.33/22.40 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.33/22.40 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.33/22.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.33/22.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.33/22.40 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.33/22.40 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.33/22.40 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.33/22.40 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.33/22.40 ( nat, (hAPP int nat nat_1 t), (one_one nat), (hAPP int nat nat_1 t), (one_one nat) ) 22.33/22.40 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.33/22.40 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((M $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) M)) _let_1))) (or (not (hBOOL (hAPP int bool zprime _let_3))) (= _let_1 (hAPP int int (hAPP int _let_0 legendre (hAPP int int _let_2 min)) _let_3))))))) ) 22.33/22.40 ( m ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((Na $$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) Na))) (hAPP nat _let_1 (ord_atMost nat) Na)))) ) 22.33/22.40 ( (zero_zero nat) ) 22.33/22.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( (one_one nat) ) 22.33/22.40 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.33/22.40 ( n ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (finite_card X_a))) (= _let_0 (ti (fun (fun X_a bool) nat) _let_0))) ) 22.33/22.40 ( int ) 22.33/22.40 ( nat ) 22.33/22.40 ( bool ) 22.33/22.40 ( real ) 22.33/22.40 ( (filter nat) ) 22.33/22.40 ( (fun int bool) ) 22.33/22.40 ( (product_prod int int) ) 22.33/22.40 ( (fun nat bool) ) 22.33/22.40 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.33/22.40 ( (product_prod real real) ) 22.33/22.40 ( (filter real) ) 22.33/22.40 ( (product_prod nat nat) ) 22.33/22.40 ( (fun nat rat) ) 22.33/22.40 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((R_3 $$unsorted)) (= (hAPP real complex (of_real complex) R_3) (hAPP real complex (hAPP real (fun real complex) rcis R_3) (zero_zero real))) ) 22.33/22.40 ( (hAPP int real (number_number_of real) min) ) 22.33/22.40 ( pi ) 22.33/22.40 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125406 $$unsorted) (BOUND_VARIABLE_125407 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (not (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (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_125406 N_1)) BOUND_VARIABLE_125407))) R_1))) )) ))) )) (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_125406) BOUND_VARIABLE_125407) sequentially)))) ) 22.33/22.40 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP int real _let_0 X)) (hAPP int real _let_0 Y)))) ) 22.33/22.40 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.33/22.40 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.33/22.40 ( (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)))), (one_one int) ) 22.33/22.40 ( (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), (one_one int) ) 22.33/22.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.33/22.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.33/22.40 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.33/22.40 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.33/22.40 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.33/22.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ) 22.33/22.40 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125458 $$unsorted)) (or (not (monoid_mult X_a)) (= (ti X_a BOUND_VARIABLE_125458) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_125458) (one_one X_a)))) ) 22.33/22.40 ( int, pls ) 22.33/22.40 ( int, min ) 22.33/22.40 ( int, s ) 22.33/22.40 ( int, s1 ) 22.33/22.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( int, m ) 22.33/22.40 ( 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))) ) 22.33/22.40 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.40 ( int, t ) 22.33/22.40 ( int, v ) 22.33/22.40 ( int, w ) 22.33/22.40 ( int, y ) 22.33/22.40 ( int, sa ) 22.33/22.40 ( int, x ) 22.33/22.40 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.33/22.40 ( int, r ) 22.33/22.40 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.33/22.40 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.33/22.40 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( int, m1 ) 22.33/22.40 ( int, skv_13 ) 22.33/22.40 ( int, skv_14 ) 22.33/22.40 ( int, skv_19 ) 22.33/22.40 ( int, skv_20 ) 22.33/22.40 ( (fun int int), bit1 ) 22.33/22.40 ( (fun int int), bit0 ) 22.33/22.40 ( (fun int int), succ ) 22.33/22.40 ( (fun int int), pred ) 22.33/22.40 ( (fun int int), (fact_fact int) ) 22.33/22.40 ( (fun int int), zfact ) 22.33/22.40 ( nat, n ) 22.33/22.40 ( nat, tn ) 22.33/22.40 ( bool, fTrue ) 22.33/22.40 ( bool, fFalse ) 22.33/22.40 ( real, pi ) 22.33/22.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.40 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.40 ( 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))))) ) 22.33/22.41 ( (fun nat real), (real_1 nat) ) 22.33/22.41 ( (fun nat real), cos_coeff ) 22.33/22.41 ( (fun nat real), sin_coeff ) 22.33/22.41 ( (fun real real), sin ) 22.33/22.41 ( (fun real real), cos ) 22.33/22.41 ( (fun real real), sqrt ) 22.33/22.41 ( (fun real real), tan ) 22.33/22.41 ( (fun real real), ln ) 22.33/22.41 ( (fun real real), arctan ) 22.33/22.41 ( (fun real real), arcsin ) 22.33/22.41 ( (fun real real), arccos ) 22.33/22.41 ( (fun nat nat), suc ) 22.33/22.41 ( (fun nat nat), (fact_fact nat) ) 22.33/22.41 ( (fun nat nat), nat_size ) 22.33/22.41 ( (fun nat nat), (size_size nat) ) 22.33/22.41 ( (fun nat nat), fact ) 22.33/22.41 ( (filter nat), sequentially ) 22.33/22.41 ( (fun int (fun int rat)), fract ) 22.33/22.41 ( complex, ii ) 22.33/22.41 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.41 ( 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)) ) 22.33/22.41 ( (fun int bool), zOdd ) 22.33/22.41 ( (fun int bool), zprime ) 22.33/22.41 ( (fun int bool), zEven ) 22.33/22.41 ( (fun int bool), nat_neg ) 22.33/22.41 ( (fun int bool), nat_is_nat ) 22.33/22.41 ( (fun int bool), (even_odd_even int) ) 22.33/22.41 ( (fun int bool), twoSqu1091635170sum2sq ) 22.33/22.41 ( (fun int (fun int int)), legacy_zgcd ) 22.33/22.41 ( (fun int (fun int int)), (gcd_gcd int) ) 22.33/22.41 ( (fun int (fun int int)), inv ) 22.33/22.41 ( (fun int (fun int int)), multInv ) 22.33/22.41 ( (fun int (fun int int)), legendre ) 22.33/22.41 ( (fun int (fun int int)), standardRes ) 22.33/22.41 ( (fun int (fun int int)), nat_tsub ) 22.33/22.41 ( (fun int (fun int int)), z3div ) 22.33/22.41 ( (fun int (fun int int)), z3mod ) 22.33/22.41 ( (fun int (fun int int)), int_lcm ) 22.33/22.41 ( (fun int (fun int int)), int_gcd ) 22.33/22.41 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.33/22.41 ( (fun bool bool), fNot ) 22.33/22.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.33/22.41 ( (fun bool (fun bool bool)), fconj ) 22.33/22.41 ( (fun bool (fun bool bool)), fdisj ) 22.33/22.41 ( (fun bool (fun bool bool)), fimplies ) 22.33/22.41 ( (fun int (fun int bool)), quadRes ) 22.33/22.41 ( (fun int (fun int bool)), d22set ) 22.33/22.41 ( (fun int (fun int bool)), norRRset ) 22.33/22.41 ( (fun int (fun int bool)), sRStar ) 22.33/22.41 ( (fun int (fun int bool)), sr ) 22.33/22.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.33/22.41 ( (fun nat bool), (even_odd_even nat) ) 22.33/22.41 ( (fun nat bool), prime ) 22.33/22.41 ( (fun real complex), cis ) 22.33/22.41 ( (fun nat (fun nat bool)), coprime ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.33/22.41 ( (fun (product_prod int int) bool), frac_1 ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.33/22.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.33/22.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.33/22.41 ( (fun (fun int bool) bool), nat_nat_set ) 22.33/22.41 ( (fun nat (fun real real)), root ) 22.33/22.41 ( (fun real (fun real real)), log ) 22.33/22.41 ( (fun real (fun real real)), powr ) 22.33/22.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.33/22.41 ( (fun complex complex), cnj ) 22.33/22.41 ( (fun complex complex), expi ) 22.33/22.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.33/22.41 ( (fun nat (fun nat nat)), nat_gcd ) 22.33/22.41 ( (fun nat (fun nat nat)), nat_lcm ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.33/22.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.33/22.41 ( (fun int (fun (fun int bool) bool)), resSet ) 22.33/22.41 ( (fun int nat), nat_1 ) 22.33/22.41 ( (fun int nat), phi ) 22.33/22.41 ( (fun complex real), re ) 22.33/22.41 ( (fun complex real), im ) 22.33/22.41 ( (fun complex real), arg ) 22.33/22.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.33/22.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.33/22.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.33/22.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.33/22.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.33/22.41 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.33/22.41 ( (fun (product_prod nat nat) bool), pred_nat ) 22.33/22.41 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.33/22.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.33/22.41 ( (fun (fun int bool) int), (the int) ) 22.33/22.41 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.33/22.41 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.33/22.41 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.33/22.41 ( (fun real (fun real complex)), rcis ) 22.33/22.41 ( (fun real (fun real complex)), complex_1 ) 22.33/22.41 ( (fun int (fun int (fun int bool))), zcong ) 22.33/22.41 ( (fun int (fun int (fun int bool))), wset ) 22.33/22.41 ( (fun int (fun int (fun int bool))), noXRRset ) 22.33/22.41 ( (fun int (fun int (fun int bool))), bnorRset ) 22.33/22.41 ( (fun int (fun int (fun int bool))), zcongm ) 22.33/22.41 ( (fun real nat), natceiling ) 22.33/22.41 ( (fun real nat), natfloor ) 22.33/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.33/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.33/22.41 ( (fun int real), (real_1 int) ) 22.33/22.41 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.33/22.41 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.33/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.33/22.41 ( (fun complex nat), (size_size complex) ) 22.33/22.41 ( (fun complex nat), complex_size ) 22.33/22.41 ( (fun (fun nat rat) bool), vanishes ) 22.33/22.41 ( (fun (product_prod int int) rat), frct ) 22.33/22.41 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.33/22.41 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.33/22.41 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.33/22.41 ( (fun rat real), ratreal ) 22.33/22.41 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.33/22.41 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.33/22.41 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.33/22.41 ( (fun rat (product_prod int int)), quotient_of ) 22.33/22.41 ( (fun int (fun nat nat)), nat_aux ) 22.33/22.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.33/22.41 ( (fun int (list int)), quickc666637781d_zero ) 22.33/22.41 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.33/22.41 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.33/22.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.33/22.41 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.33/22.41 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.33/22.41 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.33/22.41 ( (fun code_code_numeral int), code_int_of ) 22.33/22.41 ) 22.33/22.41 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y))) (not (forall ((X_1 $$unsorted)) (not (= Y (hAPP real real (exp real) X_1))) ))) ) 22.33/22.41 ( pi ) 22.33/22.41 ( (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)))) ) 22.33/22.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.41 ( skv_2 ) 22.33/22.41 ( skv_9 ) 22.33/22.41 ( skv_12 ) 22.33/22.41 ) 22.33/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125481 $$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_125481)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_125481) (one_one X_a))))) ) 22.33/22.41 ( int, (one_one int) ) 22.33/22.41 ( int, min ) 22.33/22.41 ( int, (zero_zero int) ) 22.33/22.41 ( int, s ) 22.33/22.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.33/22.41 ( int, t ) 22.33/22.41 ( int, m1 ) 22.33/22.41 ( int, skv_4 ) 22.33/22.41 ( int, skv_5 ) 22.33/22.41 ( nat, (zero_zero nat) ) 22.33/22.41 ( real, pi ) 22.33/22.41 ( 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)))) ) 22.33/22.41 ( real, (one_one real) ) 22.33/22.41 ( real, (zero_zero real) ) 22.33/22.41 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.41 ( 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))))) ) 22.33/22.41 ( 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)) ) 22.33/22.41 ) 22.33/22.41 (instantiation (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 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) pi))) (= X (hAPP real real arccos (hAPP real real cos X)))))) ) 22.33/22.41 ( pi ) 22.33/22.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.33/22.41 ( (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)))) ) 22.33/22.41 ( (zero_zero real) ) 22.33/22.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.41 ( (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))))) ) 22.33/22.41 ( (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) ) 22.33/22.41 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.33/22.41 ( (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))))) ) 22.33/22.41 ( (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)))) ) 22.33/22.41 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.33/22.41 ( skv_10 ) 22.33/22.41 ( skv_11 ) 22.33/22.41 ( skv_15 ) 22.33/22.41 ( skv_18 ) 22.33/22.41 ) 22.33/22.41 (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)))) ) 22.33/22.41 ( rat ) 22.33/22.41 ( int ) 22.35/22.41 ( (fun int int) ) 22.35/22.41 ( nat ) 22.35/22.41 ( bool ) 22.35/22.41 ( real ) 22.35/22.41 ( (fun real real) ) 22.35/22.41 ( (fun nat nat) ) 22.35/22.41 ( complex ) 22.35/22.41 ( (product_prod int int) ) 22.35/22.41 ( (fun bool bool) ) 22.35/22.41 ( (fun nat bool) ) 22.35/22.41 ( (fun nat (fun nat bool)) ) 22.35/22.41 ( quickcheck_code_int ) 22.35/22.41 ( code_code_numeral ) 22.35/22.41 ( (fun nat (product_prod int int)) ) 22.35/22.41 ( (product_prod real real) ) 22.35/22.41 ( (product_prod nat nat) ) 22.35/22.41 ( (fun (product_prod nat nat) bool) ) 22.35/22.41 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.35/22.41 ( (fun nat (product_prod nat nat)) ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real sin (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) X)) (hAPP real real cos X))) ) 22.35/22.41 ( pi ) 22.35/22.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( (zero_zero real) ) 22.35/22.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.35/22.41 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.35/22.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.35/22.41 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 22.35/22.41 ( skv_10 ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (or (= (zero_zero real) X) (= (hAPP real real arctan (hAPP real real (hAPP real _let_0 _let_1 (one_one real)) X)) (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)) pi)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP real real arctan X)))))) ) 22.35/22.41 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( (zero_zero real) ) 22.35/22.41 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( (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))))))))) ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125690 $$unsorted) (BOUND_VARIABLE_125691 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ti X_a BOUND_VARIABLE_125690))) (let ((_let_3 (ti X_a BOUND_VARIABLE_125691))) (or (not (division_ring X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_125690) (hAPP X_a X_a _let_0 BOUND_VARIABLE_125691))) (= _let_1 _let_2) (= _let_1 _let_3) (= _let_2 _let_3)))))) ) 22.35/22.41 ( real, (zero_zero real), (zero_zero real) ) 22.35/22.41 ( complex, ii, ii ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$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)))) ) 22.35/22.41 ( rat ) 22.35/22.41 ( int ) 22.35/22.41 ( nat ) 22.35/22.41 ( real ) 22.35/22.41 ( complex ) 22.35/22.41 ( quickcheck_code_int ) 22.35/22.41 ( code_code_numeral ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_125736 $$unsorted) (BOUND_VARIABLE_125737 $$unsorted) (BOUND_VARIABLE_125738 $$unsorted) (BOUND_VARIABLE_125739 $$unsorted)) (let ((_let_0 (hAPP X_b (fun X_b bool) (ord_less X_b) BOUND_VARIABLE_125736))) (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_125738) BOUND_VARIABLE_125739))) (not (hBOOL (hAPP X_b bool _let_0 (hAPP X_a X_b BOUND_VARIABLE_125737 BOUND_VARIABLE_125738)))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) Y_1) X_1))) (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_125737 Y_1)) (hAPP X_a X_b BOUND_VARIABLE_125737 X_1)))) )) (hBOOL (hAPP X_b bool _let_0 (hAPP X_a X_b BOUND_VARIABLE_125737 BOUND_VARIABLE_125739))))) ) 22.35/22.41 ( int, int, (one_one int), (number_number_of int), min, pls ) 22.35/22.41 ( int, int, min, (uminus_uminus int), min, min ) 22.35/22.41 ( int, int, (zero_zero int), bit1, pls, (one_one int) ) 22.35/22.41 ( int, int, s, succ, pls, min ) 22.35/22.41 ( int, int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (number_number_of int), pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.41 ( int, 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), t ) 22.35/22.41 ( int, int, m1, pred, pls, pls ) 22.35/22.41 ( int, int, skv_4, (uminus_uminus int), pls, s ) 22.35/22.41 ( int, int, skv_5, (fact_fact int), (zero_zero int), skv_4 ) 22.35/22.41 ( nat, int, (zero_zero nat), nat_1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( real, real, pi, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.35/22.41 ( 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)))), sin, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( real, real, (one_one real), tan, (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)))) ) 22.35/22.41 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), sqrt, (zero_zero real), skv_11 ) 22.35/22.41 ( 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))))), arctan, (zero_zero real), pi ) 22.35/22.41 ( 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, (zero_zero real), skv_10 ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((K_4 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) K_4))) (not (forall ((N_1 $$unsorted)) (not (= (ti int K_4) (hAPP nat int (semiring_1_of_nat int) N_1))) ))) ) 22.35/22.41 ( pls ) 22.35/22.41 ( (one_one int) ) 22.35/22.41 ( min ) 22.35/22.41 ( s ) 22.35/22.41 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.41 ( skv_4 ) 22.35/22.41 ( skv_5 ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_125948 $$unsorted) (BOUND_VARIABLE_125949 $$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_125948) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_125949) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_125949))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_125948) BOUND_VARIABLE_125949)))))))) ) 22.35/22.41 ( int, (one_one int), t ) 22.35/22.41 ( int, min, min ) 22.35/22.41 ( int, min, (zero_zero int) ) 22.35/22.41 ( int, (zero_zero int), pls ) 22.35/22.41 ( int, (zero_zero int), (one_one int) ) 22.35/22.41 ( int, (zero_zero int), min ) 22.35/22.41 ( 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))) ) 22.35/22.41 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.41 ( 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))) ) 22.35/22.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.35/22.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.41 ( 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))) ) 22.35/22.41 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.41 ( 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))) ) 22.35/22.41 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.35/22.41 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( nat, (zero_zero nat), n ) 22.35/22.41 ( nat, (zero_zero nat), tn ) 22.35/22.41 ( real, pi, (zero_zero real) ) 22.35/22.41 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( real, (zero_zero real), pi ) 22.35/22.41 ( 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)))) ) 22.35/22.41 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( real, (zero_zero real), skv_2 ) 22.35/22.41 ( real, (zero_zero real), skv_9 ) 22.35/22.41 ( real, (zero_zero real), skv_12 ) 22.35/22.41 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.35/22.41 ( 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) ) 22.35/22.41 ( 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 ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126026 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_126026)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_126026))))) ) 22.35/22.41 ( int, pls ) 22.35/22.41 ( int, min ) 22.35/22.41 ( int, s ) 22.35/22.41 ( int, s1 ) 22.35/22.41 ( int, m ) 22.35/22.41 ( int, t ) 22.35/22.41 ( int, v ) 22.35/22.41 ( int, w ) 22.35/22.41 ( int, y ) 22.35/22.41 ( int, sa ) 22.35/22.41 ( int, x ) 22.35/22.41 ( int, r ) 22.35/22.41 ( int, m1 ) 22.35/22.41 ( int, skv_14 ) 22.35/22.41 ( int, skv_20 ) 22.35/22.41 ( (fun int int), bit1 ) 22.35/22.41 ( (fun int int), bit0 ) 22.35/22.41 ( (fun int int), succ ) 22.35/22.41 ( (fun int int), pred ) 22.35/22.41 ( (fun int int), (fact_fact int) ) 22.35/22.41 ( (fun int int), zfact ) 22.35/22.41 ( nat, n ) 22.35/22.41 ( nat, tn ) 22.35/22.41 ( bool, fTrue ) 22.35/22.41 ( bool, fFalse ) 22.35/22.41 ( real, pi ) 22.35/22.41 ( (fun nat real), (real_1 nat) ) 22.35/22.41 ( (fun nat real), cos_coeff ) 22.35/22.41 ( (fun nat real), sin_coeff ) 22.35/22.41 ( (fun real real), sin ) 22.35/22.41 ( (fun real real), cos ) 22.35/22.41 ( (fun real real), sqrt ) 22.35/22.41 ( (fun real real), tan ) 22.35/22.41 ( (fun real real), ln ) 22.35/22.41 ( (fun real real), arctan ) 22.35/22.41 ( (fun real real), arcsin ) 22.35/22.41 ( (fun real real), arccos ) 22.35/22.41 ( (fun nat nat), suc ) 22.35/22.41 ( (fun nat nat), (fact_fact nat) ) 22.35/22.41 ( (fun nat nat), nat_size ) 22.35/22.41 ( (fun nat nat), (size_size nat) ) 22.35/22.41 ( (fun nat nat), fact ) 22.35/22.41 ( (filter nat), sequentially ) 22.35/22.41 ( (fun int (fun int rat)), fract ) 22.35/22.41 ( complex, ii ) 22.35/22.41 ( (fun int bool), zOdd ) 22.35/22.41 ( (fun int bool), zprime ) 22.35/22.41 ( (fun int bool), zEven ) 22.35/22.41 ( (fun int bool), nat_neg ) 22.35/22.41 ( (fun int bool), nat_is_nat ) 22.35/22.41 ( (fun int bool), (even_odd_even int) ) 22.35/22.41 ( (fun int bool), twoSqu1091635170sum2sq ) 22.35/22.41 ( (fun int (fun int int)), legacy_zgcd ) 22.35/22.41 ( (fun int (fun int int)), (gcd_gcd int) ) 22.35/22.41 ( (fun int (fun int int)), inv ) 22.35/22.41 ( (fun int (fun int int)), multInv ) 22.35/22.41 ( (fun int (fun int int)), legendre ) 22.35/22.41 ( (fun int (fun int int)), standardRes ) 22.35/22.41 ( (fun int (fun int int)), nat_tsub ) 22.35/22.41 ( (fun int (fun int int)), z3div ) 22.35/22.41 ( (fun int (fun int int)), z3mod ) 22.35/22.41 ( (fun int (fun int int)), int_lcm ) 22.35/22.41 ( (fun int (fun int int)), int_gcd ) 22.35/22.41 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.35/22.41 ( (fun bool bool), fNot ) 22.35/22.41 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.35/22.41 ( (fun bool (fun bool bool)), fconj ) 22.35/22.41 ( (fun bool (fun bool bool)), fdisj ) 22.35/22.41 ( (fun bool (fun bool bool)), fimplies ) 22.35/22.41 ( (fun int (fun int bool)), quadRes ) 22.35/22.41 ( (fun int (fun int bool)), d22set ) 22.35/22.41 ( (fun int (fun int bool)), norRRset ) 22.35/22.41 ( (fun int (fun int bool)), sRStar ) 22.35/22.41 ( (fun int (fun int bool)), sr ) 22.35/22.41 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.35/22.41 ( (fun nat bool), (even_odd_even nat) ) 22.35/22.41 ( (fun nat bool), prime ) 22.35/22.41 ( (fun real complex), cis ) 22.35/22.41 ( (fun nat (fun nat bool)), coprime ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.35/22.41 ( (fun (product_prod int int) bool), frac_1 ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.35/22.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.35/22.41 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.35/22.41 ( (fun (fun int bool) bool), nat_nat_set ) 22.35/22.41 ( (fun nat (fun real real)), root ) 22.35/22.41 ( (fun real (fun real real)), log ) 22.35/22.41 ( (fun real (fun real real)), powr ) 22.35/22.41 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.35/22.41 ( (fun complex complex), cnj ) 22.35/22.41 ( (fun complex complex), expi ) 22.35/22.41 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.35/22.41 ( (fun nat (fun nat nat)), nat_gcd ) 22.35/22.41 ( (fun nat (fun nat nat)), nat_lcm ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.35/22.41 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.35/22.41 ( (fun int (fun (fun int bool) bool)), resSet ) 22.35/22.41 ( (fun int nat), nat_1 ) 22.35/22.41 ( (fun int nat), phi ) 22.35/22.41 ( (fun complex real), re ) 22.35/22.41 ( (fun complex real), im ) 22.35/22.41 ( (fun complex real), arg ) 22.35/22.41 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.35/22.41 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.35/22.41 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.35/22.41 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.35/22.41 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.35/22.41 ( (fun (product_prod nat nat) bool), pred_nat ) 22.35/22.41 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.35/22.41 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.35/22.41 ( (fun (fun int bool) int), (the int) ) 22.35/22.41 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.35/22.41 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.35/22.41 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.35/22.41 ( (fun real (fun real complex)), rcis ) 22.35/22.41 ( (fun real (fun real complex)), complex_1 ) 22.35/22.41 ( (fun int (fun int (fun int bool))), zcong ) 22.35/22.41 ( (fun int (fun int (fun int bool))), wset ) 22.35/22.41 ( (fun int (fun int (fun int bool))), noXRRset ) 22.35/22.41 ( (fun int (fun int (fun int bool))), bnorRset ) 22.35/22.41 ( (fun int (fun int (fun int bool))), zcongm ) 22.35/22.41 ( (fun real nat), natceiling ) 22.35/22.41 ( (fun real nat), natfloor ) 22.35/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.35/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.35/22.41 ( (fun int real), (real_1 int) ) 22.35/22.41 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.35/22.41 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.35/22.41 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.35/22.41 ( (fun complex nat), (size_size complex) ) 22.35/22.41 ( (fun complex nat), complex_size ) 22.35/22.41 ( (fun (fun nat rat) bool), vanishes ) 22.35/22.41 ( (fun (product_prod int int) rat), frct ) 22.35/22.41 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.35/22.41 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.35/22.41 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.35/22.41 ( (fun rat real), ratreal ) 22.35/22.41 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.35/22.41 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.35/22.41 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.35/22.41 ( (fun rat (product_prod int int)), quotient_of ) 22.35/22.41 ( (fun int (fun nat nat)), nat_aux ) 22.35/22.41 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.35/22.41 ( (fun int (list int)), quickc666637781d_zero ) 22.35/22.41 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.35/22.41 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.35/22.41 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.35/22.41 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.35/22.41 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.35/22.41 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.35/22.41 ( (fun code_code_numeral int), code_int_of ) 22.35/22.41 ) 22.35/22.41 (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))))))))))))) ) 22.35/22.41 ( int ) 22.35/22.41 ( nat ) 22.35/22.41 ) 22.35/22.41 (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))) ) 22.35/22.41 ( int, zOdd ) 22.35/22.41 ( int, zprime ) 22.35/22.41 ( int, zEven ) 22.35/22.41 ( int, nat_neg ) 22.35/22.41 ( int, nat_is_nat ) 22.35/22.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_1))) (let ((_let_5 (fun int _let_4))) (hAPP _let_3 _let_1 (hAPP (fun _let_1 bool) (fun _let_3 _let_1) (combb _let_1 bool int) (fEx int)) (hAPP _let_0 _let_3 (hAPP _let_5 (fun _let_0 _let_3) (combc int _let_0 _let_1) (hAPP _let_3 _let_5 (hAPP (fun _let_1 _let_4) (fun _let_3 _let_5) (combb _let_1 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_0 (hAPP _let_2 _let_2 (combc int int int) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (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)))))))))) ) 22.35/22.41 ( int, (even_odd_even int) ) 22.35/22.41 ( int, twoSqu1091635170sum2sq ) 22.35/22.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_1 (hAPP (fun _let_1 bool) (fun _let_2 _let_1) (combb _let_1 bool int) (fEx int)) (hAPP _let_0 _let_2 (hAPP _let_4 (fun _let_0 _let_2) (combc int _let_0 _let_1) (hAPP _let_2 _let_4 (hAPP (fun _let_1 _let_3) (fun _let_2 _let_4) (combb _let_1 _let_3 int) (combb int bool int)) (fequal int))) (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 22.35/22.41 ( nat, (even_odd_even nat) ) 22.35/22.41 ( nat, prime ) 22.35/22.41 ( bool, fNot ) 22.35/22.41 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun nat (fun nat bool)))) (let ((_let_4 (fun real bool))) (let ((_let_5 (fun real _let_4))) (let ((_let_6 (fun (fun nat real) (fun nat real)))) (let ((_let_7 (fun nat _let_2))) (let ((_let_8 (fun (fun nat bool) (fun nat bool)))) (let ((_let_9 (fun (fun nat bool) _let_7))) (let ((_let_10 (fun int real))) (let ((_let_11 (fun real _let_1))) (let ((_let_12 (fun real (fun int (fun nat bool))))) (let ((_let_13 (fun (fun int (fun nat bool)) _let_1))) (let ((_let_14 (fun (fun nat bool) (fun int (fun nat bool))))) (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 int _let_7))) (let ((_let_19 (fun real _let_18))) (let ((_let_20 (fun _let_18 _let_16))) (let ((_let_21 (fun (fun int (fun nat bool)) _let_18))) (let ((_let_22 (fun int (fun nat real)))) (let ((_let_23 (fun _let_22 (fun int (fun nat bool))))) (let ((_let_24 (fun real _let_23))) (let ((_let_25 (fun (fun nat real) (fun nat bool)))) (let ((_let_26 (fun real _let_25))) (let ((_let_27 (fun int _let_6))) (let ((_let_28 (fun int _let_0))) (hAPP _let_11 _let_4 (hAPP (fun _let_1 bool) (fun _let_11 _let_4) (combb _let_1 bool real) (fEx int)) (hAPP _let_12 _let_11 (hAPP _let_13 (fun _let_12 _let_11) (combb (fun int (fun nat bool)) _let_1 real) (hAPP (fun (fun nat bool) bool) _let_13 (combb (fun nat bool) bool int) (fEx nat))) (hAPP (fun nat bool) _let_12 (hAPP _let_15 (fun (fun nat bool) _let_12) (combc real (fun nat bool) (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) (combc int (fun nat bool) (fun nat bool))) (hAPP _let_19 _let_17 (hAPP _let_20 (fun _let_19 _let_17) (combb _let_18 _let_16 real) (hAPP (fun _let_7 _let_8) _let_20 (combb _let_7 _let_8 int) (combs nat bool bool))) (hAPP _let_12 _let_19 (hAPP _let_21 (fun _let_12 _let_19) (combb (fun int (fun nat bool)) _let_18 real) (hAPP _let_9 _let_21 (combb (fun nat bool) _let_7 int) (hAPP (fun bool _let_2) _let_9 (combb bool _let_2 nat) fconj))) (hAPP _let_22 _let_12 (hAPP _let_24 (fun _let_22 _let_12) (combc real _let_22 (fun int (fun nat bool))) (hAPP _let_26 _let_24 (hAPP (fun _let_25 _let_23) (fun _let_26 _let_24) (combb _let_25 _let_23 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_5 _let_26 (hAPP (fun _let_4 _let_25) (fun _let_5 _let_26) (combb _let_4 _let_25 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_22 (hAPP _let_27 (fun (fun nat real) _let_22) (combc int (fun nat real) (fun nat real)) (hAPP _let_28 _let_27 (hAPP (fun _let_0 _let_6) (fun _let_28 _let_27) (combb _let_0 _let_6 int) (combb real real nat)) (hAPP _let_10 _let_28 (hAPP (fun real _let_0) (fun _let_10 _let_28) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_2 _let_8 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_3 _let_3 (combc nat nat bool) (fequal nat)) (zero_zero nat))))))))))))))))))))))))))))))))))) ) 22.35/22.41 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (fun int (fun int bool)))) (let ((_let_6 (real_1 int))) (let ((_let_7 (fun real bool))) (let ((_let_8 (fun (fun int bool) bool))) (let ((_let_9 (fun real _let_7))) (let ((_let_10 (fun _let_5 (fun int bool)))) (let ((_let_11 (fEx int))) (let ((_let_12 (fun int _let_3))) (let ((_let_13 (fun (fun int bool) _let_5))) (let ((_let_14 (fun int _let_2))) (let ((_let_15 (fun _let_14 _let_12))) (let ((_let_16 (fun _let_5 _let_14))) (let ((_let_17 (fun int real))) (let ((_let_18 (fun real (fun int bool)))) (let ((_let_19 (fun int _let_0))) (let ((_let_20 (fun _let_17 (fun int bool)))) (let ((_let_21 (fun real _let_5))) (let ((_let_22 (fun real _let_13))) (let ((_let_23 (fun real _let_12))) (let ((_let_24 (fun real _let_14))) (let ((_let_25 (fun int _let_17))) (let ((_let_26 (fun _let_25 _let_5))) (let ((_let_27 (fun real _let_26))) (let ((_let_28 (fun real _let_20))) (let ((_let_29 (fun _let_17 _let_17))) (let ((_let_30 (fun int _let_29))) (hAPP _let_18 _let_7 (hAPP _let_8 (fun _let_18 _let_7) (combb (fun int bool) bool real) _let_11) (hAPP _let_21 _let_18 (hAPP _let_10 (fun _let_21 _let_18) (combb _let_5 (fun int bool) real) (hAPP _let_8 _let_10 (combb (fun int bool) bool int) _let_11)) (hAPP (fun int bool) _let_21 (hAPP _let_22 (fun (fun int bool) _let_21) (combc real (fun int bool) _let_5) (hAPP _let_23 _let_22 (hAPP (fun _let_12 _let_13) (fun _let_23 _let_22) (combb _let_12 _let_13 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_24 _let_23 (hAPP _let_15 (fun _let_24 _let_23) (combb _let_14 _let_12 real) (hAPP (fun _let_2 _let_3) _let_15 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_21 _let_24 (hAPP _let_16 (fun _let_21 _let_24) (combb _let_5 _let_14 real) (hAPP _let_4 _let_16 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_25 _let_21 (hAPP _let_27 (fun _let_25 _let_21) (combc real _let_25 _let_5) (hAPP _let_28 _let_27 (hAPP (fun _let_20 _let_26) (fun _let_28 _let_27) (combb _let_20 _let_26 real) (combb _let_17 (fun int bool) int)) (hAPP _let_9 _let_28 (hAPP (fun _let_7 _let_20) (fun _let_9 _let_28) (combb _let_7 _let_20 real) (combb real bool int)) (fequal real)))) (hAPP _let_17 _let_25 (hAPP _let_30 (fun _let_17 _let_25) (combc int _let_17 _let_17) (hAPP _let_19 _let_30 (hAPP (fun _let_0 _let_29) (fun _let_19 _let_30) (combb _let_0 _let_29 int) (combb real real int)) (hAPP _let_17 _let_19 (hAPP (fun real _let_0) (fun _let_17 _let_19) (combb real _let_0 int) (inverse_divide real)) _let_6))) _let_6)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_1 _let_3 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_5 _let_5 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))))))))) ) 22.35/22.41 ( (fun int bool), nat_nat_set ) 22.35/22.41 ( (product_prod int int), frac_1 ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 22.35/22.41 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (fun _let_2 _let_4))) (let ((_let_11 (fun _let_2 _let_1))) (let ((_let_12 (fun _let_3 _let_11))) (let ((_let_13 (hAPP (fun int _let_1) _let_12 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_10 (hAPP (fun bool _let_4) (fun (fun _let_2 bool) _let_10) (combb bool _let_4 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_4 _let_7 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_11 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_3 _let_11 _let_13 _let_5)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_3))) (let ((_let_16 (fun _let_3 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_11))) (let ((_let_19 (fun _let_3 _let_3))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_3 _let_15))) (let ((_let_22 (fun _let_2 _let_0))) (let ((_let_23 (hAPP _let_3 _let_22 (hAPP (fun int _let_0) (fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb _let_3 _let_11 _let_2) _let_13) (hAPP _let_3 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_3 _let_3) (hAPP _let_22 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_22 _let_20) (combb _let_0 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_5)))) (hAPP _let_3 _let_15 (hAPP _let_24 _let_21 (combb int _let_3 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_5)))))))))))))))))))))))))))))) ) 22.35/22.41 ( (product_prod nat nat), pred_nat ) 22.35/22.41 ( (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)))) ) 22.35/22.41 ( (fun nat rat), vanishes ) 22.35/22.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 22.35/22.41 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126222 $$unsorted) (BOUND_VARIABLE_126223 $$unsorted) (BOUND_VARIABLE_126224 $$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_126222) BOUND_VARIABLE_126223) (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_126222) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_126223) BOUND_VARIABLE_126224))) BOUND_VARIABLE_126223))))) ) 22.35/22.41 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.35/22.41 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), y, w ) 22.35/22.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.35/22.41 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), sa, w ) 22.35/22.41 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.35/22.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.35/22.41 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((M $$unsorted) (N $$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)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 M)) (hAPP nat real _let_0 N)))) ) 22.35/22.41 ( (one_one nat), (one_one nat) ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126310 $$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_126310) _let_0)))) ) 22.35/22.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( 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))) ) 22.35/22.41 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.41 ( int, y ) 22.35/22.41 ( int, sa ) 22.35/22.41 ( int, x ) 22.35/22.41 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.35/22.41 ( int, r ) 22.35/22.41 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.35/22.41 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.35/22.41 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( int, skv_13 ) 22.35/22.41 ( int, skv_19 ) 22.35/22.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.41 ( 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))))) ) 22.35/22.41 ( complex, ii ) 22.35/22.41 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.41 ( 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)) ) 22.35/22.41 ) 22.35/22.41 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126327 $$unsorted)) (let ((_let_0 (exp X_a))) (or (not (real_normed_field X_a)) (not (banach X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_126327)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_126327))))) ) 22.35/22.41 ( int, pls ) 22.35/22.41 ( int, (one_one int) ) 22.35/22.41 ( int, min ) 22.35/22.41 ( 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)))) ) 22.35/22.41 ( real, (one_one real) ) 22.35/22.41 ( 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) ) 22.35/22.41 ( complex, ii ) 22.35/22.41 ( complex, (one_one complex) ) 22.35/22.41 ) 22.35/22.42 (instantiation (forall ((Ta $$unsorted) (B_1 $$unsorted) (D $$unsorted) (BOUND_VARIABLE_126402 $$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))) (not (hBOOL (hAPP (fun int bool) bool (hAPP int (fun (fun int bool) bool) (member int) Ta) B_1))) (not (forall ((Xa_1 $$unsorted) (BOUND_VARIABLE_126372 $$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_1) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 BOUND_VARIABLE_126372) B_1))) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_126372) Xa_1) (ti int BOUND_VARIABLE_126402))))))) )) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_126402))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_126402) D))))) ) 22.35/22.42 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), y ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126435 $$unsorted) (BOUND_VARIABLE_126436 $$unsorted) (BOUND_VARIABLE_126437 $$unsorted) (BOUND_VARIABLE_126438 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_126435))) (or (not (ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) (hAPP X_a X_a _let_3 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126436) BOUND_VARIABLE_126438))) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126435) BOUND_VARIABLE_126437)) BOUND_VARIABLE_126438)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_126436)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_126437) BOUND_VARIABLE_126438)))))))) ) 22.35/22.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.35/22.42 ( int, x, w, y, v ) 22.35/22.42 ( int, r, w, sa, v ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Y))) (= Y (hAPP real real sqrt (hAPP nat real (hAPP real (fun nat real) (power_power real) Y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.35/22.42 ( (hAPP int real (number_number_of real) min) ) 22.35/22.42 ( pi ) 22.35/22.42 ( (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)))) ) 22.35/22.42 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( (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)))) ) 22.35/22.42 ( skv_10 ) 22.35/22.42 ( skv_11 ) 22.35/22.42 ( skv_15 ) 22.35/22.42 ( skv_18 ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126515 $$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_126515))))) ) 22.35/22.42 ( int, (one_one nat) ) 22.35/22.42 ( real, (one_one nat) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126533 $$unsorted)) (or (not (number_ring X_a)) (not (real_algebra_1 X_a)) (= (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_126533) (hAPP real X_a (of_real X_a) (hAPP int real (number_number_of real) BOUND_VARIABLE_126533)))) ) 22.35/22.42 ( int, pls ) 22.35/22.42 ( int, (hAPP int int bit1 pls) ) 22.35/22.42 ( int, min ) 22.35/22.42 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.35/22.42 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.35/22.42 ( nat, pls ) 22.35/22.42 ( nat, (hAPP int int bit1 pls) ) 22.35/22.42 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.35/22.42 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.35/22.42 ( real, min ) 22.35/22.42 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.35/22.42 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.35/22.42 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.42 ( 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)))))))) ) 22.35/22.42 ( complex, min ) 22.35/22.42 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.35/22.42 ( quickcheck_code_int, pls ) 22.35/22.42 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.35/22.42 ( quickcheck_code_int, (one_one int) ) 22.35/22.42 ( code_code_numeral, pls ) 22.35/22.42 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (max X_a))) (or (not (ord X_a)) (= _let_0 (ti (fun (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a))) _let_0)))) ) 22.35/22.42 ( rat ) 22.35/22.42 ( int ) 22.35/22.42 ( (fun int int) ) 22.35/22.42 ( nat ) 22.35/22.42 ( bool ) 22.35/22.42 ( real ) 22.35/22.42 ( (fun nat real) ) 22.35/22.42 ( (fun real real) ) 22.35/22.42 ( (filter nat) ) 22.35/22.42 ( complex ) 22.35/22.42 ( (fun int bool) ) 22.35/22.42 ( (product_prod int int) ) 22.35/22.42 ( (fun (product_prod int int) int) ) 22.35/22.42 ( (fun int (fun int bool)) ) 22.35/22.42 ( (fun nat bool) ) 22.35/22.42 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.35/22.42 ( (fun (product_prod int int) bool) ) 22.35/22.42 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.35/22.42 ( (fun real bool) ) 22.35/22.42 ( quickcheck_code_int ) 22.35/22.42 ( code_code_numeral ) 22.35/22.42 ( (product_prod real real) ) 22.35/22.42 ( (filter real) ) 22.35/22.42 ( (product_prod nat nat) ) 22.35/22.42 ( (fun nat rat) ) 22.35/22.42 ( (fun int (fun int (fun int bool))) ) 22.35/22.42 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.35/22.42 ( (fun int real) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int rat))) (let ((_let_2 (fun int bool))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun _let_3 int))) (let ((_let_5 (fun bool bool))) (let ((_let_6 (product_snd int int))) (let ((_let_7 (product_fst int int))) (let ((_let_8 (fun _let_3 bool))) (let ((_let_9 (fun _let_8 _let_8))) (let ((_let_10 (fun _let_3 _let_5))) (let ((_let_11 (hAPP (fun bool _let_5) (fun _let_8 _let_10) (combb bool _let_5 _let_3) fconj))) (let ((_let_12 (fun _let_3 _let_2))) (let ((_let_13 (combs _let_3 bool bool))) (let ((_let_14 (fun _let_3 _let_0))) (let ((_let_15 (fun rat bool))) (let ((_let_16 (fun _let_3 rat))) (let ((_let_17 (fun _let_3 _let_1))) (= (hAPP _let_8 _let_3 (the _let_3) (hAPP _let_8 _let_8 (hAPP _let_10 _let_9 _let_13 (hAPP _let_8 _let_10 _let_11 (hAPP _let_16 _let_8 (hAPP _let_15 (fun _let_16 _let_8) (combb rat bool _let_3) (hAPP rat _let_15 (fequal rat) Xa)) (hAPP _let_4 _let_16 (hAPP _let_17 (fun _let_4 _let_16) (combs _let_3 int rat) (hAPP _let_4 _let_17 (hAPP (fun int _let_1) (fun _let_4 _let_17) (combb int _let_1 _let_3) fract) _let_7)) _let_6)))) (hAPP _let_8 _let_8 (hAPP _let_10 _let_9 _let_13 (hAPP _let_8 _let_10 _let_11 (hAPP _let_4 _let_8 (hAPP _let_2 (fun _let_4 _let_8) (combb int bool _let_3) (hAPP int _let_2 (ord_less int) (zero_zero int))) _let_6))) (hAPP int _let_8 (hAPP _let_12 (fun int _let_8) (combc _let_3 int bool) (hAPP _let_4 _let_12 (hAPP (fun int _let_2) (fun _let_4 _let_12) (combb int _let_2 _let_3) (fequal int)) (hAPP _let_4 _let_4 (hAPP _let_14 (fun _let_4 _let_4) (combs _let_3 int int) (hAPP _let_4 _let_14 (hAPP (fun int _let_0) (fun _let_4 _let_14) (combb int _let_0 _let_3) (gcd_gcd int)) _let_7)) _let_6))) (one_one int))))) (hAPP rat _let_3 quotient_of Xa)))))))))))))))))))) ) 22.35/22.42 ( (one_one rat) ) 22.35/22.42 ( (zero_zero rat) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126562 $$unsorted) (BOUND_VARIABLE_126563 $$unsorted) (BOUND_VARIABLE_126564 $$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_126563) BOUND_VARIABLE_126564))) (not (= (ti X_a BOUND_VARIABLE_126562) (ti X_a BOUND_VARIABLE_126563))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126562) BOUND_VARIABLE_126564))))) ) 22.35/22.42 ( int, pls, (zero_zero int), s ) 22.35/22.42 ( int, min, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.42 ( int, s, min, min ) 22.35/22.42 ( int, s1, (zero_zero int), (one_one int) ) 22.35/22.42 ( int, m, (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( int, t, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( int, v, (one_one int), t ) 22.35/22.42 ( int, w, (zero_zero int), skv_4 ) 22.35/22.42 ( int, y, (zero_zero int), min ) 22.35/22.42 ( int, sa, (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( int, x, (zero_zero int), skv_5 ) 22.35/22.42 ( int, r, (zero_zero int), pls ) 22.35/22.42 ( int, m1, min, pls ) 22.35/22.42 ( int, skv_14, (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( int, skv_20, (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( real, pi, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (abs_abs int))) (= (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))) (hAPP int nat nat_1 (hAPP int int _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) W) Z_1))))) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.35/22.42 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( (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 ) 22.35/22.42 ( (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))), m1 ) 22.35/22.42 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.35/22.42 ( (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_21 ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.35/22.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.35/22.42 ( y, v ) 22.35/22.42 ( y, w ) 22.35/22.42 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( sa, v ) 22.35/22.42 ( sa, w ) 22.35/22.42 ( x, v ) 22.35/22.42 ( x, w ) 22.35/22.42 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.35/22.42 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( r, v ) 22.35/22.42 ( r, w ) 22.35/22.42 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.35/22.42 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.35/22.42 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.35/22.42 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.35/22.42 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126595 $$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_126595)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_126595))))) ) 22.35/22.42 ( int, s ) 22.35/22.42 ( int, s1 ) 22.35/22.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( int, v ) 22.35/22.42 ( int, w ) 22.35/22.42 ( int, y ) 22.35/22.42 ( int, x ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.35/22.42 ( int, skv_6 ) 22.35/22.42 ( int, skv_7 ) 22.35/22.42 ( int, skv_16 ) 22.35/22.42 ( int, skv_23 ) 22.35/22.42 ( int, skv_24 ) 22.35/22.42 ( real, (hAPP int real (number_number_of real) min) ) 22.35/22.42 ( 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)))) ) 22.35/22.42 ( complex, ii ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int _let_0 _let_1 X))) (let ((_let_3 (hAPP int _let_0 _let_1 Y))) (= (hAPP int int _let_3 (hAPP int int _let_2 Z_1)) (hAPP int int _let_2 (hAPP int int _let_3 Z_1))))))) ) 22.35/22.42 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126632 $$unsorted) (BOUND_VARIABLE_126633 $$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)) (= (or (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_126633)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_126632))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126633) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_126632) _let_2)))) (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_126632) BOUND_VARIABLE_126633))))))))) ) 22.35/22.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.42 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( 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))))))))) ) 22.35/22.42 ( 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))) ) 22.35/22.42 ( 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))) ) 22.35/22.42 ( 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))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP complex real re (hAPP real complex cis A_1)) (hAPP real real cos A_1)) ) 22.35/22.42 ( pi ) 22.35/22.42 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( (zero_zero real) ) 22.35/22.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.35/22.42 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.35/22.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.35/22.42 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 22.35/22.42 ( skv_10 ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126697 $$unsorted) (BOUND_VARIABLE_126698 $$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_126697) BOUND_VARIABLE_126698))) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_126697) (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_126698) BOUND_VARIABLE_126697)) (ti X_a BOUND_VARIABLE_126698)))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.35/22.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_126742 $$unsorted) (BOUND_VARIABLE_126743 $$unsorted) (BOUND_VARIABLE_126744 $$unsorted) (BOUND_VARIABLE_126745 $$unsorted) (BOUND_VARIABLE_126746 $$unsorted) (BOUND_VARIABLE_126747 $$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_a)) (not (topological_space X_b)) (not (= (ti X_a BOUND_VARIABLE_126747) (ti X_a BOUND_VARIABLE_126746))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_126747)) (= (hAPP X_a X_b BOUND_VARIABLE_126745 X_1) (hAPP X_a X_b BOUND_VARIABLE_126744 X_1))) )) (not (= (ti X_b BOUND_VARIABLE_126742) (ti X_b BOUND_VARIABLE_126743))) (= (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_126744) BOUND_VARIABLE_126742) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_126746))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_126745) BOUND_VARIABLE_126743) (hAPP X_a _let_0 _let_5 BOUND_VARIABLE_126747))))))))))) ) 22.35/22.42 ( real, nat, pi, pi, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), n, n ) 22.35/22.42 ( real, nat, pi, pi, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), tn, n ) 22.35/22.42 ( 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 ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126921 $$unsorted) (BOUND_VARIABLE_126922 $$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_126922))) (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_126921) BOUND_VARIABLE_126922))) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_126921)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_126921)))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.35/22.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (real_1 nat))) (= (hAPP nat real _let_0 (hAPP nat nat suc N)) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real _let_0 N)) (one_one real)))) ) 22.35/22.42 ( (zero_zero nat) ) 22.35/22.42 ( (hAPP nat nat suc (zero_zero nat)) ) 22.35/22.42 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_126948 $$unsorted) (BOUND_VARIABLE_126949 $$unsorted) (BOUND_VARIABLE_126950 $$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_126948) BOUND_VARIABLE_126949)) BOUND_VARIABLE_126950) (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_126948) BOUND_VARIABLE_126950)) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_126949) BOUND_VARIABLE_126950))))))) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), m1 ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), skv_3 ) 22.35/22.42 ( 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) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( 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 ) 22.35/22.42 ( 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), m1 ) 22.35/22.42 ( 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) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.35/22.42 ( 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_21 ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, v ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 22.35/22.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, w ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((Wa $$unsorted) (Ma $$unsorted)) (let ((_let_0 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Wa)))) (= (and (or _let_0 (= (zero_zero nat) Ma)) (or (not _let_0) (= (ti int Wa) (hAPP nat int (semiring_1_of_nat int) Ma)))) (= Ma (hAPP int nat nat_1 Wa)))) ) 22.35/22.42 ( pls, n ) 22.35/22.42 ( (one_one int), (zero_zero nat) ) 22.35/22.42 ( min, (one_one nat) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.42 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((P_1 $$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))) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less int) (zero_zero 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), (one_one int) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), s ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_4 ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (zero_zero int), skv_5 ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less int) min), min, min ) 22.35/22.42 ( nat_neg, min, pls ) 22.35/22.42 ( nat_is_nat, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.35/22.42 ( nat_is_nat, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), (one_one int), t ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) pls), (zero_zero int), pls ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq int) min), (zero_zero int), min ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less int) m1), (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ( (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP int real (number_number_of real) N))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) (hAPP int nat (number_number_of nat) N)))) ) 22.35/22.42 ( (one_one real), (hAPP int int bit1 pls) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_2 (ord_less int) (zero_zero int)) M))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd A_1) M))) (not (hBOOL (hAPP int bool (hAPP int _let_2 (hAPP int (fun int _let_2) zcong A_1) B) M))) (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd B) M)))))) ) 22.35/22.42 ( 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))) ) 22.35/22.42 ( (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))) ) 22.35/22.42 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP 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))) ) 22.35/22.42 ( (hAPP int int (number_number_of int) min), (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))) ) 22.35/22.42 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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))) ) 22.35/22.42 ( 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))) ) 22.35/22.42 ( skv_5, 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))) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (hAPP real (fun real complex) complex_1 A_1))) (= (hAPP real complex _let_0 (hAPP real real (uminus_uminus real) B)) (hAPP complex complex cnj (hAPP real complex _let_0 B)))) ) 22.35/22.42 ( (one_one real), (zero_zero real) ) 22.35/22.42 ( (zero_zero real), (one_one real) ) 22.35/22.42 ( (zero_zero real), (zero_zero real) ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted)) (or (not (zero_neq_one X_a)) (not (= (one_one X_a) (zero_zero X_a)))) ) 22.35/22.42 ( rat ) 22.35/22.42 ( int ) 22.35/22.42 ( nat ) 22.35/22.42 ( real ) 22.35/22.42 ( complex ) 22.35/22.42 ( quickcheck_code_int ) 22.35/22.42 ( code_code_numeral ) 22.35/22.42 ) 22.35/22.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127228 $$unsorted) (BOUND_VARIABLE_127229 $$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_127228) BOUND_VARIABLE_127229)) BOUND_VARIABLE_127228) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127229) BOUND_VARIABLE_127228))))) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.35/22.42 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.35/22.42 ( 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) ) 22.35/22.42 ( 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) ) 22.35/22.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.35/22.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.35/22.42 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.35/22.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.37/22.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.43 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.37/22.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( nat, (one_one nat), (one_one nat) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real sqrt (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real sqrt X)))) ) 22.37/22.43 ( (one_one real) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127257 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_127257)) (= (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_127257)) BOUND_VARIABLE_127257))) ) 22.37/22.43 ( int, pls ) 22.37/22.43 ( int, min ) 22.37/22.43 ( int, s ) 22.37/22.43 ( int, s1 ) 22.37/22.43 ( int, m ) 22.37/22.43 ( int, t ) 22.37/22.43 ( int, v ) 22.37/22.43 ( int, w ) 22.37/22.43 ( int, y ) 22.37/22.43 ( int, sa ) 22.37/22.43 ( int, x ) 22.37/22.43 ( int, r ) 22.37/22.43 ( int, m1 ) 22.37/22.43 ( int, skv_14 ) 22.37/22.43 ( int, skv_20 ) 22.37/22.43 ( (fun int int), bit1 ) 22.37/22.43 ( (fun int int), bit0 ) 22.37/22.43 ( (fun int int), succ ) 22.37/22.43 ( (fun int int), pred ) 22.37/22.43 ( (fun int int), (fact_fact int) ) 22.37/22.43 ( (fun int int), zfact ) 22.37/22.43 ( nat, n ) 22.37/22.43 ( nat, tn ) 22.37/22.43 ( bool, fTrue ) 22.37/22.43 ( bool, fFalse ) 22.37/22.43 ( real, pi ) 22.37/22.43 ( real, (zero_zero real) ) 22.37/22.43 ( (fun nat real), (real_1 nat) ) 22.37/22.43 ( (fun nat real), cos_coeff ) 22.37/22.43 ( (fun nat real), sin_coeff ) 22.37/22.43 ( (fun real real), sin ) 22.37/22.43 ( (fun real real), cos ) 22.37/22.43 ( (fun real real), sqrt ) 22.37/22.43 ( (fun real real), tan ) 22.37/22.43 ( (fun real real), ln ) 22.37/22.43 ( (fun real real), arctan ) 22.37/22.43 ( (fun real real), arcsin ) 22.37/22.43 ( (fun real real), arccos ) 22.37/22.43 ( (fun nat nat), suc ) 22.37/22.43 ( (fun nat nat), (fact_fact nat) ) 22.37/22.43 ( (fun nat nat), nat_size ) 22.37/22.43 ( (fun nat nat), (size_size nat) ) 22.37/22.43 ( (fun nat nat), fact ) 22.37/22.43 ( (filter nat), sequentially ) 22.37/22.43 ( (fun int (fun int rat)), fract ) 22.37/22.43 ( complex, ii ) 22.37/22.43 ( (fun int bool), zOdd ) 22.37/22.43 ( (fun int bool), zprime ) 22.37/22.43 ( (fun int bool), zEven ) 22.37/22.43 ( (fun int bool), nat_neg ) 22.37/22.43 ( (fun int bool), nat_is_nat ) 22.37/22.43 ( (fun int bool), (even_odd_even int) ) 22.37/22.43 ( (fun int bool), twoSqu1091635170sum2sq ) 22.37/22.43 ( (fun int (fun int int)), legacy_zgcd ) 22.37/22.43 ( (fun int (fun int int)), (gcd_gcd int) ) 22.37/22.43 ( (fun int (fun int int)), inv ) 22.37/22.43 ( (fun int (fun int int)), multInv ) 22.37/22.43 ( (fun int (fun int int)), legendre ) 22.37/22.43 ( (fun int (fun int int)), standardRes ) 22.37/22.43 ( (fun int (fun int int)), nat_tsub ) 22.37/22.43 ( (fun int (fun int int)), z3div ) 22.37/22.43 ( (fun int (fun int int)), z3mod ) 22.37/22.43 ( (fun int (fun int int)), int_lcm ) 22.37/22.43 ( (fun int (fun int int)), int_gcd ) 22.37/22.43 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.37/22.43 ( (fun bool bool), fNot ) 22.37/22.43 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.37/22.43 ( (fun bool (fun bool bool)), fconj ) 22.37/22.43 ( (fun bool (fun bool bool)), fdisj ) 22.37/22.43 ( (fun bool (fun bool bool)), fimplies ) 22.37/22.43 ( (fun int (fun int bool)), quadRes ) 22.37/22.43 ( (fun int (fun int bool)), d22set ) 22.37/22.43 ( (fun int (fun int bool)), norRRset ) 22.37/22.43 ( (fun int (fun int bool)), sRStar ) 22.37/22.43 ( (fun int (fun int bool)), sr ) 22.37/22.43 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.37/22.43 ( (fun nat bool), (even_odd_even nat) ) 22.37/22.43 ( (fun nat bool), prime ) 22.37/22.43 ( (fun real complex), cis ) 22.37/22.43 ( (fun nat (fun nat bool)), coprime ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.37/22.43 ( (fun (product_prod int int) bool), frac_1 ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.37/22.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.37/22.43 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.37/22.43 ( (fun (fun int bool) bool), nat_nat_set ) 22.37/22.43 ( (fun nat (fun real real)), root ) 22.37/22.43 ( (fun real (fun real real)), log ) 22.37/22.43 ( (fun real (fun real real)), powr ) 22.37/22.43 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.37/22.43 ( (fun complex complex), cnj ) 22.37/22.43 ( (fun complex complex), expi ) 22.37/22.43 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.37/22.43 ( (fun nat (fun nat nat)), nat_gcd ) 22.37/22.43 ( (fun nat (fun nat nat)), nat_lcm ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.37/22.43 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.37/22.43 ( (fun int (fun (fun int bool) bool)), resSet ) 22.37/22.43 ( (fun int nat), nat_1 ) 22.37/22.43 ( (fun int nat), phi ) 22.37/22.43 ( (fun complex real), re ) 22.37/22.43 ( (fun complex real), im ) 22.37/22.43 ( (fun complex real), arg ) 22.37/22.43 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.37/22.43 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.37/22.43 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.37/22.43 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.37/22.43 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.37/22.43 ( (fun (product_prod nat nat) bool), pred_nat ) 22.37/22.43 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.37/22.43 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.37/22.43 ( (fun (fun int bool) int), (the int) ) 22.37/22.43 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.37/22.43 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.37/22.43 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.37/22.43 ( (fun real (fun real complex)), rcis ) 22.37/22.43 ( (fun real (fun real complex)), complex_1 ) 22.37/22.43 ( (fun int (fun int (fun int bool))), zcong ) 22.37/22.43 ( (fun int (fun int (fun int bool))), wset ) 22.37/22.43 ( (fun int (fun int (fun int bool))), noXRRset ) 22.37/22.43 ( (fun int (fun int (fun int bool))), bnorRset ) 22.37/22.43 ( (fun int (fun int (fun int bool))), zcongm ) 22.37/22.43 ( (fun real nat), natceiling ) 22.37/22.43 ( (fun real nat), natfloor ) 22.37/22.43 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.37/22.43 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.37/22.43 ( (fun int real), (real_1 int) ) 22.37/22.43 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.37/22.43 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.37/22.43 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.37/22.43 ( (fun complex nat), (size_size complex) ) 22.37/22.43 ( (fun complex nat), complex_size ) 22.37/22.43 ( (fun (fun nat rat) bool), vanishes ) 22.37/22.43 ( (fun (product_prod int int) rat), frct ) 22.37/22.43 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.37/22.43 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.37/22.43 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.37/22.43 ( (fun rat real), ratreal ) 22.37/22.43 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.37/22.43 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.37/22.43 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.37/22.43 ( (fun rat (product_prod int int)), quotient_of ) 22.37/22.43 ( (fun int (fun nat nat)), nat_aux ) 22.37/22.43 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.37/22.43 ( (fun int (list int)), quickc666637781d_zero ) 22.37/22.43 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.37/22.43 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.37/22.43 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.37/22.43 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.37/22.43 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.37/22.43 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.37/22.43 ( (fun code_code_numeral int), code_int_of ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127349 $$unsorted)) (or (not (linordered_field X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_127349)))))) ) 22.37/22.43 ( int, (one_one nat) ) 22.37/22.43 ( real, (one_one nat) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$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)))) ) 22.37/22.43 ( rat ) 22.37/22.43 ( int ) 22.37/22.43 ( (fun int int) ) 22.37/22.43 ( nat ) 22.37/22.43 ( bool ) 22.37/22.43 ( real ) 22.37/22.43 ( (fun nat real) ) 22.37/22.43 ( (fun real real) ) 22.37/22.43 ( complex ) 22.37/22.43 ( (fun int bool) ) 22.37/22.43 ( (product_prod int int) ) 22.37/22.43 ( (fun (product_prod int int) int) ) 22.37/22.43 ( (fun int (fun int bool)) ) 22.37/22.43 ( (fun nat bool) ) 22.37/22.43 ( (fun (product_prod int int) bool) ) 22.37/22.43 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.37/22.43 ( (fun real bool) ) 22.37/22.43 ( quickcheck_code_int ) 22.37/22.43 ( code_code_numeral ) 22.37/22.43 ( (fun int (fun int (fun int bool))) ) 22.37/22.43 ( (fun int real) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127463 $$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_127463) (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_127463)) (one_one X_a))))) ) 22.37/22.43 ( int, pls ) 22.37/22.43 ( int, (hAPP int int bit1 pls) ) 22.37/22.43 ( int, min ) 22.37/22.43 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.43 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.43 ( nat, pls ) 22.37/22.43 ( nat, (hAPP int int bit1 pls) ) 22.37/22.43 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.43 ( real, min ) 22.37/22.43 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.43 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.43 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.43 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.37/22.43 ( 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)))))))) ) 22.37/22.43 ( complex, min ) 22.37/22.43 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ( quickcheck_code_int, pls ) 22.37/22.43 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.37/22.43 ( quickcheck_code_int, (one_one int) ) 22.37/22.43 ( code_code_numeral, pls ) 22.37/22.43 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127496 $$unsorted) (BOUND_VARIABLE_127497 $$unsorted) (BOUND_VARIABLE_127498 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (hAPP nat (fun nat _let_1) (ord_atLeastLessThan nat) _let_0))) (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 (fun _let_1 X_a))) (let ((_let_7 (big_co1399186613setsum nat X_a))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (power_power X_a))) (let ((_let_10 (minus_minus X_a))) (let ((_let_11 (hAPP X_a _let_5 _let_9 (hAPP X_a X_a (hAPP X_a _let_3 (plus_plus X_a) BOUND_VARIABLE_127496) BOUND_VARIABLE_127498)))) (let ((_let_12 (hAPP X_a _let_5 _let_9 BOUND_VARIABLE_127496))) (let ((_let_13 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) BOUND_VARIABLE_127497) (hAPP nat nat suc _let_0)))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_127498)) (= (hAPP X_a X_a (hAPP X_a _let_3 _let_10 (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_10 (hAPP nat X_a _let_11 BOUND_VARIABLE_127497)) (hAPP nat X_a _let_12 BOUND_VARIABLE_127497))) BOUND_VARIABLE_127498)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_127497)) (hAPP nat X_a _let_12 _let_13))) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_127498) (hAPP _let_1 X_a (hAPP _let_5 _let_6 _let_7 (hAPP (fun nat _let_1) _let_5 (hAPP _let_6 (fun (fun nat _let_1) _let_5) (combb _let_1 X_a nat) (hAPP _let_5 _let_6 _let_7 (hAPP _let_5 _let_5 (hAPP _let_8 (fun _let_5 _let_5) (combs nat X_a X_a) (hAPP _let_5 _let_8 (hAPP (fun X_a _let_3) (fun _let_5 _let_8) (combb X_a _let_3 nat) _let_4) _let_11)) (hAPP (fun nat nat) _let_5 (hAPP _let_5 (fun (fun nat nat) _let_5) (combb nat X_a nat) _let_12) (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) BOUND_VARIABLE_127497) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) (hAPP (fun nat nat) (fun nat _let_1) (hAPP (fun nat _let_1) (fun (fun nat nat) (fun nat _let_1)) (combb nat _let_1 nat) _let_2) (hAPP nat (fun nat nat) (minus_minus nat) _let_13)))) (hAPP nat _let_1 _let_2 _let_13))))))))))))))))))) ) 22.37/22.43 ( int, (one_one int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP nat int (semiring_1_of_nat int) n) ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), m1 ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (hAPP nat nat suc N))) (= (hAPP nat nat fact _let_0) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_0) (hAPP nat nat fact N)))) ) 22.37/22.43 ( (zero_zero nat) ) 22.37/22.43 ( (hAPP nat nat suc (zero_zero nat)) ) 22.37/22.43 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127550 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_127550) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_127550)))) ) 22.37/22.43 ( int, (one_one int) ) 22.37/22.43 ( int, min ) 22.37/22.43 ( int, (zero_zero int) ) 22.37/22.43 ( int, v ) 22.37/22.43 ( int, w ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.37/22.43 ( int, skv_14 ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.37/22.43 ( int, skv_20 ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.37/22.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.43 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( real, (zero_zero real) ) 22.37/22.43 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( real, skv_10 ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((R_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (inverse_divide real))) (let ((_let_3 (number_number_of rat))) (= (hAPP real real (hAPP real _let_1 _let_2 (hAPP int real _let_0 R_3)) (hAPP int real _let_0 S_3)) (hAPP real real (hAPP real _let_1 _let_2 (hAPP rat real ratreal (hAPP int rat _let_3 R_3))) (hAPP rat real ratreal (hAPP int rat _let_3 S_3)))))))) ) 22.37/22.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((M $$unsorted) (N $$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))) (= _let_0 _let_1) (= (hAPP int int (number_number_of int) min) _let_1)))) ) 22.37/22.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.37/22.43 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ( (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))), t ) 22.37/22.43 ( (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))), m1 ) 22.37/22.43 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.37/22.43 ( (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))), skv_21 ) 22.37/22.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.37/22.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.37/22.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.37/22.43 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.37/22.43 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.37/22.43 ( y, v ) 22.37/22.43 ( y, w ) 22.37/22.43 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ( sa, v ) 22.37/22.43 ( sa, w ) 22.37/22.43 ( x, v ) 22.37/22.43 ( x, w ) 22.37/22.43 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.43 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ( r, v ) 22.37/22.43 ( r, w ) 22.37/22.43 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.37/22.43 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.37/22.43 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.37/22.43 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.37/22.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.37/22.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.37/22.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.37/22.43 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (uminus_uminus int))) (let ((_let_1 (one_one int))) (let ((_let_2 (product_prod int 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_mod int) _let_1) _let_3) (hAPP _let_2 int (product_snd int int) (hAPP _let_2 _let_2 negateSnd (hAPP int _let_2 (hAPP int (fun int _let_2) negDivAlg (hAPP int int _let_0 _let_1)) (hAPP int int _let_0 _let_3)))))))))) ) 22.37/22.43 ( pls ) 22.37/22.43 ( (hAPP int int bit1 pls) ) 22.37/22.43 ( min ) 22.37/22.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.43 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.43 ) 22.37/22.43 (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_lessThan nat) K_1))))) )) (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S))) ) 22.37/22.43 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((B_2 $$unsorted) (A_3 $$unsorted) (D_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) D_1))) (= (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) D_1)) (forall ((E $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (dvd_dvd int) E))) (or (not (hBOOL (hAPP int bool _let_0 A_3))) (not (hBOOL (hAPP int bool _let_0 B_2))) (hBOOL (hAPP int bool _let_0 D_1)))) ) (hBOOL (hAPP int bool _let_0 B_2)) (hBOOL (hAPP int bool _let_0 A_3))) (= (ti int D_1) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) A_3) B_2)))) ) 22.37/22.43 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.43 ( (hAPP 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)), (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.43 ) 22.37/22.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127718 $$unsorted) (BOUND_VARIABLE_127719 $$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_127719))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_127718))) (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_127719) BOUND_VARIABLE_127718))))) ) 22.37/22.43 ( 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)))) ) 22.37/22.43 ( 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) ) 22.37/22.43 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.37/22.43 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.37/22.43 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.43 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.37/22.43 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.37/22.43 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.37/22.43 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.37/22.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( nat, (one_one nat), (one_one nat) ) 22.37/22.47 ) 22.37/22.47 (instantiation (forall ((A_3 $$unsorted) (B_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) (plus_plus int) A_3) B_2)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_3) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_2) zOdd)))))) ) 22.37/22.47 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.37/22.47 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.37/22.47 ( (hAPP nat int (hAPP 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) ) 22.37/22.47 ( (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) ) 22.37/22.47 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.37/22.47 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.47 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.47 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.47 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.37/22.47 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ) 22.37/22.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127813 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_127813)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_127813) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_127813)))) ) 22.37/22.47 ( int, pls ) 22.37/22.47 ( int, min ) 22.37/22.47 ( int, s ) 22.37/22.47 ( int, s1 ) 22.37/22.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( int, m ) 22.37/22.47 ( 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))) ) 22.37/22.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.47 ( int, t ) 22.37/22.47 ( int, v ) 22.37/22.47 ( int, w ) 22.37/22.47 ( int, y ) 22.37/22.47 ( int, sa ) 22.37/22.47 ( int, x ) 22.37/22.47 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.37/22.47 ( int, r ) 22.37/22.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.37/22.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.37/22.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( int, m1 ) 22.37/22.47 ( int, skv_13 ) 22.37/22.47 ( int, skv_14 ) 22.37/22.47 ( int, skv_19 ) 22.37/22.47 ( int, skv_20 ) 22.37/22.47 ( (fun int int), bit1 ) 22.37/22.47 ( (fun int int), bit0 ) 22.37/22.47 ( (fun int int), succ ) 22.37/22.47 ( (fun int int), pred ) 22.37/22.47 ( (fun int int), (fact_fact int) ) 22.37/22.47 ( (fun int int), zfact ) 22.37/22.47 ( nat, n ) 22.37/22.47 ( nat, tn ) 22.37/22.47 ( bool, fTrue ) 22.37/22.47 ( bool, fFalse ) 22.37/22.47 ( real, pi ) 22.37/22.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.47 ( real, (zero_zero real) ) 22.37/22.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.47 ( 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))))) ) 22.37/22.47 ( (fun nat real), (real_1 nat) ) 22.37/22.47 ( (fun nat real), cos_coeff ) 22.37/22.47 ( (fun nat real), sin_coeff ) 22.37/22.47 ( (fun real real), sin ) 22.37/22.47 ( (fun real real), cos ) 22.37/22.47 ( (fun real real), sqrt ) 22.37/22.47 ( (fun real real), tan ) 22.37/22.47 ( (fun real real), ln ) 22.37/22.47 ( (fun real real), arctan ) 22.37/22.47 ( (fun real real), arcsin ) 22.37/22.47 ( (fun real real), arccos ) 22.37/22.47 ( (fun nat nat), suc ) 22.37/22.47 ( (fun nat nat), (fact_fact nat) ) 22.37/22.47 ( (fun nat nat), nat_size ) 22.37/22.47 ( (fun nat nat), (size_size nat) ) 22.37/22.47 ( (fun nat nat), fact ) 22.37/22.47 ( (filter nat), sequentially ) 22.37/22.47 ( (fun int (fun int rat)), fract ) 22.37/22.47 ( complex, ii ) 22.37/22.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.47 ( 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)) ) 22.37/22.47 ( (fun int bool), zOdd ) 22.37/22.47 ( (fun int bool), zprime ) 22.37/22.47 ( (fun int bool), zEven ) 22.37/22.47 ( (fun int bool), nat_neg ) 22.37/22.47 ( (fun int bool), nat_is_nat ) 22.37/22.47 ( (fun int bool), (even_odd_even int) ) 22.37/22.47 ( (fun int bool), twoSqu1091635170sum2sq ) 22.37/22.47 ( (fun int (fun int int)), legacy_zgcd ) 22.37/22.47 ( (fun int (fun int int)), (gcd_gcd int) ) 22.37/22.47 ( (fun int (fun int int)), inv ) 22.37/22.47 ( (fun int (fun int int)), multInv ) 22.37/22.47 ( (fun int (fun int int)), legendre ) 22.37/22.47 ( (fun int (fun int int)), standardRes ) 22.37/22.47 ( (fun int (fun int int)), nat_tsub ) 22.37/22.47 ( (fun int (fun int int)), z3div ) 22.37/22.47 ( (fun int (fun int int)), z3mod ) 22.37/22.47 ( (fun int (fun int int)), int_lcm ) 22.37/22.47 ( (fun int (fun int int)), int_gcd ) 22.37/22.47 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.37/22.47 ( (fun bool bool), fNot ) 22.37/22.47 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.37/22.47 ( (fun bool (fun bool bool)), fconj ) 22.37/22.47 ( (fun bool (fun bool bool)), fdisj ) 22.37/22.47 ( (fun bool (fun bool bool)), fimplies ) 22.37/22.47 ( (fun int (fun int bool)), quadRes ) 22.37/22.47 ( (fun int (fun int bool)), d22set ) 22.37/22.47 ( (fun int (fun int bool)), norRRset ) 22.37/22.47 ( (fun int (fun int bool)), sRStar ) 22.37/22.47 ( (fun int (fun int bool)), sr ) 22.37/22.47 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.37/22.47 ( (fun nat bool), (even_odd_even nat) ) 22.37/22.47 ( (fun nat bool), prime ) 22.37/22.47 ( (fun real complex), cis ) 22.37/22.47 ( (fun nat (fun nat bool)), coprime ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.37/22.47 ( (fun (product_prod int int) bool), frac_1 ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.37/22.47 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.37/22.47 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.37/22.47 ( (fun (fun int bool) bool), nat_nat_set ) 22.37/22.47 ( (fun nat (fun real real)), root ) 22.37/22.47 ( (fun real (fun real real)), log ) 22.37/22.47 ( (fun real (fun real real)), powr ) 22.37/22.47 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.37/22.47 ( (fun complex complex), cnj ) 22.37/22.47 ( (fun complex complex), expi ) 22.37/22.47 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.37/22.47 ( (fun nat (fun nat nat)), nat_gcd ) 22.37/22.47 ( (fun nat (fun nat nat)), nat_lcm ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.37/22.47 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.37/22.48 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.37/22.48 ( (fun int (fun (fun int bool) bool)), resSet ) 22.37/22.48 ( (fun int nat), nat_1 ) 22.37/22.48 ( (fun int nat), phi ) 22.37/22.48 ( (fun complex real), re ) 22.37/22.48 ( (fun complex real), im ) 22.37/22.48 ( (fun complex real), arg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.37/22.48 ( (fun (product_prod nat nat) bool), pred_nat ) 22.37/22.48 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.37/22.48 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.37/22.48 ( (fun (fun int bool) int), (the int) ) 22.37/22.48 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.37/22.48 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.37/22.48 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.37/22.48 ( (fun real (fun real complex)), rcis ) 22.37/22.48 ( (fun real (fun real complex)), complex_1 ) 22.37/22.48 ( (fun int (fun int (fun int bool))), zcong ) 22.37/22.48 ( (fun int (fun int (fun int bool))), wset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), noXRRset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), bnorRset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), zcongm ) 22.37/22.48 ( (fun real nat), natceiling ) 22.37/22.48 ( (fun real nat), natfloor ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.37/22.48 ( (fun int real), (real_1 int) ) 22.37/22.48 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.37/22.48 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.37/22.48 ( (fun complex nat), (size_size complex) ) 22.37/22.48 ( (fun complex nat), complex_size ) 22.37/22.48 ( (fun (fun nat rat) bool), vanishes ) 22.37/22.48 ( (fun (product_prod int int) rat), frct ) 22.37/22.48 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.37/22.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.37/22.48 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.37/22.48 ( (fun rat real), ratreal ) 22.37/22.48 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.37/22.48 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.37/22.48 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.37/22.48 ( (fun rat (product_prod int int)), quotient_of ) 22.37/22.48 ( (fun int (fun nat nat)), nat_aux ) 22.37/22.48 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.37/22.48 ( (fun int (list int)), quickc666637781d_zero ) 22.37/22.48 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.37/22.48 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.37/22.48 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.37/22.48 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.37/22.48 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.37/22.48 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.37/22.48 ( (fun code_code_numeral int), code_int_of ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (uminus T_1)) (uminus (fun T_2 T_1))) ) 22.37/22.48 ( rat, real ) 22.37/22.48 ( rat, (product_prod int int) ) 22.37/22.48 ( int, rat ) 22.37/22.48 ( int, int ) 22.37/22.48 ( int, (fun int int) ) 22.37/22.48 ( int, nat ) 22.37/22.48 ( int, bool ) 22.37/22.48 ( int, real ) 22.37/22.48 ( int, (fun nat real) ) 22.37/22.48 ( int, (fun real real) ) 22.37/22.48 ( int, (fun nat nat) ) 22.37/22.48 ( int, (fun int rat) ) 22.37/22.48 ( int, (fun int bool) ) 22.37/22.48 ( int, (product_prod int int) ) 22.37/22.48 ( int, (fun (product_prod int int) int) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.37/22.48 ( int, (fun nat int) ) 22.37/22.48 ( int, (fun bool bool) ) 22.37/22.48 ( int, (fun int (fun bool bool)) ) 22.37/22.48 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( int, (fun int (fun int bool)) ) 22.37/22.48 ( int, (fun nat bool) ) 22.37/22.48 ( int, (fun (product_prod int int) bool) ) 22.37/22.48 ( int, (fun int (fun (product_prod int int) bool)) ) 22.37/22.48 ( int, quickcheck_code_int ) 22.37/22.48 ( int, (fun (fun int bool) bool) ) 22.37/22.48 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.37/22.48 ( int, (product_prod int (product_prod int int)) ) 22.37/22.48 ( int, (fun int (product_prod int (product_prod int int))) ) 22.37/22.48 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 22.37/22.48 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.37/22.48 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.37/22.48 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.37/22.48 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.37/22.48 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.37/22.48 ( int, (fun nat (fun bool bool)) ) 22.37/22.48 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( int, (fun int (product_prod int int)) ) 22.37/22.48 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.37/22.48 ( int, (fun int (fun (fun int bool) bool)) ) 22.37/22.48 ( int, (fun (fun int int) (fun int bool)) ) 22.37/22.48 ( int, (list int) ) 22.37/22.48 ( int, (fun int (fun int (fun int bool))) ) 22.37/22.48 ( int, (fun int real) ) 22.37/22.48 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun int int), (fun int int) ) 22.37/22.48 ( (fun int int), (fun int bool) ) 22.37/22.48 ( (fun int int), (fun int (fun int int)) ) 22.37/22.48 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun int int), (fun int (fun int bool)) ) 22.37/22.48 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.37/22.48 ( nat, rat ) 22.37/22.48 ( nat, int ) 22.37/22.48 ( nat, (fun int int) ) 22.37/22.48 ( nat, nat ) 22.37/22.48 ( nat, bool ) 22.37/22.48 ( nat, real ) 22.37/22.48 ( nat, (fun real real) ) 22.37/22.48 ( nat, (fun nat nat) ) 22.37/22.48 ( nat, complex ) 22.37/22.48 ( nat, (product_prod int int) ) 22.37/22.48 ( nat, (fun bool bool) ) 22.37/22.48 ( nat, (fun nat bool) ) 22.37/22.48 ( nat, (fun nat (fun nat bool)) ) 22.37/22.48 ( nat, (fun nat (product_prod int int)) ) 22.37/22.48 ( nat, (product_prod real real) ) 22.37/22.48 ( nat, (product_prod nat nat) ) 22.37/22.48 ( nat, (fun (product_prod nat nat) bool) ) 22.37/22.48 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 22.37/22.48 ( nat, (fun nat (product_prod nat nat)) ) 22.37/22.48 ( bool, bool ) 22.37/22.48 ( bool, (fun bool bool) ) 22.37/22.48 ( real, nat ) 22.37/22.48 ( real, bool ) 22.37/22.48 ( real, real ) 22.37/22.48 ( real, (fun nat real) ) 22.37/22.48 ( real, (fun real real) ) 22.37/22.48 ( real, (fun (filter nat) bool) ) 22.37/22.48 ( real, complex ) 22.37/22.48 ( real, (fun int bool) ) 22.37/22.48 ( real, (fun bool bool) ) 22.37/22.48 ( real, (fun int (fun int bool)) ) 22.37/22.48 ( real, (fun real complex) ) 22.37/22.48 ( real, (fun real bool) ) 22.37/22.48 ( real, (fun nat (product_prod real real)) ) 22.37/22.48 ( real, (fun real (fun nat (product_prod real real))) ) 22.37/22.48 ( real, (fun (filter real) bool) ) 22.37/22.48 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 22.37/22.48 ( real, (fun int (fun int (fun bool bool))) ) 22.37/22.48 ( real, (fun int (fun nat bool)) ) 22.37/22.48 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 22.37/22.48 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( real, (fun int (fun nat (fun bool bool))) ) 22.37/22.48 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.37/22.48 ( real, (fun (fun nat real) (fun nat bool)) ) 22.37/22.48 ( real, (fun (fun int real) (fun int bool)) ) 22.37/22.48 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.37/22.48 ( (fun nat real), (fun nat real) ) 22.37/22.48 ( (fun nat real), (fun nat bool) ) 22.37/22.48 ( (fun nat real), (fun nat (fun real real)) ) 22.37/22.48 ( (fun nat real), (fun int (fun nat real)) ) 22.37/22.48 ( (fun real real), (fun real real) ) 22.37/22.48 ( (fun real real), (fun real (fun real bool)) ) 22.37/22.48 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun real real), (fun real (fun real real)) ) 22.37/22.48 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun nat nat), (fun nat real) ) 22.37/22.48 ( (fun nat nat), (fun nat (fun nat bool)) ) 22.37/22.48 ( (fun nat nat), (fun nat (fun nat nat)) ) 22.37/22.48 ( (filter nat), bool ) 22.37/22.48 ( complex, nat ) 22.37/22.48 ( complex, real ) 22.37/22.48 ( complex, complex ) 22.37/22.48 ( (fun int bool), int ) 22.37/22.48 ( (fun int bool), bool ) 22.37/22.48 ( (fun int bool), (fun int bool) ) 22.37/22.48 ( (fun int bool), (fun int (fun int int)) ) 22.37/22.48 ( (fun int bool), (fun int (fun bool bool)) ) 22.37/22.48 ( (fun int bool), (fun int (fun int bool)) ) 22.37/22.48 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 22.37/22.48 ( (fun int bool), (fun real (fun int (fun int bool))) ) 22.37/22.48 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 22.37/22.48 ( (product_prod int int), rat ) 22.37/22.48 ( (product_prod int int), int ) 22.37/22.48 ( (product_prod int int), (fun int int) ) 22.37/22.48 ( (product_prod int int), bool ) 22.37/22.48 ( (product_prod int int), (fun int bool) ) 22.37/22.48 ( (product_prod int int), (product_prod int int) ) 22.37/22.48 ( (product_prod int int), (fun (product_prod int int) int) ) 22.37/22.48 ( (product_prod int int), (fun bool bool) ) 22.37/22.48 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.37/22.48 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 22.37/22.48 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.37/22.48 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 22.37/22.48 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 22.37/22.48 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 22.37/22.48 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 22.37/22.48 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 22.37/22.48 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (fun int (fun int bool)), (fun int bool) ) 22.37/22.48 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 22.37/22.48 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 22.37/22.48 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 22.37/22.48 ( (fun nat bool), bool ) 22.37/22.48 ( (fun nat bool), (fun nat bool) ) 22.37/22.48 ( (fun nat bool), (fun nat (fun bool bool)) ) 22.37/22.48 ( (fun nat bool), (fun int (fun nat bool)) ) 22.37/22.48 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 22.37/22.48 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 22.37/22.48 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (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)))) ) 22.37/22.48 ( (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)))) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (fun real bool), real ) 22.37/22.48 ( (fun real bool), (fun real bool) ) 22.37/22.48 ( (fun real bool), (fun real (fun bool bool)) ) 22.37/22.48 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 22.37/22.48 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 22.37/22.48 ( quickcheck_code_int, int ) 22.37/22.48 ( quickcheck_code_int, nat ) 22.37/22.48 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 22.37/22.48 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 22.37/22.48 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 22.37/22.48 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 22.37/22.48 ( code_code_numeral, int ) 22.37/22.48 ( code_code_numeral, nat ) 22.37/22.48 ( code_code_numeral, (fun nat nat) ) 22.37/22.48 ( code_code_numeral, code_code_numeral ) 22.37/22.48 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 22.37/22.48 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.37/22.48 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.37/22.48 ( (product_prod real real), bool ) 22.37/22.48 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 22.37/22.48 ( (filter real), bool ) 22.37/22.48 ( (product_prod nat nat), bool ) 22.37/22.48 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 22.37/22.48 ( (fun nat rat), bool ) 22.37/22.48 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 22.37/22.48 ( (fun int real), (fun int bool) ) 22.37/22.48 ( (fun int real), (fun int real) ) 22.37/22.48 ( (fun int real), (fun int (fun real real)) ) 22.37/22.48 ( (fun int real), (fun int (fun int real)) ) 22.37/22.48 ( (fun real (fun int bool)), (fun real bool) ) 22.37/22.48 ( (fun int (fun nat bool)), (fun int bool) ) 22.37/22.48 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 22.37/22.48 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 22.37/22.48 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 22.37/22.48 ( (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))) ) 22.37/22.48 ( (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)))) ) 22.37/22.48 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.37/22.48 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 22.37/22.48 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 22.37/22.48 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.37/22.48 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 22.37/22.48 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 22.37/22.48 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.37/22.48 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 22.37/22.48 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 22.37/22.48 ( (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)))) ) 22.37/22.48 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.37/22.48 ( (fun int (fun int real)), (fun int (fun int bool)) ) 22.37/22.48 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 22.37/22.48 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun real complex))) (= (hAPP real complex (hAPP real _let_0 complex_1 (hAPP real real (uminus_uminus real) B)) A_1) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_0 complex_1 A_1) B)) ii))) ) 22.37/22.48 ( (one_one real), (zero_zero real) ) 22.37/22.48 ( (zero_zero real), (one_one real) ) 22.37/22.48 ( (zero_zero real), (zero_zero real) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127903 $$unsorted) (BOUND_VARIABLE_127904 $$unsorted) (BOUND_VARIABLE_127905 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127903))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_127904) BOUND_VARIABLE_127905)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_127904)) BOUND_VARIABLE_127905)))))) ) 22.37/22.48 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), m1 ) 22.37/22.48 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_127924 $$unsorted) (BOUND_VARIABLE_127925 $$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_127924) BOUND_VARIABLE_127925)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_127924)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_127925))))))) ) 22.37/22.48 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.37/22.48 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.37/22.48 ( 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) ) 22.37/22.48 ( 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) ) 22.37/22.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.37/22.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.48 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.48 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.37/22.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( nat, (one_one nat), (one_one nat) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X $$unsorted) (Y $$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)))) (let ((_let_3 (hAPP complex real re Y))) (let ((_let_4 (hAPP real _let_0 _let_1 (hAPP complex real im X)))) (let ((_let_5 (hAPP complex real im Y))) (= (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))) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X) Y)))))))) ) 22.37/22.48 ( ii, ii ) 22.37/22.48 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.37/22.48 ( (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 ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (not (forall ((X_1 $$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 (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) _let_2))) (not (= Y (hAPP real real sin X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y_1) _let_2))) (not (= Y (hAPP real real sin Y_1))) (= X_1 Y_1)) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) _let_2)) X_1))))) ))))) ) 22.37/22.48 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.48 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero real) ) 22.37/22.48 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( skv_10 ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) (hAPP real real ln Xa))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (one_one real)) Xa))))))) ) 22.37/22.48 ( pi ) 22.37/22.48 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (one_one real) ) 22.37/22.48 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( skv_2 ) 22.37/22.48 ( skv_9 ) 22.37/22.48 ( skv_12 ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Xa) Ya))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) Ya))) (not (hBOOL (hAPP _let_0 bool (hAPP real (fun _let_0 bool) (member real) X_1) (field_char_0_Rats real))))))) ))) ) 22.37/22.48 ( pi, (zero_zero real) ) 22.37/22.48 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.48 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero real), pi ) 22.37/22.48 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero real), skv_2 ) 22.37/22.48 ( (zero_zero real), skv_9 ) 22.37/22.48 ( (zero_zero real), skv_12 ) 22.37/22.48 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.37/22.48 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 22.37/22.48 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_1) _let_1) P_5))) (= _let_1 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))))) ) 22.37/22.48 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (hAPP int int (hAPP int (fun int int) legendre A_1) P_5))) (let ((_let_1 (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_5) A_1)))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int (fun int (fun int bool)) zcong A_1) (zero_zero int)) P_5)) (and (or _let_1 (= (hAPP int int (number_number_of int) min) _let_0)) (or (not _let_1) (= (one_one int) _let_0)))))) ) 22.37/22.48 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128064 $$unsorted)) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_128064)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_128064) BOUND_VARIABLE_128064))) ) 22.37/22.48 ( int, pls ) 22.37/22.48 ( int, min ) 22.37/22.48 ( int, s ) 22.37/22.48 ( int, s1 ) 22.37/22.48 ( int, m ) 22.37/22.48 ( int, t ) 22.37/22.48 ( int, v ) 22.37/22.48 ( int, w ) 22.37/22.48 ( int, y ) 22.37/22.48 ( int, sa ) 22.37/22.48 ( int, x ) 22.37/22.48 ( int, r ) 22.37/22.48 ( int, m1 ) 22.37/22.48 ( int, skv_14 ) 22.37/22.48 ( int, skv_20 ) 22.37/22.48 ( (fun int int), bit1 ) 22.37/22.48 ( (fun int int), bit0 ) 22.37/22.48 ( (fun int int), succ ) 22.37/22.48 ( (fun int int), pred ) 22.37/22.48 ( (fun int int), (fact_fact int) ) 22.37/22.48 ( (fun int int), zfact ) 22.37/22.48 ( nat, n ) 22.37/22.48 ( nat, tn ) 22.37/22.48 ( bool, fTrue ) 22.37/22.48 ( bool, fFalse ) 22.37/22.48 ( real, pi ) 22.37/22.48 ( real, (one_one real) ) 22.37/22.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.37/22.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (fun nat real), (real_1 nat) ) 22.37/22.48 ( (fun nat real), cos_coeff ) 22.37/22.48 ( (fun nat real), sin_coeff ) 22.37/22.48 ( (fun real real), sin ) 22.37/22.48 ( (fun real real), cos ) 22.37/22.48 ( (fun real real), sqrt ) 22.37/22.48 ( (fun real real), tan ) 22.37/22.48 ( (fun real real), ln ) 22.37/22.48 ( (fun real real), arctan ) 22.37/22.48 ( (fun real real), arcsin ) 22.37/22.48 ( (fun real real), arccos ) 22.37/22.48 ( (fun nat nat), suc ) 22.37/22.48 ( (fun nat nat), (fact_fact nat) ) 22.37/22.48 ( (fun nat nat), nat_size ) 22.37/22.48 ( (fun nat nat), (size_size nat) ) 22.37/22.48 ( (fun nat nat), fact ) 22.37/22.48 ( (filter nat), sequentially ) 22.37/22.48 ( (fun int (fun int rat)), fract ) 22.37/22.48 ( complex, ii ) 22.37/22.48 ( (fun int bool), zOdd ) 22.37/22.48 ( (fun int bool), zprime ) 22.37/22.48 ( (fun int bool), zEven ) 22.37/22.48 ( (fun int bool), nat_neg ) 22.37/22.48 ( (fun int bool), nat_is_nat ) 22.37/22.48 ( (fun int bool), (even_odd_even int) ) 22.37/22.48 ( (fun int bool), twoSqu1091635170sum2sq ) 22.37/22.48 ( (fun int (fun int int)), legacy_zgcd ) 22.37/22.48 ( (fun int (fun int int)), (gcd_gcd int) ) 22.37/22.48 ( (fun int (fun int int)), inv ) 22.37/22.48 ( (fun int (fun int int)), multInv ) 22.37/22.48 ( (fun int (fun int int)), legendre ) 22.37/22.48 ( (fun int (fun int int)), standardRes ) 22.37/22.48 ( (fun int (fun int int)), nat_tsub ) 22.37/22.48 ( (fun int (fun int int)), z3div ) 22.37/22.48 ( (fun int (fun int int)), z3mod ) 22.37/22.48 ( (fun int (fun int int)), int_lcm ) 22.37/22.48 ( (fun int (fun int int)), int_gcd ) 22.37/22.48 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.37/22.48 ( (fun bool bool), fNot ) 22.37/22.48 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.37/22.48 ( (fun bool (fun bool bool)), fconj ) 22.37/22.48 ( (fun bool (fun bool bool)), fdisj ) 22.37/22.48 ( (fun bool (fun bool bool)), fimplies ) 22.37/22.48 ( (fun int (fun int bool)), quadRes ) 22.37/22.48 ( (fun int (fun int bool)), d22set ) 22.37/22.48 ( (fun int (fun int bool)), norRRset ) 22.37/22.48 ( (fun int (fun int bool)), sRStar ) 22.37/22.48 ( (fun int (fun int bool)), sr ) 22.37/22.48 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.37/22.48 ( (fun nat bool), (even_odd_even nat) ) 22.37/22.48 ( (fun nat bool), prime ) 22.37/22.48 ( (fun real complex), cis ) 22.37/22.48 ( (fun nat (fun nat bool)), coprime ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.37/22.48 ( (fun (product_prod int int) bool), frac_1 ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.37/22.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.37/22.48 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.37/22.48 ( (fun (fun int bool) bool), nat_nat_set ) 22.37/22.48 ( (fun nat (fun real real)), root ) 22.37/22.48 ( (fun real (fun real real)), log ) 22.37/22.48 ( (fun real (fun real real)), powr ) 22.37/22.48 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.37/22.48 ( (fun complex complex), cnj ) 22.37/22.48 ( (fun complex complex), expi ) 22.37/22.48 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.37/22.48 ( (fun nat (fun nat nat)), nat_gcd ) 22.37/22.48 ( (fun nat (fun nat nat)), nat_lcm ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.37/22.48 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.37/22.48 ( (fun int (fun (fun int bool) bool)), resSet ) 22.37/22.48 ( (fun int nat), nat_1 ) 22.37/22.48 ( (fun int nat), phi ) 22.37/22.48 ( (fun complex real), re ) 22.37/22.48 ( (fun complex real), im ) 22.37/22.48 ( (fun complex real), arg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.37/22.48 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.37/22.48 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.37/22.48 ( (fun (product_prod nat nat) bool), pred_nat ) 22.37/22.48 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.37/22.48 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.37/22.48 ( (fun (fun int bool) int), (the int) ) 22.37/22.48 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.37/22.48 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.37/22.48 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.37/22.48 ( (fun real (fun real complex)), rcis ) 22.37/22.48 ( (fun real (fun real complex)), complex_1 ) 22.37/22.48 ( (fun int (fun int (fun int bool))), zcong ) 22.37/22.48 ( (fun int (fun int (fun int bool))), wset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), noXRRset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), bnorRset ) 22.37/22.48 ( (fun int (fun int (fun int bool))), zcongm ) 22.37/22.48 ( (fun real nat), natceiling ) 22.37/22.48 ( (fun real nat), natfloor ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.37/22.48 ( (fun int real), (real_1 int) ) 22.37/22.48 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.37/22.48 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.37/22.48 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.37/22.48 ( (fun complex nat), (size_size complex) ) 22.37/22.48 ( (fun complex nat), complex_size ) 22.37/22.48 ( (fun (fun nat rat) bool), vanishes ) 22.37/22.48 ( (fun (product_prod int int) rat), frct ) 22.37/22.48 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.37/22.48 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.37/22.48 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.37/22.48 ( (fun rat real), ratreal ) 22.37/22.48 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.37/22.48 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.37/22.48 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.37/22.48 ( (fun rat (product_prod int int)), quotient_of ) 22.37/22.48 ( (fun int (fun nat nat)), nat_aux ) 22.37/22.48 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.37/22.48 ( (fun int (list int)), quickc666637781d_zero ) 22.37/22.48 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.37/22.48 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.37/22.48 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.37/22.48 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.37/22.48 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.37/22.48 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.37/22.48 ( (fun code_code_numeral int), code_int_of ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X) (zero_zero real)))) (= (hAPP int real (number_number_of real) min) (hAPP real real (sgn_sgn real) X))) ) 22.37/22.48 ( pi ) 22.37/22.48 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (one_one real) ) 22.37/22.48 ( (zero_zero real) ) 22.37/22.48 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (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))))) ) 22.37/22.48 ( (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)) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= X (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_1) (hAPP nat nat (hAPP nat _let_0 (div_div nat) X) _let_1))))))) ) 22.37/22.48 ( (zero_zero nat) ) 22.37/22.48 ( (one_one nat) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128234 $$unsorted) (BOUND_VARIABLE_128235 $$unsorted) (BOUND_VARIABLE_128236 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (real_normed_vector X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP (fun nat X_a) (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_128235) BOUND_VARIABLE_128236) sequentially))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_128234))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP nat X_a BOUND_VARIABLE_128235 N_1)) BOUND_VARIABLE_128236))) BOUND_VARIABLE_128234))) )) )))) ) 22.37/22.48 ( real, pi, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N))) (or (= (zero_zero nat) _let_2) (= (hAPP nat nat _let_1 _let_2) (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_2) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) _let_2) (one_one nat))))))))) ) 22.37/22.48 ( (one_one nat), (one_one nat) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) N))) (or (not (= (zero_zero nat) _let_0)) (= (one_one nat) (hAPP nat nat (fact_fact nat) _let_0)))) ) 22.37/22.48 ( (one_one nat), (one_one nat) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_128301 $$unsorted) (BOUND_VARIABLE_128302 $$unsorted) (BOUND_VARIABLE_128303 $$unsorted) (BOUND_VARIABLE_128304 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_128302))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_128304))) (or (not (topological_space X_a)) (not (topological_space X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_128303) _let_3))) (not (= (ti X_b BOUND_VARIABLE_128303) (ti X_b BOUND_VARIABLE_128301))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_128301) _let_3))))))) ) 22.37/22.48 ( real, real, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128327 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_128327) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_128327)) (zero_zero X_a))))) ) 22.37/22.48 ( real, (one_one int) ) 22.37/22.48 ( real, (zero_zero int) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP real nat natceiling X) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (one_one nat)))))) ) 22.37/22.48 ( (zero_zero nat), pi ) 22.37/22.48 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (zero_zero nat), skv_2 ) 22.37/22.48 ( (zero_zero nat), skv_9 ) 22.37/22.48 ( (zero_zero nat), skv_12 ) 22.37/22.48 ( (one_one nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int succ (hAPP int int bit0 K_4)) (hAPP int int bit1 K_4)) ) 22.37/22.48 ( pls ) 22.37/22.48 ( (hAPP int int bit1 pls) ) 22.37/22.48 ( min ) 22.37/22.48 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.48 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.48 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.37/22.48 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.37/22.48 ( (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)))))) ) 22.37/22.48 ( (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))))))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (one_one real))) (= (= _let_0 (hAPP real real sqrt Xa)) (= _let_0 Xa))) ) 22.37/22.48 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.48 ( (one_one real) ) 22.37/22.48 ( (zero_zero real) ) 22.37/22.48 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128378 $$unsorted) (BOUND_VARIABLE_128379 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (= (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_128379) (hAPP X_a X_a _let_0 BOUND_VARIABLE_128378)) (= (ti X_a BOUND_VARIABLE_128379) (ti X_a BOUND_VARIABLE_128378))))) ) 22.37/22.48 ( int, pls, (one_one int) ) 22.37/22.48 ( int, (one_one int), min ) 22.37/22.48 ( int, min, pls ) 22.37/22.48 ( int, min, (one_one int) ) 22.37/22.48 ( int, min, min ) 22.37/22.48 ( 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)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.48 ( 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)))), (one_one real) ) 22.37/22.48 ( 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)))), (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.37/22.48 ( 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)))) ) 22.37/22.48 ( 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) ) 22.37/22.48 ( complex, ii, (one_one complex) ) 22.37/22.48 ( complex, (one_one complex), ii ) 22.37/22.48 ( complex, (one_one complex), (one_one complex) ) 22.37/22.48 ) 22.37/22.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128400 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (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)) (= (hAPP X_a X_a (exp X_a) BOUND_VARIABLE_128400) (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_0 _let_4 (hAPP (fun real _let_3) (fun _let_0 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_128400)))))))))) ) 22.37/22.48 ( int, s ) 22.37/22.48 ( int, s1 ) 22.37/22.48 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.48 ( int, v ) 22.37/22.48 ( int, w ) 22.37/22.48 ( int, y ) 22.37/22.48 ( int, x ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.37/22.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.37/22.49 ( int, skv_6 ) 22.37/22.49 ( int, skv_7 ) 22.37/22.49 ( int, skv_16 ) 22.37/22.49 ( int, skv_23 ) 22.37/22.49 ( int, skv_24 ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) min) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( complex, ii ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128419 $$unsorted) (BOUND_VARIABLE_128420 $$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_128419))) (or (not (idom X_a)) (= (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_128419) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_128420) _let_0)) (or (= (ti X_a BOUND_VARIABLE_128420) _let_3) (= _let_3 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128420))))))))) ) 22.37/22.49 ( int, s, s1 ) 22.37/22.49 ( int, s1, s ) 22.37/22.49 ( int, s1, s1 ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.37/22.49 ( int, v, w ) 22.37/22.49 ( int, w, v ) 22.37/22.49 ( int, w, w ) 22.37/22.49 ( int, y, y ) 22.37/22.49 ( int, y, x ) 22.37/22.49 ( int, x, y ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), skv_7 ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( int, skv_6, skv_6 ) 22.37/22.49 ( int, skv_6, skv_16 ) 22.37/22.49 ( int, skv_7, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.37/22.49 ( int, skv_16, skv_6 ) 22.37/22.49 ( int, skv_23, skv_24 ) 22.37/22.49 ( int, skv_24, skv_23 ) 22.37/22.49 ( int, skv_24, skv_24 ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) min), (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)))) ) 22.37/22.49 ( 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) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( complex, ii, ii ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128473 $$unsorted) (BOUND_VARIABLE_128474 $$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 _let_2) BOUND_VARIABLE_128474))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_128473) _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_128474) BOUND_VARIABLE_128473)) _let_2)))))) ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.37/22.49 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.37/22.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.37/22.49 ( 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) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$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_3) B_2)))) (hBOOL (hAPP X_b bool (hAPP X_a _let_0 F A_3) B_2))))) ) 22.37/22.49 ( int, int, (ord_less int), (one_one int), t ) 22.37/22.49 ( int, int, (ord_less int), min, min ) 22.37/22.49 ( int, int, (ord_less int), min, (zero_zero int) ) 22.37/22.49 ( int, int, (ord_less int), (zero_zero int), pls ) 22.37/22.49 ( int, int, (ord_less int), (zero_zero int), (one_one int) ) 22.37/22.49 ( int, int, (ord_less int), (zero_zero int), min ) 22.37/22.49 ( int, int, (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))) ) 22.37/22.49 ( int, int, (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( int, int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( int, int, (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( int, int, (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( int, int, (ord_less_eq int), (one_one int), t ) 22.37/22.49 ( int, int, (ord_less_eq int), min, pls ) 22.37/22.49 ( int, int, (ord_less_eq int), min, min ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), pls ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), (one_one int) ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), min ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), s ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), skv_4 ) 22.37/22.49 ( int, int, (ord_less_eq int), (zero_zero int), skv_5 ) 22.37/22.49 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( int, int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( 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) ) 22.37/22.49 ( 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) (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)) ) 22.37/22.49 ( int, int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( int, int, (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( int, int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( int, (fun int bool), (member int), (one_one int), zEven ) 22.37/22.49 ( nat, nat, (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( nat, nat, (ord_less nat), (zero_zero nat), n ) 22.37/22.49 ( nat, nat, (ord_less nat), (zero_zero nat), tn ) 22.37/22.49 ( real, real, (ord_less real), pi, (zero_zero real) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( real, real, (ord_less real), (zero_zero real), pi ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( real, real, (ord_less real), (zero_zero real), skv_2 ) 22.37/22.49 ( real, real, (ord_less real), (zero_zero real), skv_9 ) 22.37/22.49 ( real, real, (ord_less real), (zero_zero real), skv_12 ) 22.37/22.49 ( 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) ) 22.37/22.49 ( 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) ) 22.37/22.49 ( 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 ) 22.37/22.49 ( real, real, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( real, real, (ord_less_eq real), (zero_zero real), pi ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( 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)))) ) 22.37/22.49 ( real, real, (ord_less_eq real), (zero_zero real), skv_10 ) 22.37/22.49 ( real, real, (ord_less_eq real), (zero_zero real), skv_11 ) 22.37/22.49 ( real, real, (ord_less_eq real), (zero_zero real), skv_15 ) 22.37/22.49 ( real, real, (ord_less_eq real), (zero_zero real), skv_18 ) 22.37/22.49 ( 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) ) 22.37/22.49 ( real, real, (ord_less_eq real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( real, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real), sequentially ) 22.37/22.49 ( 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))))) ) 22.37/22.49 ( (fun nat real), real, (sums real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))), (one_one real) ) 22.37/22.49 ( (fun nat int), (fun nat bool), (nat_tr1645093318rphism nat int), (semiring_1_of_nat int), (hAPP bool (fun nat bool) (combk bool nat) fTrue) ) 22.37/22.49 ( (fun int nat), (fun int bool), (nat_tr1645093318rphism int nat), nat_1, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((Xa $$unsorted)) (= (not (forall ((Y_1 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) Y_1) (ti int Xa))) )) (hBOOL (hAPP int bool (even_odd_even int) Xa))) ) 22.37/22.49 ( (one_one int) ) 22.37/22.49 ( (zero_zero int) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128548 $$unsorted) (BOUND_VARIABLE_128549 $$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_128549) BOUND_VARIABLE_128548) (hAPP X_a X_a (uminus_uminus X_a) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128548) BOUND_VARIABLE_128549)))))) ) 22.37/22.49 ( 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) ) 22.37/22.49 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.49 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.49 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.49 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.49 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.37/22.49 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.37/22.49 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.37/22.49 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.49 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 22.37/22.49 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.37/22.49 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.37/22.49 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.37/22.49 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.37/22.49 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (dist_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0)))) ) 22.37/22.49 ( rat ) 22.37/22.49 ( int ) 22.37/22.49 ( nat ) 22.37/22.49 ( real ) 22.37/22.49 ( complex ) 22.37/22.49 ( (fun real bool) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (frac X_a))) (= _let_0 (ti (fun int (fun int X_a)) _let_0))) ) 22.37/22.49 ( rat ) 22.37/22.49 ( int ) 22.37/22.49 ( bool ) 22.37/22.49 ( real ) 22.37/22.49 ( (fun int bool) ) 22.37/22.49 ( (product_prod int int) ) 22.37/22.49 ( (fun bool bool) ) 22.37/22.49 ( (fun int (fun int bool)) ) 22.37/22.49 ( (fun (product_prod int int) bool) ) 22.37/22.49 ( (fun (fun int bool) bool) ) 22.37/22.49 ( (product_prod int (product_prod int int)) ) 22.37/22.49 ( (fun int (product_prod int (product_prod int int))) ) 22.37/22.49 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 22.37/22.49 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.37/22.49 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.37/22.49 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.37/22.49 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128728 $$unsorted) (BOUND_VARIABLE_128729 $$unsorted) (BOUND_VARIABLE_128746 $$unsorted) (BOUND_VARIABLE_128747 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (let ((_let_5 (fun nat X_a))) (let ((_let_6 (power_power X_a))) (let ((_let_7 (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_128728) (hAPP int nat _let_0 BOUND_VARIABLE_128729)))) (or (not (monoid_mult X_a)) (and (or (not (hBOOL (hAPP int bool _let_1 (hAPP int int _let_2 BOUND_VARIABLE_128729)))) (= (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_128728) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_128729))) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_128728) _let_7)) _let_7))) (or (hBOOL (hAPP int bool _let_1 (hAPP int int _let_2 BOUND_VARIABLE_128747))) (= (one_one X_a) (hAPP nat X_a (hAPP X_a _let_5 _let_6 BOUND_VARIABLE_128746) (hAPP int nat _let_0 (hAPP int int bit1 BOUND_VARIABLE_128747))))))))))))))) ) 22.37/22.49 ( int, s, min, s, min ) 22.37/22.49 ( int, s1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), s1, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, v, (hAPP int int bit1 pls), v, (hAPP int int bit1 pls) ) 22.37/22.49 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)), w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.37/22.49 ( int, y, (hAPP int int bit1 (hAPP int int bit1 pls)), y, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.37/22.49 ( int, x, pls, x, pls ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((A_1 $$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)))) ) 22.37/22.49 ( (one_one int), t ) 22.37/22.49 ( min, min ) 22.37/22.49 ( min, (zero_zero int) ) 22.37/22.49 ( (zero_zero int), pls ) 22.37/22.49 ( (zero_zero int), (one_one int) ) 22.37/22.49 ( (zero_zero int), min ) 22.37/22.49 ( (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))) ) 22.37/22.49 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.49 ( 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))) ) 22.37/22.49 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.49 ) 22.37/22.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128784 $$unsorted) (BOUND_VARIABLE_128785 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (zero_neq_one X_a)) (not (no_zero_divisors X_a)) (not (mult_zero X_a)) (not (power X_a)) (= (and (= _let_0 (ti X_a BOUND_VARIABLE_128784)) (not (= (zero_zero nat) BOUND_VARIABLE_128785))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_128784) BOUND_VARIABLE_128785))))) ) 22.37/22.49 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.49 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (power_power X_a))) (or (not (power X_a)) (= _let_0 (ti (fun X_a (fun nat X_a)) _let_0)))) ) 22.37/22.50 ( rat ) 22.37/22.50 ( int ) 22.37/22.50 ( (fun int int) ) 22.37/22.50 ( nat ) 22.37/22.50 ( bool ) 22.37/22.50 ( real ) 22.37/22.50 ( (fun real real) ) 22.37/22.50 ( (fun nat nat) ) 22.37/22.50 ( complex ) 22.37/22.50 ( (product_prod int int) ) 22.37/22.50 ( (fun bool bool) ) 22.37/22.50 ( (fun nat bool) ) 22.37/22.50 ( (fun nat (fun nat bool)) ) 22.37/22.50 ( quickcheck_code_int ) 22.37/22.50 ( code_code_numeral ) 22.37/22.50 ( (fun nat (product_prod int int)) ) 22.37/22.50 ( (product_prod real real) ) 22.37/22.50 ( (product_prod nat nat) ) 22.37/22.50 ( (fun (product_prod nat nat) bool) ) 22.37/22.50 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.37/22.50 ( (fun nat (product_prod nat nat)) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((A_3 $$unsorted) (A_2 $$unsorted) (Ma $$unsorted)) (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_0))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (hAPP int _let_4 zcong A_3))) (let ((_let_6 (hAPP int _let_0 norRRset Ma))) (let ((_let_7 (hAPP _let_0 int (hilbert_Eps int) (hAPP _let_0 _let_0 (hAPP _let_2 _let_3 (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 (hAPP _let_4 _let_4 (combc int int bool) _let_5) Ma))) (hAPP _let_0 _let_0 (hAPP (fun int (fun _let_0 bool)) _let_3 (combc int _let_0 bool) (member int)) _let_6))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (one_one int)) Ma))) (not (hBOOL (hAPP int bool (hAPP _let_0 _let_0 is_RRset A_2) Ma))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) A_3) A_2))) (and (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) _let_7) _let_6)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_5 _let_7) Ma)))))))))))) ) 22.37/22.50 ( (one_one int), zEven, t ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N)) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int _let_0 M)) (hAPP nat int _let_0 N))))) ) 22.37/22.50 ( (one_one nat), (hAPP int nat nat_1 t) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0))))) ) 22.37/22.50 ( rat ) 22.37/22.50 ( int ) 22.37/22.50 ( (fun int int) ) 22.37/22.50 ( nat ) 22.37/22.50 ( bool ) 22.37/22.50 ( real ) 22.37/22.50 ( (fun nat real) ) 22.37/22.50 ( (fun real real) ) 22.37/22.50 ( (filter nat) ) 22.37/22.50 ( complex ) 22.37/22.50 ( (fun int bool) ) 22.37/22.50 ( (product_prod int int) ) 22.37/22.50 ( (fun (product_prod int int) int) ) 22.37/22.50 ( (fun int (fun int bool)) ) 22.37/22.50 ( (fun nat bool) ) 22.37/22.50 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.37/22.50 ( (fun (product_prod int int) bool) ) 22.37/22.50 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.37/22.50 ( (fun real bool) ) 22.37/22.50 ( quickcheck_code_int ) 22.37/22.50 ( code_code_numeral ) 22.37/22.50 ( (product_prod real real) ) 22.37/22.50 ( (filter real) ) 22.37/22.50 ( (product_prod nat nat) ) 22.37/22.50 ( (fun nat rat) ) 22.37/22.50 ( (fun int (fun int (fun int bool))) ) 22.37/22.50 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.37/22.50 ( (fun int real) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (boolean_algebra T_1)) (boolean_algebra (fun T_2 T_1))) ) 22.37/22.50 ( rat, real ) 22.37/22.50 ( rat, (product_prod int int) ) 22.37/22.50 ( int, rat ) 22.37/22.50 ( int, int ) 22.37/22.50 ( int, (fun int int) ) 22.37/22.50 ( int, nat ) 22.37/22.50 ( int, bool ) 22.37/22.50 ( int, real ) 22.37/22.50 ( int, (fun nat real) ) 22.37/22.50 ( int, (fun real real) ) 22.37/22.50 ( int, (fun nat nat) ) 22.37/22.50 ( int, (fun int rat) ) 22.37/22.50 ( int, (fun int bool) ) 22.37/22.50 ( int, (product_prod int int) ) 22.37/22.50 ( int, (fun (product_prod int int) int) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.37/22.50 ( int, (fun nat int) ) 22.37/22.50 ( int, (fun bool bool) ) 22.37/22.50 ( int, (fun int (fun bool bool)) ) 22.37/22.50 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( int, (fun int (fun int bool)) ) 22.37/22.50 ( int, (fun nat bool) ) 22.37/22.50 ( int, (fun (product_prod int int) bool) ) 22.37/22.50 ( int, (fun int (fun (product_prod int int) bool)) ) 22.37/22.50 ( int, quickcheck_code_int ) 22.37/22.50 ( int, (fun (fun int bool) bool) ) 22.37/22.50 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.37/22.50 ( int, (product_prod int (product_prod int int)) ) 22.37/22.50 ( int, (fun int (product_prod int (product_prod int int))) ) 22.37/22.50 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 22.37/22.50 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.37/22.50 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.37/22.50 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.37/22.50 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.37/22.50 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.37/22.50 ( int, (fun nat (fun bool bool)) ) 22.37/22.50 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( int, (fun int (product_prod int int)) ) 22.37/22.50 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.37/22.50 ( int, (fun int (fun (fun int bool) bool)) ) 22.37/22.50 ( int, (fun (fun int int) (fun int bool)) ) 22.37/22.50 ( int, (list int) ) 22.37/22.50 ( int, (fun int (fun int (fun int bool))) ) 22.37/22.50 ( int, (fun int real) ) 22.37/22.50 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun int int), (fun int int) ) 22.37/22.50 ( (fun int int), (fun int bool) ) 22.37/22.50 ( (fun int int), (fun int (fun int int)) ) 22.37/22.50 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun int int), (fun int (fun int bool)) ) 22.37/22.50 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.37/22.50 ( nat, rat ) 22.37/22.50 ( nat, int ) 22.37/22.50 ( nat, (fun int int) ) 22.37/22.50 ( nat, nat ) 22.37/22.50 ( nat, bool ) 22.37/22.50 ( nat, real ) 22.37/22.50 ( nat, (fun real real) ) 22.37/22.50 ( nat, (fun nat nat) ) 22.37/22.50 ( nat, complex ) 22.37/22.50 ( nat, (product_prod int int) ) 22.37/22.50 ( nat, (fun bool bool) ) 22.37/22.50 ( nat, (fun nat bool) ) 22.37/22.50 ( nat, (fun nat (fun nat bool)) ) 22.37/22.50 ( nat, (fun nat (product_prod int int)) ) 22.37/22.50 ( nat, (product_prod real real) ) 22.37/22.50 ( nat, (product_prod nat nat) ) 22.37/22.50 ( nat, (fun (product_prod nat nat) bool) ) 22.37/22.50 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 22.37/22.50 ( nat, (fun nat (product_prod nat nat)) ) 22.37/22.50 ( bool, bool ) 22.37/22.50 ( bool, (fun bool bool) ) 22.37/22.50 ( real, nat ) 22.37/22.50 ( real, bool ) 22.37/22.50 ( real, real ) 22.37/22.50 ( real, (fun nat real) ) 22.37/22.50 ( real, (fun real real) ) 22.37/22.50 ( real, (fun (filter nat) bool) ) 22.37/22.50 ( real, complex ) 22.37/22.50 ( real, (fun int bool) ) 22.37/22.50 ( real, (fun bool bool) ) 22.37/22.50 ( real, (fun int (fun int bool)) ) 22.37/22.50 ( real, (fun real complex) ) 22.37/22.50 ( real, (fun real bool) ) 22.37/22.50 ( real, (fun nat (product_prod real real)) ) 22.37/22.50 ( real, (fun real (fun nat (product_prod real real))) ) 22.37/22.50 ( real, (fun (filter real) bool) ) 22.37/22.50 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 22.37/22.50 ( real, (fun int (fun int (fun bool bool))) ) 22.37/22.50 ( real, (fun int (fun nat bool)) ) 22.37/22.50 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 22.37/22.50 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( real, (fun int (fun nat (fun bool bool))) ) 22.37/22.50 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.37/22.50 ( real, (fun (fun nat real) (fun nat bool)) ) 22.37/22.50 ( real, (fun (fun int real) (fun int bool)) ) 22.37/22.50 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.37/22.50 ( (fun nat real), (fun nat real) ) 22.37/22.50 ( (fun nat real), (fun nat bool) ) 22.37/22.50 ( (fun nat real), (fun nat (fun real real)) ) 22.37/22.50 ( (fun nat real), (fun int (fun nat real)) ) 22.37/22.50 ( (fun real real), (fun real real) ) 22.37/22.50 ( (fun real real), (fun real (fun real bool)) ) 22.37/22.50 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun real real), (fun real (fun real real)) ) 22.37/22.50 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun nat nat), (fun nat real) ) 22.37/22.50 ( (fun nat nat), (fun nat (fun nat bool)) ) 22.37/22.50 ( (fun nat nat), (fun nat (fun nat nat)) ) 22.37/22.50 ( (filter nat), bool ) 22.37/22.50 ( complex, nat ) 22.37/22.50 ( complex, real ) 22.37/22.50 ( complex, complex ) 22.37/22.50 ( (fun int bool), int ) 22.37/22.50 ( (fun int bool), bool ) 22.37/22.50 ( (fun int bool), (fun int bool) ) 22.37/22.50 ( (fun int bool), (fun int (fun int int)) ) 22.37/22.50 ( (fun int bool), (fun int (fun bool bool)) ) 22.37/22.50 ( (fun int bool), (fun int (fun int bool)) ) 22.37/22.50 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 22.37/22.50 ( (fun int bool), (fun real (fun int (fun int bool))) ) 22.37/22.50 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 22.37/22.50 ( (product_prod int int), rat ) 22.37/22.50 ( (product_prod int int), int ) 22.37/22.50 ( (product_prod int int), (fun int int) ) 22.37/22.50 ( (product_prod int int), bool ) 22.37/22.50 ( (product_prod int int), (fun int bool) ) 22.37/22.50 ( (product_prod int int), (product_prod int int) ) 22.37/22.50 ( (product_prod int int), (fun (product_prod int int) int) ) 22.37/22.50 ( (product_prod int int), (fun bool bool) ) 22.37/22.50 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.37/22.50 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 22.37/22.50 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.37/22.50 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 22.37/22.50 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 22.37/22.50 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 22.37/22.50 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 22.37/22.50 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 22.37/22.50 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (fun int (fun int bool)), (fun int bool) ) 22.37/22.50 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 22.37/22.50 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 22.37/22.50 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 22.37/22.50 ( (fun nat bool), bool ) 22.37/22.50 ( (fun nat bool), (fun nat bool) ) 22.37/22.50 ( (fun nat bool), (fun nat (fun bool bool)) ) 22.37/22.50 ( (fun nat bool), (fun int (fun nat bool)) ) 22.37/22.50 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 22.37/22.50 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 22.37/22.50 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 22.37/22.50 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (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)))) ) 22.37/22.50 ( (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)))) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (fun real bool), real ) 22.37/22.50 ( (fun real bool), (fun real bool) ) 22.37/22.50 ( (fun real bool), (fun real (fun bool bool)) ) 22.37/22.50 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 22.37/22.50 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 22.37/22.50 ( quickcheck_code_int, int ) 22.37/22.50 ( quickcheck_code_int, nat ) 22.37/22.50 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 22.37/22.50 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 22.37/22.50 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 22.37/22.50 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 22.37/22.50 ( code_code_numeral, int ) 22.37/22.50 ( code_code_numeral, nat ) 22.37/22.50 ( code_code_numeral, (fun nat nat) ) 22.37/22.50 ( code_code_numeral, code_code_numeral ) 22.37/22.50 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 22.37/22.50 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.37/22.50 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.37/22.50 ( (product_prod real real), bool ) 22.37/22.50 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 22.37/22.50 ( (filter real), bool ) 22.37/22.50 ( (product_prod nat nat), bool ) 22.37/22.50 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 22.37/22.50 ( (fun nat rat), bool ) 22.37/22.50 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 22.37/22.50 ( (fun int real), (fun int bool) ) 22.37/22.50 ( (fun int real), (fun int real) ) 22.37/22.50 ( (fun int real), (fun int (fun real real)) ) 22.37/22.50 ( (fun int real), (fun int (fun int real)) ) 22.37/22.50 ( (fun real (fun int bool)), (fun real bool) ) 22.37/22.50 ( (fun int (fun nat bool)), (fun int bool) ) 22.37/22.50 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 22.37/22.50 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 22.37/22.50 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 22.37/22.50 ( (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))) ) 22.37/22.50 ( (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)))) ) 22.37/22.50 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.37/22.50 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 22.37/22.50 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 22.37/22.50 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.37/22.50 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 22.37/22.50 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 22.37/22.50 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.37/22.50 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 22.37/22.50 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 22.37/22.50 ( (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)))) ) 22.37/22.50 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.37/22.50 ( (fun int (fun int real)), (fun int (fun int bool)) ) 22.37/22.50 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 22.37/22.50 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128881 $$unsorted) (BOUND_VARIABLE_128882 $$unsorted) (BOUND_VARIABLE_128883 $$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_128883) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128882) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_128881) BOUND_VARIABLE_128883))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_128881) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_128882) BOUND_VARIABLE_128883)))))))) ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.37/22.50 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.37/22.50 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.37/22.50 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (hAPP real real ln X)) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) (one_one real)))))) ) 22.37/22.50 ( pi ) 22.37/22.50 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (one_one real) ) 22.37/22.50 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.37/22.50 ( skv_2 ) 22.37/22.50 ( skv_9 ) 22.37/22.50 ( skv_12 ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_128926 $$unsorted) (BOUND_VARIABLE_128927 $$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_128926) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_128927)) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_128926) BOUND_VARIABLE_128927)))) ) 22.37/22.50 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.37/22.50 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.37/22.50 ( 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) ) 22.37/22.50 ( 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) ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.50 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( nat, (one_one nat), (one_one nat) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((Na $$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) Na)) Ma)) (= (one_one int) (hAPP int int (abs_abs int) Na)))) ) 22.37/22.50 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.37/22.50 ( 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))) ) 22.37/22.50 ( v, y ) 22.37/22.50 ( v, sa ) 22.37/22.50 ( v, x ) 22.37/22.50 ( v, r ) 22.37/22.50 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.37/22.50 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.37/22.50 ( w, y ) 22.37/22.50 ( w, sa ) 22.37/22.50 ( w, x ) 22.37/22.50 ( w, r ) 22.37/22.50 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.37/22.50 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.37/22.50 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.37/22.50 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.50 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.50 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.37/22.50 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.50 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.50 ( skv_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))) ) 22.37/22.50 ) 22.37/22.50 (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)))) ) 22.37/22.50 ( int ) 22.37/22.50 ( (fun int int) ) 22.37/22.50 ( nat ) 22.37/22.50 ( bool ) 22.37/22.50 ( real ) 22.37/22.50 ( (fun nat real) ) 22.37/22.50 ( (fun real real) ) 22.37/22.50 ( complex ) 22.37/22.50 ( (fun int bool) ) 22.37/22.50 ( (product_prod int int) ) 22.37/22.50 ( (fun (product_prod int int) int) ) 22.37/22.50 ( (fun int (fun int bool)) ) 22.37/22.50 ( (fun nat bool) ) 22.37/22.50 ( (fun (product_prod int int) bool) ) 22.37/22.50 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.37/22.50 ( (fun real bool) ) 22.37/22.50 ( code_code_numeral ) 22.37/22.50 ( (fun int (fun int (fun int bool))) ) 22.37/22.50 ( (fun int real) ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129202 $$unsorted) (BOUND_VARIABLE_129203 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (times_times X_a))) (let ((_let_4 (zero_zero X_a))) (let ((_let_5 (hAPP X_a X_a _let_2 BOUND_VARIABLE_129203))) (let ((_let_6 (hAPP X_a X_a _let_2 BOUND_VARIABLE_129202))) (or (not (division_ring X_a)) (= _let_4 (ti X_a BOUND_VARIABLE_129203)) (= _let_4 (ti X_a BOUND_VARIABLE_129202)) (= (hAPP X_a X_a (uminus_uminus 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_3 _let_5) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129203) BOUND_VARIABLE_129202))) _let_6)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_5) _let_6)))))))))) ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.37/22.50 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.50 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 22.37/22.50 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.37/22.50 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 22.37/22.50 ) 22.37/22.50 (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)))) ) 22.37/22.50 ( rat ) 22.37/22.50 ( int ) 22.37/22.50 ( nat ) 22.37/22.50 ( real ) 22.37/22.50 ( complex ) 22.37/22.50 ( quickcheck_code_int ) 22.37/22.50 ( code_code_numeral ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129237 $$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_129237))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_129237))))) ) 22.37/22.50 ( real, (zero_zero real) ) 22.37/22.50 ( complex, ii ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (ti X_a A_1))) (let ((_let_1 (product_prod X_a X_b))) (or (not (= _let_0 (hAPP _let_1 X_a (product_fst X_a X_b) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) X) Y)))) (= _let_0 (ti X_a X))))) ) 22.37/22.50 ( int, int, (one_one int), (one_one int), v ) 22.37/22.50 ( int, int, (zero_zero int), (one_one int), s1 ) 22.37/22.50 ( int, int, s, (one_one int), r ) 22.37/22.50 ) 22.37/22.50 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129288 $$unsorted) (BOUND_VARIABLE_129289 $$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_129288)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_129289)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_129288) BOUND_VARIABLE_129289))))))) ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.37/22.50 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.37/22.50 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.37/22.50 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.37/22.51 ( int, y, v ) 22.37/22.51 ( int, y, w ) 22.37/22.51 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( int, sa, v ) 22.37/22.51 ( int, sa, w ) 22.37/22.51 ( int, x, v ) 22.37/22.51 ( int, x, w ) 22.37/22.51 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.37/22.51 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( int, r, v ) 22.37/22.51 ( int, r, w ) 22.37/22.51 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.37/22.51 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.37/22.51 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.37/22.51 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.37/22.51 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.37/22.51 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.37/22.51 ( 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)))))) ) 22.37/22.51 ( 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 ) 22.37/22.51 ( complex, ii, ii ) 22.37/22.51 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.37/22.51 ( 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 ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (= _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Xa)) (= _let_0 Xa)))) ) 22.37/22.51 ( (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))) ) 22.37/22.51 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.51 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.51 ( (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))) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129339 $$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)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_129339)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129339) _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_129339)))))))) ) 22.37/22.51 ( int, pls ) 22.37/22.51 ( int, (one_one int) ) 22.37/22.51 ( int, min ) 22.37/22.51 ( int, (zero_zero int) ) 22.37/22.51 ( int, s ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( int, t ) 22.37/22.51 ( int, m1 ) 22.37/22.51 ( int, skv_4 ) 22.37/22.51 ( int, skv_5 ) 22.37/22.51 ( nat, (zero_zero nat) ) 22.37/22.51 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.51 ( nat, n ) 22.37/22.51 ( nat, tn ) 22.37/22.51 ( real, pi ) 22.37/22.51 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( real, (one_one real) ) 22.37/22.51 ( real, (zero_zero real) ) 22.37/22.51 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( 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))))) ) 22.37/22.51 ( 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)) ) 22.37/22.51 ( real, skv_2 ) 22.37/22.51 ( real, skv_9 ) 22.37/22.51 ( real, skv_12 ) 22.37/22.51 ( complex, ii ) 22.37/22.51 ) 22.37/22.51 (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))))) ) 22.37/22.51 ( 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))) ) 22.37/22.51 ( 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))) ) 22.37/22.51 ( (product_prod int int), (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun _let_1 int))) (let ((_let_3 (fun _let_1 bool))) (let ((_let_4 (fun _let_1 _let_0))) (hAPP int _let_3 (hAPP _let_4 (fun int _let_3) (combc _let_1 int bool) (hAPP _let_2 _let_4 (hAPP (fun int _let_0) (fun _let_2 _let_4) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real 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_2 (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) X)) (hAPP real real (hAPP real _let_2 (minus_minus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X)) _let_3)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real sin X)) _let_3))))))) ) 22.37/22.51 ( pi ) 22.37/22.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( (zero_zero real) ) 22.37/22.51 ( (hAPP real 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))))) ) 22.37/22.51 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.37/22.51 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.37/22.51 ( (hAPP real real (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))))) ) 22.37/22.51 ( (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)))) ) 22.37/22.51 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real (hAPP 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_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (uminus_uminus real) _let_0)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (= X (hAPP real real arctan (hAPP real real tan X))))))) ) 22.37/22.51 ( pi ) 22.37/22.51 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( (one_one real) ) 22.37/22.51 ( (zero_zero real) ) 22.37/22.51 ( (hAPP real 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))))) ) 22.37/22.51 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( (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))))) ) 22.37/22.51 ( (hAPP real real (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))))) ) 22.37/22.51 ( (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)))) ) 22.37/22.51 ( (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)) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129417 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (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_129417))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_129417)))) ) 22.37/22.51 ( int, t ) 22.37/22.51 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_0 (fun int bool))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) U) L)) (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) L) U)))) ) 22.37/22.51 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.37/22.51 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.37/22.51 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129432 $$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 X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_129432) BOUND_VARIABLE_129432)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129432) _let_2))))))) ) 22.37/22.51 ( int, (one_one int) ) 22.37/22.51 ( 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)))) ) 22.37/22.51 ( 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) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.37/22.51 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.37/22.51 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.37/22.51 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.37/22.51 ( nat, (one_one nat) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X))) (not (hBOOL (hAPP real bool _let_0 Y))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP real (fun real real) (times_times real) X) Y))))) ) 22.37/22.51 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.51 ( 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))))) ) 22.37/22.51 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.37/22.51 ( (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)))) ) 22.37/22.51 ) 22.37/22.51 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 X) Y)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Y) X)) (= (ti int X) (ti int Y))))) ) 22.37/22.51 ( pls, (zero_zero int) ) 22.37/22.51 ( (one_one int), (zero_zero int) ) 22.37/22.51 ( (one_one int), t ) 22.37/22.51 ( min, min ) 22.37/22.51 ( min, (zero_zero int) ) 22.37/22.51 ( (zero_zero int), pls ) 22.37/22.51 ( (zero_zero int), (one_one int) ) 22.37/22.51 ( (zero_zero int), min ) 22.37/22.51 ( (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))) ) 22.37/22.51 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( 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))) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.37/22.51 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.37/22.51 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.46/22.55 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.46/22.55 ( t, (one_one int) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((Z_1 $$unsorted)) (or (hBOOL (hAPP int bool nat_neg Z_1)) (= (ti int Z_1) (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 Z_1)))) ) 22.46/22.55 ( pls ) 22.46/22.55 ( (one_one int) ) 22.46/22.55 ( min ) 22.46/22.55 ( (zero_zero int) ) 22.46/22.55 ( s ) 22.46/22.55 ( s1 ) 22.46/22.55 ( m ) 22.46/22.55 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( (hAPP int int (number_number_of int) min) ) 22.46/22.55 ( t ) 22.46/22.55 ( v ) 22.46/22.55 ( w ) 22.46/22.55 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.55 ( y ) 22.46/22.55 ( sa ) 22.46/22.55 ( x ) 22.46/22.55 ( r ) 22.46/22.55 ( m1 ) 22.46/22.55 ( skv_14 ) 22.46/22.55 ( skv_20 ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_129592 $$unsorted) (BOUND_VARIABLE_129593 $$unsorted) (BOUND_VARIABLE_129594 $$unsorted) (BOUND_VARIABLE_129595 $$unsorted)) (let ((_let_0 (fun X_b bool))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_129594) BOUND_VARIABLE_129595))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) BOUND_VARIABLE_129592) (hAPP X_a X_b BOUND_VARIABLE_129593 BOUND_VARIABLE_129594)))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) Y_1) X_1))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) (hAPP X_a X_b BOUND_VARIABLE_129593 Y_1)) (hAPP X_a X_b BOUND_VARIABLE_129593 X_1)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less X_b) BOUND_VARIABLE_129592) (hAPP X_a X_b BOUND_VARIABLE_129593 BOUND_VARIABLE_129595))))) ) 22.46/22.55 ( 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 ) 22.46/22.55 ( int, int, min, (number_number_of int), min, (zero_zero int) ) 22.46/22.55 ( int, int, (zero_zero 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))) ) 22.46/22.55 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (uminus_uminus int), min, min ) 22.46/22.55 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), pred, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, nat, (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)))) (hAPP int int (abs_abs int) v)), (semiring_1_of_nat int), (zero_zero nat), n ) 22.46/22.55 ( real, 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( 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)))), sin, (zero_zero real), pi ) 22.46/22.55 ( 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)))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.55 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), arctan, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.55 ( real, real, skv_10, tan, pi, (zero_zero real) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129626 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (zero_zero X_a))) (or (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_129626)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129626) _let_2))))))) ) 22.46/22.55 ( real, (zero_zero real) ) 22.46/22.55 ( complex, ii ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129647 $$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) _let_0) BOUND_VARIABLE_129647)))) ) 22.46/22.55 ( 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))) m1))) ) 22.46/22.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((I_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP int _let_0 nat_aux I_1) N) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) (hAPP int nat nat_1 I_1)) N))) ) 22.46/22.55 ( (one_one int), (one_one nat) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129672 $$unsorted) (BOUND_VARIABLE_129679 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (divisi14063676e_zero X_a)) (and (or (= _let_0 (ti X_a BOUND_VARIABLE_129672)) (= (one_one X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_129672) BOUND_VARIABLE_129672))) (or (not (= _let_0 (ti X_a BOUND_VARIABLE_129679))) (= _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_129679) BOUND_VARIABLE_129679)))))))) ) 22.46/22.55 ( int, pls, pls ) 22.46/22.55 ( int, min, min ) 22.46/22.55 ( int, s, s ) 22.46/22.55 ( int, s1, s1 ) 22.46/22.55 ( int, m, m ) 22.46/22.55 ( int, t, t ) 22.46/22.55 ( int, v, v ) 22.46/22.55 ( int, w, w ) 22.46/22.55 ( int, y, y ) 22.46/22.55 ( int, sa, sa ) 22.46/22.55 ( int, x, x ) 22.46/22.55 ( int, r, r ) 22.46/22.55 ( int, m1, m1 ) 22.46/22.55 ( int, skv_14, skv_14 ) 22.46/22.55 ( int, skv_20, skv_20 ) 22.46/22.55 ( (fun int int), bit1, bit1 ) 22.46/22.55 ( (fun int int), bit0, bit0 ) 22.46/22.55 ( (fun int int), succ, succ ) 22.46/22.55 ( (fun int int), pred, pred ) 22.46/22.55 ( (fun int int), (fact_fact int), (fact_fact int) ) 22.46/22.55 ( (fun int int), zfact, zfact ) 22.46/22.55 ( nat, n, n ) 22.46/22.55 ( nat, tn, tn ) 22.46/22.55 ( bool, fTrue, fTrue ) 22.46/22.55 ( bool, fFalse, fFalse ) 22.46/22.55 ( real, pi, pi ) 22.46/22.55 ( (fun nat real), (real_1 nat), (real_1 nat) ) 22.46/22.55 ( (fun nat real), cos_coeff, cos_coeff ) 22.46/22.55 ( (fun nat real), sin_coeff, sin_coeff ) 22.46/22.55 ( (fun real real), sin, sin ) 22.46/22.55 ( (fun real real), cos, cos ) 22.46/22.55 ( (fun real real), sqrt, sqrt ) 22.46/22.55 ( (fun real real), tan, tan ) 22.46/22.55 ( (fun real real), ln, ln ) 22.46/22.55 ( (fun real real), arctan, arctan ) 22.46/22.55 ( (fun real real), arcsin, arcsin ) 22.46/22.55 ( (fun real real), arccos, arccos ) 22.46/22.55 ( (fun nat nat), suc, suc ) 22.46/22.55 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 22.46/22.55 ( (fun nat nat), nat_size, nat_size ) 22.46/22.55 ( (fun nat nat), (size_size nat), (size_size nat) ) 22.46/22.55 ( (fun nat nat), fact, fact ) 22.46/22.55 ( (filter nat), sequentially, sequentially ) 22.46/22.55 ( (fun int (fun int rat)), fract, fract ) 22.46/22.55 ( complex, ii, ii ) 22.46/22.55 ( (fun int bool), zOdd, zOdd ) 22.46/22.55 ( (fun int bool), zprime, zprime ) 22.46/22.55 ( (fun int bool), zEven, zEven ) 22.46/22.55 ( (fun int bool), nat_neg, nat_neg ) 22.46/22.55 ( (fun int bool), nat_is_nat, nat_is_nat ) 22.46/22.55 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 22.46/22.55 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.46/22.55 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 22.46/22.55 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 22.46/22.55 ( (fun int (fun int int)), inv, inv ) 22.46/22.55 ( (fun int (fun int int)), multInv, multInv ) 22.46/22.55 ( (fun int (fun int int)), legendre, legendre ) 22.46/22.55 ( (fun int (fun int int)), standardRes, standardRes ) 22.46/22.55 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 22.46/22.55 ( (fun int (fun int int)), z3div, z3div ) 22.46/22.55 ( (fun int (fun int int)), z3mod, z3mod ) 22.46/22.55 ( (fun int (fun int int)), int_lcm, int_lcm ) 22.46/22.55 ( (fun int (fun int int)), int_gcd, int_gcd ) 22.46/22.55 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.46/22.55 ( (fun bool bool), fNot, fNot ) 22.46/22.55 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 22.46/22.55 ( (fun bool (fun bool bool)), fconj, fconj ) 22.46/22.55 ( (fun bool (fun bool bool)), fdisj, fdisj ) 22.46/22.55 ( (fun bool (fun bool bool)), fimplies, fimplies ) 22.46/22.55 ( (fun int (fun int bool)), quadRes, quadRes ) 22.46/22.55 ( (fun int (fun int bool)), d22set, d22set ) 22.46/22.55 ( (fun int (fun int bool)), norRRset, norRRset ) 22.46/22.55 ( (fun int (fun int bool)), sRStar, sRStar ) 22.46/22.55 ( (fun int (fun int bool)), sr, sr ) 22.46/22.55 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 22.46/22.55 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 22.46/22.55 ( (fun nat bool), prime, prime ) 22.46/22.55 ( (fun real complex), cis, cis ) 22.46/22.55 ( (fun nat (fun nat bool)), coprime, coprime ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 22.46/22.55 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 22.46/22.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 22.46/22.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 22.46/22.55 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 22.46/22.55 ( (fun nat (fun real real)), root, root ) 22.46/22.55 ( (fun real (fun real real)), log, log ) 22.46/22.55 ( (fun real (fun real real)), powr, powr ) 22.46/22.55 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 22.46/22.55 ( (fun complex complex), cnj, cnj ) 22.46/22.55 ( (fun complex complex), expi, expi ) 22.46/22.55 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 22.46/22.55 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 22.46/22.55 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 22.46/22.55 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 22.46/22.55 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 22.46/22.55 ( (fun int nat), nat_1, nat_1 ) 22.46/22.55 ( (fun int nat), phi, phi ) 22.46/22.55 ( (fun complex real), re, re ) 22.46/22.55 ( (fun complex real), im, im ) 22.46/22.55 ( (fun complex real), arg, arg ) 22.46/22.55 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 22.46/22.55 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 22.46/22.55 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 22.46/22.55 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 22.46/22.55 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 22.46/22.55 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 22.46/22.55 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 22.46/22.55 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 22.46/22.55 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 22.46/22.55 ( (fun (fun int bool) int), (the int), (the int) ) 22.46/22.55 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 22.46/22.55 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 22.46/22.55 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 22.46/22.55 ( (fun real (fun real complex)), rcis, rcis ) 22.46/22.55 ( (fun real (fun real complex)), complex_1, complex_1 ) 22.46/22.55 ( (fun int (fun int (fun int bool))), zcong, zcong ) 22.46/22.55 ( (fun int (fun int (fun int bool))), wset, wset ) 22.46/22.55 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 22.46/22.55 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 22.46/22.55 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 22.46/22.55 ( (fun real nat), natceiling, natceiling ) 22.46/22.55 ( (fun real nat), natfloor, natfloor ) 22.46/22.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 22.46/22.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 22.46/22.55 ( (fun int real), (real_1 int), (real_1 int) ) 22.46/22.55 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 22.46/22.55 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 22.46/22.55 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 22.46/22.55 ( (fun complex nat), (size_size complex), (size_size complex) ) 22.46/22.55 ( (fun complex nat), complex_size, complex_size ) 22.46/22.55 ( (fun (fun nat rat) bool), vanishes, vanishes ) 22.46/22.55 ( (fun (product_prod int int) rat), frct, frct ) 22.46/22.55 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 22.46/22.55 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 22.46/22.55 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.46/22.55 ( (fun rat real), ratreal, ratreal ) 22.46/22.55 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 22.46/22.55 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 22.46/22.55 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 22.46/22.55 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 22.46/22.55 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 22.46/22.55 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 22.46/22.55 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 22.46/22.55 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 22.46/22.55 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.46/22.55 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 22.46/22.55 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 22.46/22.55 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 22.46/22.55 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 22.46/22.55 ( (fun code_code_numeral int), code_int_of, code_int_of ) 22.46/22.55 ) 22.46/22.55 (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 W) Z_1) (hAPP real real (hAPP real _let_0 _let_1 Z_1) W)))) ) 22.46/22.55 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( 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))))) ) 22.46/22.55 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.46/22.55 ( (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.46/22.55 ( (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)))))) ) 22.46/22.55 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( (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 ) 22.46/22.55 ( (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)))) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int real (number_number_of real) _let_1))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun real bool))) (let ((_let_5 (ord_less_eq real))) (let ((_let_6 (abs_abs real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_4 _let_5 (hAPP real real _let_6 X)) (hAPP real real (hAPP real _let_0 (inverse_divide real) _let_3) _let_2)))) (hBOOL (hAPP real bool (hAPP real _let_4 _let_5 (hAPP real real _let_6 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_0 (plus_plus real) _let_3) X))) X))) (hAPP real real (hAPP real _let_0 (times_times real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_1))))))))))))) ) 22.46/22.55 ( (hAPP int real (number_number_of real) min) ) 22.46/22.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129779 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (abs_abs X_a))) (or (not (linord1117847801e_zero X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_129779)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_129779)))))) ) 22.46/22.55 ( int, v ) 22.46/22.55 ( int, w ) 22.46/22.55 ( int, skv_14 ) 22.46/22.55 ( int, skv_20 ) 22.46/22.55 ( real, (zero_zero real) ) 22.46/22.55 ( complex, ii ) 22.46/22.55 ) 22.46/22.55 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted) (Xa $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 Xa))) (hBOOL (hAPP X_a bool P_1 (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1)))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 22.46/22.55 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( 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) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) min), min ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 22.46/22.55 ( int, nat_neg, (one_one int) ) 22.46/22.55 ( int, nat_neg, (zero_zero int) ) 22.46/22.55 ( int, nat_neg, (hAPP int int (number_number_of int) min) ) 22.46/22.55 ( int, nat_is_nat, (one_one int) ) 22.46/22.55 ( int, nat_is_nat, (zero_zero int) ) 22.46/22.55 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 22.46/22.55 ( int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 22.46/22.55 ( int, (even_odd_even int), (one_one int) ) 22.46/22.55 ( int, (even_odd_even int), (zero_zero int) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) pls), min ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 22.46/22.55 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( 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) (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)) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.55 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.55 ( nat, (even_odd_even nat), (zero_zero nat) ) 22.46/22.55 ( nat, (even_odd_even nat), (one_one nat) ) 22.46/22.55 ( 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))) ) 22.46/22.55 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 22.46/22.55 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 22.46/22.55 ( nat, prime, (zero_zero nat) ) 22.46/22.55 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.55 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 22.46/22.55 ( 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)))) ) 22.46/22.55 ( 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)))) ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 22.46/22.55 ( 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)))) ) 22.46/22.55 ( 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)))) ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 22.46/22.55 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 22.46/22.56 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 22.46/22.56 ( 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)))) ) 22.46/22.56 ( 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))) ) 22.46/22.56 ( 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) ) 22.46/22.56 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 22.46/22.56 ( 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)))) ) 22.46/22.56 ( 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))) ) 22.46/22.56 ( 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) ) 22.46/22.56 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 22.46/22.56 ( 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 ) 22.46/22.56 ( 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 ) 22.46/22.56 ( 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) ) 22.46/22.56 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 22.46/22.56 ( (filter nat), (trivial_limit nat), sequentially ) 22.46/22.56 ( (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)) ) 22.46/22.56 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 22.46/22.56 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.46/22.56 ( (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) ) 22.46/22.56 ( (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))))) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129803 $$unsorted) (BOUND_VARIABLE_129804 $$unsorted) (BOUND_VARIABLE_129805 $$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_inverse_zero X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_129805)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_129803) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_129804) BOUND_VARIABLE_129805)) (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_129804) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_129803) BOUND_VARIABLE_129805))) BOUND_VARIABLE_129805)))))) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3 ) 22.46/22.56 ( int, y, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w ) 22.46/22.56 ( int, sa, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w ) 22.46/22.56 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (= Y (hAPP real real cos (hAPP real real arccos Y)))))) ) 22.46/22.56 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (zero_zero real) ) 22.46/22.56 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( skv_10 ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_129970 $$unsorted)) (or (not (archim1804426504_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_129970))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP 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_1))) BOUND_VARIABLE_129970)))) ))) ) 22.46/22.56 ( int, pls ) 22.46/22.56 ( int, (one_one int) ) 22.46/22.56 ( int, min ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( nat, n ) 22.46/22.56 ( nat, tn ) 22.46/22.56 ( real, pi ) 22.46/22.56 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( real, skv_2 ) 22.46/22.56 ( real, skv_9 ) 22.46/22.56 ( real, skv_12 ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130022 $$unsorted) (BOUND_VARIABLE_130023 $$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 (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_130022) BOUND_VARIABLE_130023))) (or (not (linord1117847801e_zero X_a)) (= (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130022) BOUND_VARIABLE_130023))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130023) BOUND_VARIABLE_130022)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_130022)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_130023)))))))))) ) 22.46/22.56 ( int, pls, min ) 22.46/22.56 ( int, pls, (zero_zero int) ) 22.46/22.56 ( int, (one_one int), (zero_zero int) ) 22.46/22.56 ( int, (one_one int), t ) 22.46/22.56 ( int, min, pls ) 22.46/22.56 ( int, min, min ) 22.46/22.56 ( int, min, (zero_zero int) ) 22.46/22.56 ( int, (zero_zero int), pls ) 22.46/22.56 ( int, (zero_zero int), (one_one int) ) 22.46/22.56 ( int, (zero_zero int), min ) 22.46/22.56 ( int, (zero_zero int), s ) 22.46/22.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.56 ( int, (zero_zero int), skv_4 ) 22.46/22.56 ( int, (zero_zero int), skv_5 ) 22.46/22.56 ( int, s, (zero_zero int) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.46/22.56 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.46/22.56 ( int, t, (one_one int) ) 22.46/22.56 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.46/22.56 ( int, y, v ) 22.46/22.56 ( int, y, w ) 22.46/22.56 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, sa, v ) 22.46/22.56 ( int, sa, w ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, x, v ) 22.46/22.56 ( int, x, w ) 22.46/22.56 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.46/22.56 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, r, v ) 22.46/22.56 ( int, r, w ) 22.46/22.56 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.46/22.56 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.46/22.56 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.46/22.56 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.56 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, skv_4, (zero_zero int) ) 22.46/22.56 ( int, skv_5, (zero_zero int) ) 22.46/22.56 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( real, pi, (zero_zero real) ) 22.46/22.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.46/22.56 ( 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)))) ) 22.46/22.56 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.46/22.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.46/22.56 ( real, (hAPP real real (hAPP 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))) ) 22.46/22.56 ( real, (hAPP real real (hAPP 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) ) 22.46/22.56 ( real, (zero_zero real), pi ) 22.46/22.56 ( 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)))) ) 22.46/22.56 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( real, (zero_zero real), skv_10 ) 22.46/22.56 ( real, (zero_zero real), skv_11 ) 22.46/22.56 ( real, (zero_zero real), skv_15 ) 22.46/22.56 ( real, (zero_zero real), skv_18 ) 22.46/22.56 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.46/22.56 ( 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)))))) ) 22.46/22.56 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.46/22.56 ( 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 ) 22.46/22.56 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( real, skv_10, (zero_zero real) ) 22.46/22.56 ( real, skv_11, (zero_zero real) ) 22.46/22.56 ( real, skv_15, (zero_zero real) ) 22.46/22.56 ( real, skv_18, (zero_zero real) ) 22.46/22.56 ( complex, ii, ii ) 22.46/22.56 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.46/22.56 ( 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 ) 22.46/22.56 ) 22.46/22.56 (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 (topological_space 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))))) ) 22.46/22.56 ( rat ) 22.46/22.56 ( int ) 22.46/22.56 ( (fun int int) ) 22.46/22.56 ( nat ) 22.46/22.56 ( bool ) 22.46/22.56 ( real ) 22.46/22.56 ( (fun real real) ) 22.46/22.56 ( (fun nat nat) ) 22.46/22.56 ( (filter nat) ) 22.46/22.56 ( complex ) 22.46/22.56 ( (fun int bool) ) 22.46/22.56 ( (product_prod int int) ) 22.46/22.56 ( (fun bool bool) ) 22.46/22.56 ( (fun nat bool) ) 22.46/22.56 ( (fun nat (fun nat bool)) ) 22.46/22.56 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.46/22.56 ( quickcheck_code_int ) 22.46/22.56 ( code_code_numeral ) 22.46/22.56 ( (fun nat (product_prod int int)) ) 22.46/22.56 ( (product_prod real real) ) 22.46/22.56 ( (filter real) ) 22.46/22.56 ( (product_prod nat nat) ) 22.46/22.56 ( (fun (product_prod nat nat) bool) ) 22.46/22.56 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.46/22.56 ( (fun nat (product_prod nat nat)) ) 22.46/22.56 ( (fun nat rat) ) 22.46/22.56 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (hAPP int int _let_2 W))) (let ((_let_5 (hAPP int _let_3 negDivAlg _let_0))) (let ((_let_6 (hAPP int _let_1 _let_5 _let_4))) (let ((_let_7 (hAPP int int (hAPP int (fun int int) (plus_plus int) _let_0) _let_4))) (let ((_let_8 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_7)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) _let_4))) (and (or _let_8 (= _let_6 (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust _let_4) (hAPP int _let_1 _let_5 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4))))) (or (not _let_8) (= _let_6 (hAPP int _let_1 (hAPP int _let_3 (product_Pair int int) (hAPP int int _let_2 min)) _let_7)))))))))))))) ) 22.46/22.56 ( pls ) 22.46/22.56 ( (hAPP int int bit1 pls) ) 22.46/22.56 ( min ) 22.46/22.56 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.46/22.56 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((N_3 $$unsorted)) (= (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) N_3)) (not (forall ((M_2 $$unsorted)) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) X_1) N_3))) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) X_1) M_2)))) )) ))) ) 22.46/22.56 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (the X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)))) ) 22.46/22.56 ( int ) 22.46/22.56 ( nat ) 22.46/22.56 ( bool ) 22.46/22.56 ( real ) 22.46/22.56 ( (filter nat) ) 22.46/22.56 ( complex ) 22.46/22.56 ( (fun int bool) ) 22.46/22.56 ( (product_prod int int) ) 22.46/22.56 ( (fun nat bool) ) 22.46/22.56 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.46/22.56 ( (product_prod real real) ) 22.46/22.56 ( (filter real) ) 22.46/22.56 ( (product_prod nat nat) ) 22.46/22.56 ( (fun nat rat) ) 22.46/22.56 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$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)))) ) 22.46/22.56 ( rat ) 22.46/22.56 ( int ) 22.46/22.56 ( (fun int int) ) 22.46/22.56 ( nat ) 22.46/22.56 ( bool ) 22.46/22.56 ( real ) 22.46/22.56 ( (fun real real) ) 22.46/22.56 ( (fun nat nat) ) 22.46/22.56 ( complex ) 22.46/22.56 ( (product_prod int int) ) 22.46/22.56 ( (fun bool bool) ) 22.46/22.56 ( (fun nat bool) ) 22.46/22.56 ( (fun nat (fun nat bool)) ) 22.46/22.56 ( quickcheck_code_int ) 22.46/22.56 ( code_code_numeral ) 22.46/22.56 ( (fun nat (product_prod int int)) ) 22.46/22.56 ( (product_prod real real) ) 22.46/22.56 ( (product_prod nat nat) ) 22.46/22.56 ( (fun (product_prod nat nat) bool) ) 22.46/22.56 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.46/22.56 ( (fun nat (product_prod nat nat)) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((Z_4 $$unsorted) (Z_1 $$unsorted) (W_2 $$unsorted) (W $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 W_2) W))) (not (hBOOL (hAPP int bool (hAPP int _let_2 (ord_less_eq int) Z_4) Z_1))) (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 (hAPP int int (hAPP int _let_0 _let_1 W_2) Z_4)) (hAPP int int (hAPP int _let_0 _let_1 W) Z_1)))))))) ) 22.46/22.56 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one 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) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((Xa $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) A_2))) (hBOOL (hAPP int bool nat_is_nat Xa)))) ) 22.46/22.56 ( (one_one int), zEven ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Q_6 $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (let ((_let_3 (zero_zero int))) (let ((_let_4 (ord_less_eq int))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 _let_3) B_8)))) (or (not (= (ti int A_9) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) B_8) Q_6)) Y))) (and (not _let_5) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 Y) _let_3))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 B_8) Y))))) (and _let_5 (or (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 Y) B_8))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 _let_3) Y))))) (= _let_3 (ti int B_8)) (= (hAPP int int (hAPP int _let_0 (div_mod int) A_9) B_8) (ti int Y))))))))) ) 22.46/22.56 ( min, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.46/22.56 ( s, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.56 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, (one_one int) ) 22.46/22.56 ( m, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 22.46/22.56 ( v, x, v, (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.46/22.56 ( sa, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.46/22.56 ( r, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 22.46/22.56 ( m1, r, v, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_130297 $$unsorted) (BOUND_VARIABLE_130298 $$unsorted) (BOUND_VARIABLE_130299 $$unsorted) (BOUND_VARIABLE_130300 $$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_130298))) (let ((_let_3 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_130300))) (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_130299) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 _let_2 BOUND_VARIABLE_130297) _let_3))) (= (ti X_b BOUND_VARIABLE_130299) (ti X_b BOUND_VARIABLE_130297))))))) ) 22.46/22.56 ( 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)))) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X $$unsorted) (Y $$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 real real sqrt (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 X) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 Y) _let_2))) (hAPP complex real (norm_norm complex) (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y)))))) ) 22.46/22.56 ( (one_one real), (zero_zero real) ) 22.46/22.56 ( (zero_zero real), (one_one real) ) 22.46/22.56 ( (zero_zero real), (zero_zero real) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((B_2 $$unsorted) (A_3 $$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_3) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_3) B_2)) zOdd)))))) ) 22.46/22.56 ( (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)))) ) 22.46/22.56 ( (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) ) 22.46/22.56 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.46/22.56 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.46/22.56 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.56 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.56 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.46/22.56 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.46/22.56 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.46/22.56 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.46/22.56 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.56 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.46/22.56 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((Xa $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) Xa))) (not (forall ((Y_1 $$unsorted)) (not (= Xa (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_1)))) ))) ) 22.46/22.56 ( (zero_zero nat) ) 22.46/22.56 ( (one_one nat) ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 pls)))) (or (not (number_ring X_a)) (not (field X_a)) (= _let_0 (hAPP X_a X_a (inverse_inverse X_a) _let_0)))) ) 22.46/22.56 ( rat ) 22.46/22.56 ( int ) 22.46/22.56 ( nat ) 22.46/22.56 ( real ) 22.46/22.56 ( complex ) 22.46/22.56 ( quickcheck_code_int ) 22.46/22.56 ( code_code_numeral ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP nat real (real_1 nat) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= N (hAPP real nat natfloor X))))) ) 22.46/22.56 ( (zero_zero nat), pi ) 22.46/22.56 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.56 ( (zero_zero nat), skv_10 ) 22.46/22.56 ( (zero_zero nat), skv_11 ) 22.46/22.56 ( (zero_zero nat), skv_15 ) 22.46/22.56 ( (zero_zero nat), skv_18 ) 22.46/22.56 ) 22.46/22.56 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130499 $$unsorted) (BOUND_VARIABLE_130500 $$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_130499) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_130500) _let_0)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 (zero_zero X_a)) BOUND_VARIABLE_130500))) (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_130499) BOUND_VARIABLE_130500)))))))) ) 22.46/22.56 ( int, (one_one int), t ) 22.46/22.56 ( int, min, pls ) 22.46/22.56 ( int, min, min ) 22.46/22.56 ( int, (zero_zero int), pls ) 22.46/22.56 ( int, (zero_zero int), (one_one int) ) 22.46/22.56 ( int, (zero_zero int), min ) 22.46/22.56 ( int, (zero_zero int), s ) 22.46/22.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.56 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.56 ( int, (zero_zero int), skv_4 ) 22.46/22.56 ( int, (zero_zero int), skv_5 ) 22.46/22.56 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.56 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.46/22.56 ( real, (hAPP real real (hAPP 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))) ) 22.46/22.56 ( real, (zero_zero real), pi ) 22.46/22.56 ( 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)))) ) 22.46/22.57 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( real, (zero_zero real), skv_10 ) 22.46/22.57 ( real, (zero_zero real), skv_11 ) 22.46/22.57 ( real, (zero_zero real), skv_15 ) 22.46/22.57 ( real, (zero_zero real), skv_18 ) 22.46/22.57 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.46/22.57 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130528 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP X_a real (norm_norm X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_130528)) (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_130528))) ) 22.46/22.57 ( int, (zero_zero nat) ) 22.46/22.57 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.57 ( int, (one_one nat) ) 22.46/22.57 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.57 ( int, n ) 22.46/22.57 ( real, (zero_zero nat) ) 22.46/22.57 ( real, (one_one nat) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130601 $$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_130601)))) (= _let_0 (ti X_a BOUND_VARIABLE_130601)) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_130601))))) ) 22.46/22.57 ( int, pls ) 22.46/22.57 ( int, min ) 22.46/22.57 ( int, s ) 22.46/22.57 ( int, s1 ) 22.46/22.57 ( int, m ) 22.46/22.57 ( int, t ) 22.46/22.57 ( int, v ) 22.46/22.57 ( int, w ) 22.46/22.57 ( int, y ) 22.46/22.57 ( int, sa ) 22.46/22.57 ( int, x ) 22.46/22.57 ( int, r ) 22.46/22.57 ( int, m1 ) 22.46/22.57 ( int, skv_14 ) 22.46/22.57 ( int, skv_20 ) 22.46/22.57 ( (fun int int), bit1 ) 22.46/22.57 ( (fun int int), bit0 ) 22.46/22.57 ( (fun int int), succ ) 22.46/22.57 ( (fun int int), pred ) 22.46/22.57 ( (fun int int), (fact_fact int) ) 22.46/22.57 ( (fun int int), zfact ) 22.46/22.57 ( nat, n ) 22.46/22.57 ( nat, tn ) 22.46/22.57 ( bool, fTrue ) 22.46/22.57 ( bool, fFalse ) 22.46/22.57 ( real, pi ) 22.46/22.57 ( real, (zero_zero real) ) 22.46/22.57 ( (fun nat real), (real_1 nat) ) 22.46/22.57 ( (fun nat real), cos_coeff ) 22.46/22.57 ( (fun nat real), sin_coeff ) 22.46/22.57 ( (fun real real), sin ) 22.46/22.57 ( (fun real real), cos ) 22.46/22.57 ( (fun real real), sqrt ) 22.46/22.57 ( (fun real real), tan ) 22.46/22.57 ( (fun real real), ln ) 22.46/22.57 ( (fun real real), arctan ) 22.46/22.57 ( (fun real real), arcsin ) 22.46/22.57 ( (fun real real), arccos ) 22.46/22.57 ( (fun nat nat), suc ) 22.46/22.57 ( (fun nat nat), (fact_fact nat) ) 22.46/22.57 ( (fun nat nat), nat_size ) 22.46/22.57 ( (fun nat nat), (size_size nat) ) 22.46/22.57 ( (fun nat nat), fact ) 22.46/22.57 ( (filter nat), sequentially ) 22.46/22.57 ( (fun int (fun int rat)), fract ) 22.46/22.57 ( complex, ii ) 22.46/22.57 ( (fun int bool), zOdd ) 22.46/22.57 ( (fun int bool), zprime ) 22.46/22.57 ( (fun int bool), zEven ) 22.46/22.57 ( (fun int bool), nat_neg ) 22.46/22.57 ( (fun int bool), nat_is_nat ) 22.46/22.57 ( (fun int bool), (even_odd_even int) ) 22.46/22.57 ( (fun int bool), twoSqu1091635170sum2sq ) 22.46/22.57 ( (fun int (fun int int)), legacy_zgcd ) 22.46/22.57 ( (fun int (fun int int)), (gcd_gcd int) ) 22.46/22.57 ( (fun int (fun int int)), inv ) 22.46/22.57 ( (fun int (fun int int)), multInv ) 22.46/22.57 ( (fun int (fun int int)), legendre ) 22.46/22.57 ( (fun int (fun int int)), standardRes ) 22.46/22.57 ( (fun int (fun int int)), nat_tsub ) 22.46/22.57 ( (fun int (fun int int)), z3div ) 22.46/22.57 ( (fun int (fun int int)), z3mod ) 22.46/22.57 ( (fun int (fun int int)), int_lcm ) 22.46/22.57 ( (fun int (fun int int)), int_gcd ) 22.46/22.57 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.46/22.57 ( (fun bool bool), fNot ) 22.46/22.57 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.46/22.57 ( (fun bool (fun bool bool)), fconj ) 22.46/22.57 ( (fun bool (fun bool bool)), fdisj ) 22.46/22.57 ( (fun bool (fun bool bool)), fimplies ) 22.46/22.57 ( (fun int (fun int bool)), quadRes ) 22.46/22.57 ( (fun int (fun int bool)), d22set ) 22.46/22.57 ( (fun int (fun int bool)), norRRset ) 22.46/22.57 ( (fun int (fun int bool)), sRStar ) 22.46/22.57 ( (fun int (fun int bool)), sr ) 22.46/22.57 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.46/22.57 ( (fun nat bool), (even_odd_even nat) ) 22.46/22.57 ( (fun nat bool), prime ) 22.46/22.57 ( (fun real complex), cis ) 22.46/22.57 ( (fun nat (fun nat bool)), coprime ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.46/22.57 ( (fun (product_prod int int) bool), frac_1 ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.46/22.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.46/22.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.46/22.57 ( (fun (fun int bool) bool), nat_nat_set ) 22.46/22.57 ( (fun nat (fun real real)), root ) 22.46/22.57 ( (fun real (fun real real)), log ) 22.46/22.57 ( (fun real (fun real real)), powr ) 22.46/22.57 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.46/22.57 ( (fun complex complex), cnj ) 22.46/22.57 ( (fun complex complex), expi ) 22.46/22.57 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.46/22.57 ( (fun nat (fun nat nat)), nat_gcd ) 22.46/22.57 ( (fun nat (fun nat nat)), nat_lcm ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.46/22.57 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.46/22.57 ( (fun int (fun (fun int bool) bool)), resSet ) 22.46/22.57 ( (fun int nat), nat_1 ) 22.46/22.57 ( (fun int nat), phi ) 22.46/22.57 ( (fun complex real), re ) 22.46/22.57 ( (fun complex real), im ) 22.46/22.57 ( (fun complex real), arg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.46/22.57 ( (fun (product_prod nat nat) bool), pred_nat ) 22.46/22.57 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.46/22.57 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.46/22.57 ( (fun (fun int bool) int), (the int) ) 22.46/22.57 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.46/22.57 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.46/22.57 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.46/22.57 ( (fun real (fun real complex)), rcis ) 22.46/22.57 ( (fun real (fun real complex)), complex_1 ) 22.46/22.57 ( (fun int (fun int (fun int bool))), zcong ) 22.46/22.57 ( (fun int (fun int (fun int bool))), wset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), noXRRset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), bnorRset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), zcongm ) 22.46/22.57 ( (fun real nat), natceiling ) 22.46/22.57 ( (fun real nat), natfloor ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.46/22.57 ( (fun int real), (real_1 int) ) 22.46/22.57 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.46/22.57 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.46/22.57 ( (fun complex nat), (size_size complex) ) 22.46/22.57 ( (fun complex nat), complex_size ) 22.46/22.57 ( (fun (fun nat rat) bool), vanishes ) 22.46/22.57 ( (fun (product_prod int int) rat), frct ) 22.46/22.57 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.46/22.57 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.46/22.57 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.46/22.57 ( (fun rat real), ratreal ) 22.46/22.57 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.46/22.57 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.46/22.57 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.46/22.57 ( (fun rat (product_prod int int)), quotient_of ) 22.46/22.57 ( (fun int (fun nat nat)), nat_aux ) 22.46/22.57 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.46/22.57 ( (fun int (list int)), quickc666637781d_zero ) 22.46/22.57 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.46/22.57 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.46/22.57 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.46/22.57 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.46/22.57 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.46/22.57 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.46/22.57 ( (fun code_code_numeral int), code_int_of ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130632 $$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_130632) (ring_1_Ints X_a)))) (not (forall ((Z_2 $$unsorted)) (not (= (hAPP int X_a (ring_1_of_int X_a) Z_2) (ti X_a BOUND_VARIABLE_130632))) )))) ) 22.46/22.57 ( int, (one_one int) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130652 $$unsorted)) (or (not (finite_finite X_a)) (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) BOUND_VARIABLE_130652))) ) 22.46/22.57 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130661 $$unsorted) (BOUND_VARIABLE_130662 $$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)) (= (or (and (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_130661) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_130662) (zero_zero X_a)))) (and (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130662)) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130661)))) (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_130661) BOUND_VARIABLE_130662)))))) ) 22.46/22.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.46/22.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.46/22.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.46/22.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.46/22.57 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.46/22.57 ( int, y, v ) 22.46/22.57 ( int, y, w ) 22.46/22.57 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.57 ( int, sa, v ) 22.46/22.57 ( int, sa, w ) 22.46/22.57 ( int, x, v ) 22.46/22.57 ( int, x, w ) 22.46/22.57 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.46/22.57 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.57 ( int, r, v ) 22.46/22.57 ( int, r, w ) 22.46/22.57 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.46/22.57 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.46/22.57 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.46/22.57 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.46/22.57 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.57 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.57 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.46/22.57 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.46/22.57 ( 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)))))) ) 22.46/22.57 ( 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 ) 22.46/22.57 ( complex, ii, ii ) 22.46/22.57 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.46/22.57 ( 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 ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130726 $$unsorted) (BOUND_VARIABLE_130727 $$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_130726)) (hAPP X_a real _let_0 BOUND_VARIABLE_130727))) (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_130726) BOUND_VARIABLE_130727)))))) ) 22.46/22.57 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.46/22.57 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.46/22.57 ( 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)))), (one_one int) ) 22.46/22.57 ( 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) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.57 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( nat, (one_one nat), (one_one nat) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((W $$unsorted)) (= (hAPP int int (number_number_of int) W) (hAPP int int (ring_1_of_int int) W)) ) 22.46/22.57 ( pls ) 22.46/22.57 ( (hAPP int int bit1 pls) ) 22.46/22.57 ( min ) 22.46/22.57 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.46/22.57 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.57 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130773 $$unsorted)) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_130773)) (= (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_130773)) BOUND_VARIABLE_130773))) ) 22.46/22.57 ( int, pls ) 22.46/22.57 ( int, min ) 22.46/22.57 ( int, s ) 22.46/22.57 ( int, s1 ) 22.46/22.57 ( int, m ) 22.46/22.57 ( int, t ) 22.46/22.57 ( int, v ) 22.46/22.57 ( int, w ) 22.46/22.57 ( int, y ) 22.46/22.57 ( int, sa ) 22.46/22.57 ( int, x ) 22.46/22.57 ( int, r ) 22.46/22.57 ( int, m1 ) 22.46/22.57 ( int, skv_14 ) 22.46/22.57 ( int, skv_20 ) 22.46/22.57 ( (fun int int), bit1 ) 22.46/22.57 ( (fun int int), bit0 ) 22.46/22.57 ( (fun int int), succ ) 22.46/22.57 ( (fun int int), pred ) 22.46/22.57 ( (fun int int), (fact_fact int) ) 22.46/22.57 ( (fun int int), zfact ) 22.46/22.57 ( nat, n ) 22.46/22.57 ( nat, tn ) 22.46/22.57 ( bool, fTrue ) 22.46/22.57 ( bool, fFalse ) 22.46/22.57 ( real, pi ) 22.46/22.57 ( real, (zero_zero real) ) 22.46/22.57 ( (fun nat real), (real_1 nat) ) 22.46/22.57 ( (fun nat real), cos_coeff ) 22.46/22.57 ( (fun nat real), sin_coeff ) 22.46/22.57 ( (fun real real), sin ) 22.46/22.57 ( (fun real real), cos ) 22.46/22.57 ( (fun real real), sqrt ) 22.46/22.57 ( (fun real real), tan ) 22.46/22.57 ( (fun real real), ln ) 22.46/22.57 ( (fun real real), arctan ) 22.46/22.57 ( (fun real real), arcsin ) 22.46/22.57 ( (fun real real), arccos ) 22.46/22.57 ( (fun nat nat), suc ) 22.46/22.57 ( (fun nat nat), (fact_fact nat) ) 22.46/22.57 ( (fun nat nat), nat_size ) 22.46/22.57 ( (fun nat nat), (size_size nat) ) 22.46/22.57 ( (fun nat nat), fact ) 22.46/22.57 ( (filter nat), sequentially ) 22.46/22.57 ( (fun int (fun int rat)), fract ) 22.46/22.57 ( complex, ii ) 22.46/22.57 ( (fun int bool), zOdd ) 22.46/22.57 ( (fun int bool), zprime ) 22.46/22.57 ( (fun int bool), zEven ) 22.46/22.57 ( (fun int bool), nat_neg ) 22.46/22.57 ( (fun int bool), nat_is_nat ) 22.46/22.57 ( (fun int bool), (even_odd_even int) ) 22.46/22.57 ( (fun int bool), twoSqu1091635170sum2sq ) 22.46/22.57 ( (fun int (fun int int)), legacy_zgcd ) 22.46/22.57 ( (fun int (fun int int)), (gcd_gcd int) ) 22.46/22.57 ( (fun int (fun int int)), inv ) 22.46/22.57 ( (fun int (fun int int)), multInv ) 22.46/22.57 ( (fun int (fun int int)), legendre ) 22.46/22.57 ( (fun int (fun int int)), standardRes ) 22.46/22.57 ( (fun int (fun int int)), nat_tsub ) 22.46/22.57 ( (fun int (fun int int)), z3div ) 22.46/22.57 ( (fun int (fun int int)), z3mod ) 22.46/22.57 ( (fun int (fun int int)), int_lcm ) 22.46/22.57 ( (fun int (fun int int)), int_gcd ) 22.46/22.57 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.46/22.57 ( (fun bool bool), fNot ) 22.46/22.57 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.46/22.57 ( (fun bool (fun bool bool)), fconj ) 22.46/22.57 ( (fun bool (fun bool bool)), fdisj ) 22.46/22.57 ( (fun bool (fun bool bool)), fimplies ) 22.46/22.57 ( (fun int (fun int bool)), quadRes ) 22.46/22.57 ( (fun int (fun int bool)), d22set ) 22.46/22.57 ( (fun int (fun int bool)), norRRset ) 22.46/22.57 ( (fun int (fun int bool)), sRStar ) 22.46/22.57 ( (fun int (fun int bool)), sr ) 22.46/22.57 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.46/22.57 ( (fun nat bool), (even_odd_even nat) ) 22.46/22.57 ( (fun nat bool), prime ) 22.46/22.57 ( (fun real complex), cis ) 22.46/22.57 ( (fun nat (fun nat bool)), coprime ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.46/22.57 ( (fun (product_prod int int) bool), frac_1 ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.46/22.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.46/22.57 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.46/22.57 ( (fun (fun int bool) bool), nat_nat_set ) 22.46/22.57 ( (fun nat (fun real real)), root ) 22.46/22.57 ( (fun real (fun real real)), log ) 22.46/22.57 ( (fun real (fun real real)), powr ) 22.46/22.57 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.46/22.57 ( (fun complex complex), cnj ) 22.46/22.57 ( (fun complex complex), expi ) 22.46/22.57 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.46/22.57 ( (fun nat (fun nat nat)), nat_gcd ) 22.46/22.57 ( (fun nat (fun nat nat)), nat_lcm ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.46/22.57 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.46/22.57 ( (fun int (fun (fun int bool) bool)), resSet ) 22.46/22.57 ( (fun int nat), nat_1 ) 22.46/22.57 ( (fun int nat), phi ) 22.46/22.57 ( (fun complex real), re ) 22.46/22.57 ( (fun complex real), im ) 22.46/22.57 ( (fun complex real), arg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.46/22.57 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.46/22.57 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.46/22.57 ( (fun (product_prod nat nat) bool), pred_nat ) 22.46/22.57 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.46/22.57 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.46/22.57 ( (fun (fun int bool) int), (the int) ) 22.46/22.57 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.46/22.57 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.46/22.57 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.46/22.57 ( (fun real (fun real complex)), rcis ) 22.46/22.57 ( (fun real (fun real complex)), complex_1 ) 22.46/22.57 ( (fun int (fun int (fun int bool))), zcong ) 22.46/22.57 ( (fun int (fun int (fun int bool))), wset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), noXRRset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), bnorRset ) 22.46/22.57 ( (fun int (fun int (fun int bool))), zcongm ) 22.46/22.57 ( (fun real nat), natceiling ) 22.46/22.57 ( (fun real nat), natfloor ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.46/22.57 ( (fun int real), (real_1 int) ) 22.46/22.57 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.46/22.57 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.46/22.57 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.46/22.57 ( (fun complex nat), (size_size complex) ) 22.46/22.57 ( (fun complex nat), complex_size ) 22.46/22.57 ( (fun (fun nat rat) bool), vanishes ) 22.46/22.57 ( (fun (product_prod int int) rat), frct ) 22.46/22.57 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.46/22.57 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.46/22.57 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.46/22.57 ( (fun rat real), ratreal ) 22.46/22.57 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.46/22.57 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.46/22.57 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.46/22.57 ( (fun rat (product_prod int int)), quotient_of ) 22.46/22.57 ( (fun int (fun nat nat)), nat_aux ) 22.46/22.57 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.46/22.57 ( (fun int (list int)), quickc666637781d_zero ) 22.46/22.57 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.46/22.57 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.46/22.57 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.46/22.57 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.46/22.57 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.46/22.57 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.46/22.57 ( (fun code_code_numeral int), code_int_of ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130796 $$unsorted) (BOUND_VARIABLE_130797 $$unsorted) (BOUND_VARIABLE_130798 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_130796))) (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_130798))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130797))) (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_130798) BOUND_VARIABLE_130797))))) ) 22.46/22.57 ( int, (zero_zero 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) ) 22.46/22.57 ( int, (zero_zero int), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.46/22.57 ( 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) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 22.46/22.57 ( 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) ) 22.46/22.57 ( int, m1, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.46/22.57 ( 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) ) 22.46/22.57 ( int, skv_5, (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) ) 22.46/22.57 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na)) (not (forall ((M_2 $$unsorted)) (not (= Na (hAPP nat nat suc M_2))) ))) ) 22.46/22.57 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.57 ( n ) 22.46/22.57 ( tn ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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) (plus_plus int) A_3) B_2)) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 A_3) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_2) zEven)))))) ) 22.46/22.57 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.46/22.57 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.46/22.57 ( (hAPP nat int (hAPP 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) ) 22.46/22.57 ( (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) ) 22.46/22.57 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.46/22.57 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.46/22.57 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.46/22.57 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.57 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.46/22.57 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ) 22.46/22.57 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130838 $$unsorted) (BOUND_VARIABLE_130839 $$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_130839) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_130838) _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_130839) BOUND_VARIABLE_130838)) _let_2)))))) ) 22.46/22.57 ( 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)))) ) 22.46/22.57 ( 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) ) 22.46/22.57 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.46/22.57 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.46/22.57 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.57 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.57 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.46/22.57 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.57 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.46/22.57 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.46/22.58 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.46/22.58 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( nat, (one_one nat), (one_one nat) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130864 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_130864) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_130864)) (zero_zero X_a))))) ) 22.46/22.58 ( real, (one_one int) ) 22.46/22.58 ( real, (zero_zero int) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130886 $$unsorted) (BOUND_VARIABLE_130887 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_char_0 X_a)) (= (= (ti int BOUND_VARIABLE_130887) (ti int BOUND_VARIABLE_130886)) (= (hAPP int X_a _let_0 BOUND_VARIABLE_130886) (hAPP int X_a _let_0 BOUND_VARIABLE_130887))))) ) 22.46/22.58 ( rat, r, m ) 22.46/22.58 ( int, m, r ) 22.46/22.58 ( int, r, r ) 22.46/22.58 ( real, s1, v ) 22.46/22.58 ( complex, s1, s1 ) 22.46/22.58 ( complex, v, s1 ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130915 $$unsorted) (BOUND_VARIABLE_130916 $$unsorted) (BOUND_VARIABLE_130917 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_130917)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_130917) BOUND_VARIABLE_130916))) (= (= (hAPP X_a X_a (hAPP X_a _let_0 (div_div X_a) BOUND_VARIABLE_130916) BOUND_VARIABLE_130917) (ti X_a BOUND_VARIABLE_130915)) (= (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_130915) BOUND_VARIABLE_130917) (ti X_a BOUND_VARIABLE_130916))))) ) 22.46/22.58 ( int, s1, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.46/22.58 ( int, v, (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X $$unsorted) (Y $$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) Y)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real re X)) (hAPP complex real im Y))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real im X)) (hAPP complex real re Y)))))) ) 22.46/22.58 ( ii, ii ) 22.46/22.58 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.46/22.58 ( (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 ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_130953 $$unsorted) (BOUND_VARIABLE_130954 $$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_130954))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_130953))) (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_130954) BOUND_VARIABLE_130953))))) ) 22.46/22.58 ( 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)))) ) 22.46/22.58 ( 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) ) 22.46/22.58 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.46/22.58 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.46/22.58 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.58 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.46/22.58 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.46/22.58 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.46/22.58 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( nat, (one_one nat), (one_one nat) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131033 $$unsorted) (BOUND_VARIABLE_131034 $$unsorted) (BOUND_VARIABLE_131035 $$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_131035) (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_131034) BOUND_VARIABLE_131035)) BOUND_VARIABLE_131033)) (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_131033) BOUND_VARIABLE_131035)) BOUND_VARIABLE_131034))))))) ) 22.46/22.58 ( int, pls, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( 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))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( 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))) ) 22.46/22.58 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.46/22.58 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int int (number_number_of int) min))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zOdd))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Xa))) (= _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) _let_1) (hAPP int nat nat_1 Xa)))))) ) 22.46/22.58 ( pls ) 22.46/22.58 ( (one_one int) ) 22.46/22.58 ( min ) 22.46/22.58 ( (zero_zero int) ) 22.46/22.58 ( s ) 22.46/22.58 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.58 ( t ) 22.46/22.58 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.58 ( skv_4 ) 22.46/22.58 ( skv_5 ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (or (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N)) (= M (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N))))) ) 22.46/22.58 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.58 ( (zero_zero nat), n ) 22.46/22.58 ( (zero_zero nat), tn ) 22.46/22.58 ( (hAPP int nat nat_1 t), (one_one nat) ) 22.46/22.58 ) 22.46/22.58 (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)))) ) 22.46/22.58 ( nat, real ) 22.46/22.58 ( real, real ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (inverse_inverse real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real _let_0 X) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_0 (hAPP real real sqrt X))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.46/22.58 ( pi ) 22.46/22.58 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.58 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( (one_one real) ) 22.46/22.58 ( (zero_zero real) ) 22.46/22.58 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.46/22.58 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.46/22.58 ( skv_2 ) 22.46/22.58 ( skv_9 ) 22.46/22.58 ( skv_12 ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131122 $$unsorted) (BOUND_VARIABLE_131123 $$unsorted) (BOUND_VARIABLE_131124 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_131122))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_131123)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_131124)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_131122))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131123) BOUND_VARIABLE_131124)))))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131167 $$unsorted) (BOUND_VARIABLE_131168 $$unsorted) (BOUND_VARIABLE_131169 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (ord_less_eq X_a))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_131168))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) _let_4)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) BOUND_VARIABLE_131169) _let_4))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_4) _let_1)))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_131167) _let_6))) (or _let_5 (and (or _let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_1) BOUND_VARIABLE_131169))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_6) BOUND_VARIABLE_131167)))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_131167) _let_4)) BOUND_VARIABLE_131169)))))))))))) ) 22.46/22.58 ( real, pi, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((N $$unsorted)) (= (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) N) (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP nat real (real_1 nat) N)) pi))) ) 22.46/22.58 ( (zero_zero nat) ) 22.46/22.58 ( (one_one nat) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((Z_1 $$unsorted)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int (uminus_uminus int) Z_1)) Z_1)) ) 22.46/22.58 ( pls ) 22.46/22.58 ( (one_one int) ) 22.46/22.58 ( min ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2))) (not (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_1)) K_2))) ))) ))) ) 22.46/22.58 ( real ) 22.46/22.58 ( complex ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((N $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (not (forall ((X_1 $$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) (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_1)) (one_one nat))))))) ))) ) 22.46/22.58 ( (zero_zero nat) ) 22.46/22.58 ( (one_one nat) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) min) (hAPP int int succ K_4)) ) 22.46/22.58 ( pls ) 22.46/22.58 ( min ) 22.46/22.58 ( (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)))) ) 22.46/22.58 ( y ) 22.46/22.58 ( x ) 22.46/22.58 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.46/22.58 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.46/22.58 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.46/22.58 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.46/22.58 ( (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))) m1))) ) 22.46/22.58 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131469 $$unsorted) (BOUND_VARIABLE_131470 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_131469))) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_131470)) (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_131470)) BOUND_VARIABLE_131469)))) ) 22.46/22.58 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.46/22.58 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, v, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, w, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, y, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, x, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, skv_6, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, skv_7, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, skv_16, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, skv_23, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( int, skv_24, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 22.46/22.58 ) 22.46/22.58 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131489 $$unsorted) (BOUND_VARIABLE_131490 $$unsorted) (BOUND_VARIABLE_131491 $$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_131491))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131489) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_131490) BOUND_VARIABLE_131491))) (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_131489) BOUND_VARIABLE_131491)) BOUND_VARIABLE_131490))))))) ) 22.46/22.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w) ) 22.46/22.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v) ) 22.46/22.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14) ) 22.46/22.58 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.46/22.58 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.59 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.59 ) 22.54/22.59 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131519 $$unsorted) (BOUND_VARIABLE_131520 $$unsorted) (BOUND_VARIABLE_131521 $$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_131519))) (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_131521)) BOUND_VARIABLE_131520) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_131520)) BOUND_VARIABLE_131521)))))) ) 22.54/22.62 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.62 ( 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))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.62 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.63 ( 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) ) 22.54/22.63 ( 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 ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X $$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)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 (hAPP real real sin X))) (hAPP real real cos X)))))) ) 22.54/22.63 ( pi ) 22.54/22.63 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.63 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( (zero_zero real) ) 22.54/22.63 ( (hAPP real 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))))) ) 22.54/22.63 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.54/22.63 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.54/22.63 ( (hAPP real real (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))))) ) 22.54/22.63 ( (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)))) ) 22.54/22.63 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.54/22.63 ( skv_10 ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (semiring_1_of_nat int))) (= (= (hAPP nat int _let_1 Ma) (hAPP int int (uminus_uminus int) (hAPP nat int _let_1 Na))) (and (= _let_0 Na) (= _let_0 Ma))))) ) 22.54/22.63 ( (zero_zero nat), (zero_zero nat) ) 22.54/22.63 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.63 ( (one_one nat), (one_one nat) ) 22.54/22.63 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.63 ( n, n ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131634 $$unsorted) (BOUND_VARIABLE_131635 $$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_131634) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_131635))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_131634)) (hAPP int int (number_number_of int) BOUND_VARIABLE_131635))))) ) 22.54/22.63 ( 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 ) 22.54/22.63 ( nat, (hAPP int nat nat_1 t), (hAPP int int bit1 pls) ) 22.54/22.63 ( code_code_numeral, (zero_zero code_code_numeral), (hAPP int int bit1 pls) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Na))) (= (hAPP _let_0 int (hAPP (fun int int) (fun _let_0 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) Na)) (hAPP int int (fact_fact int) Na)))) ) 22.54/22.63 ( pls ) 22.54/22.63 ( (one_one int) ) 22.54/22.63 ( min ) 22.54/22.63 ( (zero_zero int) ) 22.54/22.63 ( s ) 22.54/22.63 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.63 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.63 ( skv_4 ) 22.54/22.63 ( skv_5 ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (times_times nat))) (let ((_let_2 (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (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_eq int) (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) P_5))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (one_one int)))) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))))))) (hAPP nat nat (hAPP nat _let_0 _let_1 _let_2) _let_2)))))) ) 22.54/22.63 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( y ) 22.54/22.63 ( x ) 22.54/22.63 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.54/22.63 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.54/22.63 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.63 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.54/22.63 ( (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))) m1))) ) 22.54/22.63 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131713 $$unsorted) (BOUND_VARIABLE_131714 $$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 (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_131713) BOUND_VARIABLE_131714))) (or (not (linord1117847801e_zero X_a)) (= (and (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) _let_4))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131714) BOUND_VARIABLE_131713))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_4) _let_2))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_131713) BOUND_VARIABLE_131714)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_131713)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_131714)))))))))) ) 22.54/22.63 ( int, pls, (zero_zero int) ) 22.54/22.63 ( int, (one_one int), (zero_zero int) ) 22.54/22.63 ( int, (one_one int), t ) 22.54/22.63 ( int, min, min ) 22.54/22.63 ( int, min, (zero_zero int) ) 22.54/22.63 ( int, (zero_zero int), pls ) 22.54/22.63 ( int, (zero_zero int), (one_one int) ) 22.54/22.63 ( int, (zero_zero int), min ) 22.54/22.63 ( 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))) ) 22.54/22.63 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( 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))) ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.54/22.63 ( int, t, (one_one int) ) 22.54/22.63 ( 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))) ) 22.54/22.63 ( int, y, v ) 22.54/22.63 ( int, y, w ) 22.54/22.63 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( int, sa, v ) 22.54/22.63 ( int, sa, w ) 22.54/22.63 ( int, x, v ) 22.54/22.63 ( int, x, w ) 22.54/22.63 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.63 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( int, r, v ) 22.54/22.63 ( int, r, w ) 22.54/22.63 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.54/22.63 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.54/22.63 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.54/22.63 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.63 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( 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))) ) 22.54/22.63 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.63 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.63 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.63 ( nat, (zero_zero nat), n ) 22.54/22.63 ( nat, (zero_zero nat), tn ) 22.54/22.63 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.54/22.63 ( nat, n, (zero_zero nat) ) 22.54/22.63 ( nat, tn, (zero_zero nat) ) 22.54/22.63 ( real, pi, (zero_zero real) ) 22.54/22.63 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( 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)) ) 22.54/22.63 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.63 ( 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)))) ) 22.54/22.63 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.54/22.63 ( real, (hAPP real real (hAPP 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))) ) 22.54/22.63 ( real, (hAPP real real (hAPP 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) ) 22.54/22.63 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( real, (zero_zero real), pi ) 22.54/22.63 ( 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)))) ) 22.54/22.63 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( 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))))) ) 22.54/22.63 ( real, (zero_zero real), skv_2 ) 22.54/22.63 ( real, (zero_zero real), skv_9 ) 22.54/22.63 ( real, (zero_zero real), skv_12 ) 22.54/22.63 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.54/22.63 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.63 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.54/22.63 ( 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)))))) ) 22.54/22.63 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.63 ( 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) ) 22.54/22.63 ( 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 ) 22.54/22.63 ( 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 ) 22.54/22.63 ( real, skv_2, (zero_zero real) ) 22.54/22.63 ( real, skv_9, (zero_zero real) ) 22.54/22.63 ( real, skv_12, (zero_zero real) ) 22.54/22.63 ( complex, ii, ii ) 22.54/22.63 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.54/22.63 ( 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 ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) B_2))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_3) B_2))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) A_3)))))) ) 22.54/22.63 ( (one_one int), (one_one int) ) 22.54/22.63 ( (zero_zero int), (one_one int) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_131761 $$unsorted) (BOUND_VARIABLE_131762 $$unsorted) (BOUND_VARIABLE_131763 $$unsorted)) (let ((_let_0 (filter real))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_a)) (not (forall ((S_2 $$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_1 $$unsorted)) (not (= (hAPP nat real S_2 N_1) BOUND_VARIABLE_131763)) )) (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) S_2) BOUND_VARIABLE_131763) sequentially))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_1 (hAPP _let_2 (fun X_a _let_1) (tendsto nat X_a) (hAPP _let_0 _let_2 (hAPP (fun real X_a) (fun _let_0 _let_2) (combb real X_a nat) BOUND_VARIABLE_131761) S_2)) BOUND_VARIABLE_131762) sequentially)))))) )) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 (hAPP (fun real X_a) (fun X_a _let_1) (tendsto real X_a) BOUND_VARIABLE_131761) BOUND_VARIABLE_131762) (hAPP real _let_0 (at real) BOUND_VARIABLE_131763)))))) ) 22.54/22.63 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132099 $$unsorted) (BOUND_VARIABLE_132100 $$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_132099)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_132100))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132100) BOUND_VARIABLE_132099)))))))) ) 22.54/22.63 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.63 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.54/22.63 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 22.54/22.63 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.54/22.63 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132117 $$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_132117) BOUND_VARIABLE_132117))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_132117))))) ) 22.54/22.63 ( int, (one_one int) ) 22.54/22.63 ( 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)))) ) 22.54/22.63 ( 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) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.54/22.63 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.63 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.63 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.63 ( nat, (one_one nat) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((Xa $$unsorted)) (= (not (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun int int))) (not (= (ti int Xa) (hAPP int int (hAPP int _let_0 (plus_plus int) (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_1)) (one_one int))))) )) (not (hBOOL (hAPP int bool (even_odd_even int) Xa)))) ) 22.54/22.63 ( (one_one int) ) 22.54/22.63 ( (zero_zero int) ) 22.54/22.63 ) 22.54/22.63 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132201 $$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 X_a) _let_0) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_132201))) (not (= _let_0 (ti X_a BOUND_VARIABLE_132201)))))) ) 22.54/22.63 ( int, pls ) 22.54/22.63 ( int, min ) 22.54/22.63 ( int, s ) 22.54/22.63 ( int, s1 ) 22.54/22.63 ( int, m ) 22.54/22.63 ( int, t ) 22.54/22.63 ( int, v ) 22.54/22.63 ( int, w ) 22.54/22.63 ( int, y ) 22.54/22.63 ( int, sa ) 22.54/22.63 ( int, x ) 22.54/22.63 ( int, r ) 22.54/22.63 ( int, m1 ) 22.54/22.63 ( int, skv_14 ) 22.54/22.63 ( int, skv_20 ) 22.54/22.63 ( (fun int int), bit1 ) 22.54/22.63 ( (fun int int), bit0 ) 22.54/22.63 ( (fun int int), succ ) 22.54/22.63 ( (fun int int), pred ) 22.54/22.63 ( (fun int int), (fact_fact int) ) 22.54/22.63 ( (fun int int), zfact ) 22.54/22.63 ( nat, n ) 22.54/22.63 ( nat, tn ) 22.54/22.63 ( bool, fTrue ) 22.54/22.63 ( bool, fFalse ) 22.54/22.63 ( real, pi ) 22.54/22.63 ( (fun nat real), (real_1 nat) ) 22.54/22.63 ( (fun nat real), cos_coeff ) 22.54/22.63 ( (fun nat real), sin_coeff ) 22.54/22.63 ( (fun real real), sin ) 22.54/22.63 ( (fun real real), cos ) 22.54/22.63 ( (fun real real), sqrt ) 22.54/22.63 ( (fun real real), tan ) 22.54/22.63 ( (fun real real), ln ) 22.54/22.63 ( (fun real real), arctan ) 22.54/22.63 ( (fun real real), arcsin ) 22.54/22.63 ( (fun real real), arccos ) 22.54/22.63 ( (fun nat nat), suc ) 22.54/22.63 ( (fun nat nat), (fact_fact nat) ) 22.54/22.63 ( (fun nat nat), nat_size ) 22.54/22.63 ( (fun nat nat), (size_size nat) ) 22.54/22.63 ( (fun nat nat), fact ) 22.54/22.63 ( (filter nat), sequentially ) 22.54/22.63 ( (fun int (fun int rat)), fract ) 22.54/22.63 ( complex, ii ) 22.54/22.63 ( (fun int bool), zOdd ) 22.54/22.63 ( (fun int bool), zprime ) 22.54/22.63 ( (fun int bool), zEven ) 22.54/22.63 ( (fun int bool), nat_neg ) 22.54/22.63 ( (fun int bool), nat_is_nat ) 22.54/22.63 ( (fun int bool), (even_odd_even int) ) 22.54/22.63 ( (fun int bool), twoSqu1091635170sum2sq ) 22.54/22.63 ( (fun int (fun int int)), legacy_zgcd ) 22.54/22.63 ( (fun int (fun int int)), (gcd_gcd int) ) 22.54/22.63 ( (fun int (fun int int)), inv ) 22.54/22.63 ( (fun int (fun int int)), multInv ) 22.54/22.63 ( (fun int (fun int int)), legendre ) 22.54/22.63 ( (fun int (fun int int)), standardRes ) 22.54/22.63 ( (fun int (fun int int)), nat_tsub ) 22.54/22.63 ( (fun int (fun int int)), z3div ) 22.54/22.63 ( (fun int (fun int int)), z3mod ) 22.54/22.63 ( (fun int (fun int int)), int_lcm ) 22.54/22.63 ( (fun int (fun int int)), int_gcd ) 22.54/22.63 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.54/22.63 ( (fun bool bool), fNot ) 22.54/22.63 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.54/22.63 ( (fun bool (fun bool bool)), fconj ) 22.54/22.63 ( (fun bool (fun bool bool)), fdisj ) 22.54/22.63 ( (fun bool (fun bool bool)), fimplies ) 22.54/22.63 ( (fun int (fun int bool)), quadRes ) 22.54/22.63 ( (fun int (fun int bool)), d22set ) 22.54/22.63 ( (fun int (fun int bool)), norRRset ) 22.54/22.64 ( (fun int (fun int bool)), sRStar ) 22.54/22.64 ( (fun int (fun int bool)), sr ) 22.54/22.64 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.54/22.64 ( (fun nat bool), (even_odd_even nat) ) 22.54/22.64 ( (fun nat bool), prime ) 22.54/22.64 ( (fun real complex), cis ) 22.54/22.64 ( (fun nat (fun nat bool)), coprime ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.54/22.64 ( (fun (product_prod int int) bool), frac_1 ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.54/22.64 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.54/22.64 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.54/22.64 ( (fun (fun int bool) bool), nat_nat_set ) 22.54/22.64 ( (fun nat (fun real real)), root ) 22.54/22.64 ( (fun real (fun real real)), log ) 22.54/22.64 ( (fun real (fun real real)), powr ) 22.54/22.64 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.54/22.64 ( (fun complex complex), cnj ) 22.54/22.64 ( (fun complex complex), expi ) 22.54/22.64 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.54/22.64 ( (fun nat (fun nat nat)), nat_gcd ) 22.54/22.64 ( (fun nat (fun nat nat)), nat_lcm ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.54/22.64 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.54/22.64 ( (fun int (fun (fun int bool) bool)), resSet ) 22.54/22.64 ( (fun int nat), nat_1 ) 22.54/22.64 ( (fun int nat), phi ) 22.54/22.64 ( (fun complex real), re ) 22.54/22.64 ( (fun complex real), im ) 22.54/22.64 ( (fun complex real), arg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.54/22.64 ( (fun (product_prod nat nat) bool), pred_nat ) 22.54/22.64 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.54/22.64 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.54/22.64 ( (fun (fun int bool) int), (the int) ) 22.54/22.64 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.54/22.64 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.54/22.64 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.54/22.64 ( (fun real (fun real complex)), rcis ) 22.54/22.64 ( (fun real (fun real complex)), complex_1 ) 22.54/22.64 ( (fun int (fun int (fun int bool))), zcong ) 22.54/22.64 ( (fun int (fun int (fun int bool))), wset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), noXRRset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), bnorRset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), zcongm ) 22.54/22.64 ( (fun real nat), natceiling ) 22.54/22.64 ( (fun real nat), natfloor ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.54/22.64 ( (fun int real), (real_1 int) ) 22.54/22.64 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.54/22.64 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.54/22.64 ( (fun complex nat), (size_size complex) ) 22.54/22.64 ( (fun complex nat), complex_size ) 22.54/22.64 ( (fun (fun nat rat) bool), vanishes ) 22.54/22.64 ( (fun (product_prod int int) rat), frct ) 22.54/22.64 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.54/22.64 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.54/22.64 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.54/22.64 ( (fun rat real), ratreal ) 22.54/22.64 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.54/22.64 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.54/22.64 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.54/22.64 ( (fun rat (product_prod int int)), quotient_of ) 22.54/22.64 ( (fun int (fun nat nat)), nat_aux ) 22.54/22.64 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.54/22.64 ( (fun int (list int)), quickc666637781d_zero ) 22.54/22.64 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.54/22.64 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.54/22.64 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.54/22.64 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.54/22.64 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.54/22.64 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.54/22.64 ( (fun code_code_numeral int), code_int_of ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132217 $$unsorted) (BOUND_VARIABLE_132218 $$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_132217)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_132218)))) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_132217) BOUND_VARIABLE_132218)))))))) ) 22.54/22.64 ( 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) ) 22.54/22.64 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.64 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.54/22.64 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.64 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.54/22.64 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.54/22.64 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132236 $$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_132236) BOUND_VARIABLE_132236)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132236) _let_2))))))) ) 22.54/22.64 ( int, (one_one int) ) 22.54/22.64 ( 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)))) ) 22.54/22.64 ( 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) ) 22.54/22.64 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.64 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.54/22.64 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( nat, (one_one nat) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP nat nat suc X) (hAPP nat nat suc Y))) (= X Y)) ) 22.54/22.64 ( (zero_zero nat), (zero_zero nat) ) 22.54/22.64 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.54/22.64 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 22.54/22.64 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.54/22.64 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero nat) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132277 $$unsorted)) (or (not (ring_1 X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_132277))) (= (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP int nat nat_1 BOUND_VARIABLE_132277)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_132277))) ) 22.54/22.64 ( int, (one_one int) ) 22.54/22.64 ( int, (zero_zero int) ) 22.54/22.64 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.64 ( real, (one_one int) ) 22.54/22.64 ( real, (zero_zero int) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real _let_0 X)) (hAPP int real _let_0 Y)))) ) 22.54/22.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.54/22.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.54/22.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.54/22.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.54/22.64 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.54/22.64 ( y, v ) 22.54/22.64 ( y, w ) 22.54/22.64 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( sa, v ) 22.54/22.64 ( sa, w ) 22.54/22.64 ( x, v ) 22.54/22.64 ( x, w ) 22.54/22.64 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.64 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( r, v ) 22.54/22.64 ( r, w ) 22.54/22.64 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.54/22.64 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.54/22.64 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.54/22.64 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.54/22.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.54/22.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.64 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.64 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (number_number_of int) K_4) (hAPP quickcheck_code_int int quickcheck_int_of (hAPP int quickcheck_code_int (number_number_of quickcheck_code_int) K_4))) ) 22.54/22.64 ( pls ) 22.54/22.64 ( (hAPP int int bit1 pls) ) 22.54/22.64 ( (one_one int) ) 22.54/22.64 ( min ) 22.54/22.64 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.64 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((N $$unsorted) (K_4 $$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))))) ) 22.54/22.64 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.54/22.64 ( 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))) ) 22.54/22.64 ( v, y ) 22.54/22.64 ( v, sa ) 22.54/22.64 ( v, x ) 22.54/22.64 ( v, r ) 22.54/22.64 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.54/22.64 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.54/22.64 ( w, y ) 22.54/22.64 ( w, sa ) 22.54/22.64 ( w, x ) 22.54/22.64 ( w, r ) 22.54/22.64 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.54/22.64 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.54/22.64 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.54/22.64 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.64 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.54/22.64 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.64 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.64 ( skv_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))) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132495 $$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_132495) _let_0)))) ) 22.54/22.64 ( real, pi ) 22.54/22.64 ( real, (one_one real) ) 22.54/22.64 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.64 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132513 $$unsorted)) (or (not (real_normed_vector X_a)) (= (= (zero_zero real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_132513)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_132513)))) ) 22.54/22.64 ( int, pls ) 22.54/22.64 ( int, min ) 22.54/22.64 ( int, s ) 22.54/22.64 ( int, s1 ) 22.54/22.64 ( int, m ) 22.54/22.64 ( int, t ) 22.54/22.64 ( int, v ) 22.54/22.64 ( int, w ) 22.54/22.64 ( int, y ) 22.54/22.64 ( int, sa ) 22.54/22.64 ( int, x ) 22.54/22.64 ( int, r ) 22.54/22.64 ( int, m1 ) 22.54/22.64 ( int, skv_14 ) 22.54/22.64 ( int, skv_20 ) 22.54/22.64 ( (fun int int), bit1 ) 22.54/22.64 ( (fun int int), bit0 ) 22.54/22.64 ( (fun int int), succ ) 22.54/22.64 ( (fun int int), pred ) 22.54/22.64 ( (fun int int), (fact_fact int) ) 22.54/22.64 ( (fun int int), zfact ) 22.54/22.64 ( nat, n ) 22.54/22.64 ( nat, tn ) 22.54/22.64 ( bool, fTrue ) 22.54/22.64 ( bool, fFalse ) 22.54/22.64 ( real, pi ) 22.54/22.64 ( (fun nat real), (real_1 nat) ) 22.54/22.64 ( (fun nat real), cos_coeff ) 22.54/22.64 ( (fun nat real), sin_coeff ) 22.54/22.64 ( (fun real real), sin ) 22.54/22.64 ( (fun real real), cos ) 22.54/22.64 ( (fun real real), sqrt ) 22.54/22.64 ( (fun real real), tan ) 22.54/22.64 ( (fun real real), ln ) 22.54/22.64 ( (fun real real), arctan ) 22.54/22.64 ( (fun real real), arcsin ) 22.54/22.64 ( (fun real real), arccos ) 22.54/22.64 ( (fun nat nat), suc ) 22.54/22.64 ( (fun nat nat), (fact_fact nat) ) 22.54/22.64 ( (fun nat nat), nat_size ) 22.54/22.64 ( (fun nat nat), (size_size nat) ) 22.54/22.64 ( (fun nat nat), fact ) 22.54/22.64 ( (filter nat), sequentially ) 22.54/22.64 ( (fun int (fun int rat)), fract ) 22.54/22.64 ( complex, ii ) 22.54/22.64 ( (fun int bool), zOdd ) 22.54/22.64 ( (fun int bool), zprime ) 22.54/22.64 ( (fun int bool), zEven ) 22.54/22.64 ( (fun int bool), nat_neg ) 22.54/22.64 ( (fun int bool), nat_is_nat ) 22.54/22.64 ( (fun int bool), (even_odd_even int) ) 22.54/22.64 ( (fun int bool), twoSqu1091635170sum2sq ) 22.54/22.64 ( (fun int (fun int int)), legacy_zgcd ) 22.54/22.64 ( (fun int (fun int int)), (gcd_gcd int) ) 22.54/22.64 ( (fun int (fun int int)), inv ) 22.54/22.64 ( (fun int (fun int int)), multInv ) 22.54/22.64 ( (fun int (fun int int)), legendre ) 22.54/22.64 ( (fun int (fun int int)), standardRes ) 22.54/22.64 ( (fun int (fun int int)), nat_tsub ) 22.54/22.64 ( (fun int (fun int int)), z3div ) 22.54/22.64 ( (fun int (fun int int)), z3mod ) 22.54/22.64 ( (fun int (fun int int)), int_lcm ) 22.54/22.64 ( (fun int (fun int int)), int_gcd ) 22.54/22.64 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.54/22.64 ( (fun bool bool), fNot ) 22.54/22.64 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.54/22.64 ( (fun bool (fun bool bool)), fconj ) 22.54/22.64 ( (fun bool (fun bool bool)), fdisj ) 22.54/22.64 ( (fun bool (fun bool bool)), fimplies ) 22.54/22.64 ( (fun int (fun int bool)), quadRes ) 22.54/22.64 ( (fun int (fun int bool)), d22set ) 22.54/22.64 ( (fun int (fun int bool)), norRRset ) 22.54/22.64 ( (fun int (fun int bool)), sRStar ) 22.54/22.64 ( (fun int (fun int bool)), sr ) 22.54/22.64 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.54/22.64 ( (fun nat bool), (even_odd_even nat) ) 22.54/22.64 ( (fun nat bool), prime ) 22.54/22.64 ( (fun real complex), cis ) 22.54/22.64 ( (fun nat (fun nat bool)), coprime ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.54/22.64 ( (fun (product_prod int int) bool), frac_1 ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.54/22.64 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.54/22.64 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.54/22.64 ( (fun (fun int bool) bool), nat_nat_set ) 22.54/22.64 ( (fun nat (fun real real)), root ) 22.54/22.64 ( (fun real (fun real real)), log ) 22.54/22.64 ( (fun real (fun real real)), powr ) 22.54/22.64 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.54/22.64 ( (fun complex complex), cnj ) 22.54/22.64 ( (fun complex complex), expi ) 22.54/22.64 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.54/22.64 ( (fun nat (fun nat nat)), nat_gcd ) 22.54/22.64 ( (fun nat (fun nat nat)), nat_lcm ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.54/22.64 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.54/22.64 ( (fun int (fun (fun int bool) bool)), resSet ) 22.54/22.64 ( (fun int nat), nat_1 ) 22.54/22.64 ( (fun int nat), phi ) 22.54/22.64 ( (fun complex real), re ) 22.54/22.64 ( (fun complex real), im ) 22.54/22.64 ( (fun complex real), arg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.54/22.64 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.54/22.64 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.54/22.64 ( (fun (product_prod nat nat) bool), pred_nat ) 22.54/22.64 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.54/22.64 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.54/22.64 ( (fun (fun int bool) int), (the int) ) 22.54/22.64 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.54/22.64 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.54/22.64 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.54/22.64 ( (fun real (fun real complex)), rcis ) 22.54/22.64 ( (fun real (fun real complex)), complex_1 ) 22.54/22.64 ( (fun int (fun int (fun int bool))), zcong ) 22.54/22.64 ( (fun int (fun int (fun int bool))), wset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), noXRRset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), bnorRset ) 22.54/22.64 ( (fun int (fun int (fun int bool))), zcongm ) 22.54/22.64 ( (fun real nat), natceiling ) 22.54/22.64 ( (fun real nat), natfloor ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.54/22.64 ( (fun int real), (real_1 int) ) 22.54/22.64 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.54/22.64 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.54/22.64 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.54/22.64 ( (fun complex nat), (size_size complex) ) 22.54/22.64 ( (fun complex nat), complex_size ) 22.54/22.64 ( (fun (fun nat rat) bool), vanishes ) 22.54/22.64 ( (fun (product_prod int int) rat), frct ) 22.54/22.64 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.54/22.64 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.54/22.64 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.54/22.64 ( (fun rat real), ratreal ) 22.54/22.64 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.54/22.64 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.54/22.64 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.54/22.64 ( (fun rat (product_prod int int)), quotient_of ) 22.54/22.64 ( (fun int (fun nat nat)), nat_aux ) 22.54/22.64 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.54/22.64 ( (fun int (list int)), quickc666637781d_zero ) 22.54/22.64 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.54/22.64 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.54/22.64 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.54/22.64 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.54/22.64 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.54/22.64 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.54/22.64 ( (fun code_code_numeral int), code_int_of ) 22.54/22.64 ) 22.54/22.64 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132534 $$unsorted) (BOUND_VARIABLE_132535 $$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_132535)) (= (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_132534) BOUND_VARIABLE_132535)) (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_132535) BOUND_VARIABLE_132534)) BOUND_VARIABLE_132535)))))) ) 22.54/22.64 ( 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)))) ) 22.54/22.64 ( 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) ) 22.54/22.64 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.54/22.64 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.54/22.64 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.64 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.54/22.64 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.54/22.64 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.64 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.54/22.64 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.54/22.64 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( nat, (one_one nat), (one_one nat) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X $$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))) (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)))))) (hBOOL (hAPP real bool _let_2 (hAPP real real sin X))))))) ) 22.54/22.65 ( pi ) 22.54/22.65 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( (one_one real) ) 22.54/22.65 ( (zero_zero real) ) 22.54/22.65 ( (hAPP real 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))))) ) 22.54/22.65 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.54/22.65 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( (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))))) ) 22.54/22.65 ( (hAPP real real (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))))) ) 22.54/22.65 ( (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)))) ) 22.54/22.65 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.54/22.65 ( (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)) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132573 $$unsorted) (BOUND_VARIABLE_132574 $$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)) (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) (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_132573) _let_0)) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_132574) _let_0)))))))) ) 22.54/22.65 ( int, v, w ) 22.54/22.65 ( int, x, y ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.54/22.65 ( int, skv_6, skv_7 ) 22.54/22.65 ( int, skv_23, skv_24 ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X $$unsorted)) (= (hAPP real real sin (hAPP real real (hAPP real (fun real real) (plus_plus real) pi) X)) (hAPP real real (uminus_uminus real) (hAPP real real sin X))) ) 22.54/22.65 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132643 $$unsorted) (BOUND_VARIABLE_132644 $$unsorted) (BOUND_VARIABLE_132645 $$unsorted) (BOUND_VARIABLE_132646 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_132645))) (let ((_let_4 (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_132646))) (or (not (semiri456707255roduct X_a)) (= (not (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_132643)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_132644)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_3 BOUND_VARIABLE_132644)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_132643)))) (and (not (= (ti X_a BOUND_VARIABLE_132643) (ti X_a BOUND_VARIABLE_132644))) (not (= (ti X_a BOUND_VARIABLE_132645) (ti X_a BOUND_VARIABLE_132646))))))))))) ) 22.54/22.65 ( int, v, w, x, y ) 22.54/22.65 ( int, v, w, r, sa ) 22.54/22.65 ( int, v, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.54/22.65 ( int, w, v, x, y ) 22.54/22.65 ( int, w, v, r, sa ) 22.54/22.65 ( int, w, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))))) (let ((_let_7 (hAPP int _let_4 _let_5 A_1))) (let ((_let_8 (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls)))))) (let ((_let_9 (hAPP int _let_4 _let_5 B))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int _let_7 _let_6)) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int _let_8 (hAPP nat int _let_7 _let_2))) B))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int _let_8 A_1)) (hAPP nat int _let_9 _let_2)))) (hAPP nat int _let_9 _let_6)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 A_1) B)) _let_6)))))))))))) ) 22.54/22.65 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.54/22.65 ) 22.54/22.65 (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))) ) 22.54/22.65 ( (one_one int) ) 22.54/22.65 ( (zero_zero int) ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.65 ( (hAPP int int (number_number_of int) min) ) 22.54/22.65 ( t ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (sums X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= _let_0 (ti (fun (fun nat X_a) (fun X_a bool)) _let_0)))) ) 22.54/22.65 ( rat ) 22.54/22.65 ( int ) 22.54/22.65 ( (fun int int) ) 22.54/22.65 ( nat ) 22.54/22.65 ( bool ) 22.54/22.65 ( real ) 22.54/22.65 ( (fun real real) ) 22.54/22.65 ( (fun nat nat) ) 22.54/22.65 ( (filter nat) ) 22.54/22.65 ( complex ) 22.54/22.65 ( (fun int bool) ) 22.54/22.65 ( (product_prod int int) ) 22.54/22.65 ( (fun bool bool) ) 22.54/22.65 ( (fun nat bool) ) 22.54/22.65 ( (fun nat (fun nat bool)) ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.54/22.65 ( quickcheck_code_int ) 22.54/22.65 ( code_code_numeral ) 22.54/22.65 ( (fun nat (product_prod int int)) ) 22.54/22.65 ( (product_prod real real) ) 22.54/22.65 ( (filter real) ) 22.54/22.65 ( (product_prod nat nat) ) 22.54/22.65 ( (fun (product_prod nat nat) bool) ) 22.54/22.65 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.54/22.65 ( (fun nat (product_prod nat nat)) ) 22.54/22.65 ( (fun nat rat) ) 22.54/22.65 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (zero_zero complex))) (= (= _let_0 (hAPP complex complex cnj Z)) (= _let_0 Z))) ) 22.54/22.65 ( (zero_zero complex) ) 22.54/22.65 ( ii ) 22.54/22.65 ( (one_one complex) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((E_1 $$unsorted) (B $$unsorted) (D_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (gcd_gcd int))) (let ((_let_4 (dvd_dvd int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_4 D_3) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_4 E_1) B))) (not (= _let_1 (hAPP int int (hAPP int _let_0 _let_3 A_1) B))) (= _let_1 (hAPP int int (hAPP int _let_0 _let_3 D_3) E_1)))))))) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((P_1 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 K))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_1)))) (hBOOL (hAPP nat bool P_1 N_1))) )) (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) ) 22.54/22.65 ( (even_odd_even nat), (zero_zero nat) ) 22.54/22.65 ( (even_odd_even nat), (one_one nat) ) 22.54/22.65 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.65 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 22.54/22.65 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 22.54/22.65 ( prime, (zero_zero nat) ) 22.54/22.65 ( prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.65 ( prime, (hAPP nat nat suc (zero_zero nat)) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132774 $$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_132774)) (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_132774)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_132774))))))) ) 22.54/22.65 ( int, pls ) 22.54/22.65 ( int, min ) 22.54/22.65 ( int, s ) 22.54/22.65 ( int, s1 ) 22.54/22.65 ( int, m ) 22.54/22.65 ( int, t ) 22.54/22.65 ( int, v ) 22.54/22.65 ( int, w ) 22.54/22.65 ( int, y ) 22.54/22.65 ( int, sa ) 22.54/22.65 ( int, x ) 22.54/22.65 ( int, r ) 22.54/22.65 ( int, m1 ) 22.54/22.65 ( int, skv_14 ) 22.54/22.65 ( int, skv_20 ) 22.54/22.65 ( (fun int int), bit1 ) 22.54/22.65 ( (fun int int), bit0 ) 22.54/22.65 ( (fun int int), succ ) 22.54/22.65 ( (fun int int), pred ) 22.54/22.65 ( (fun int int), (fact_fact int) ) 22.54/22.65 ( (fun int int), zfact ) 22.54/22.65 ( nat, n ) 22.54/22.65 ( nat, tn ) 22.54/22.65 ( bool, fTrue ) 22.54/22.65 ( bool, fFalse ) 22.54/22.65 ( real, pi ) 22.54/22.65 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ( real, (zero_zero real) ) 22.54/22.65 ( (fun nat real), (real_1 nat) ) 22.54/22.65 ( (fun nat real), cos_coeff ) 22.54/22.65 ( (fun nat real), sin_coeff ) 22.54/22.65 ( (fun real real), sin ) 22.54/22.65 ( (fun real real), cos ) 22.54/22.65 ( (fun real real), sqrt ) 22.54/22.65 ( (fun real real), tan ) 22.54/22.65 ( (fun real real), ln ) 22.54/22.65 ( (fun real real), arctan ) 22.54/22.65 ( (fun real real), arcsin ) 22.54/22.65 ( (fun real real), arccos ) 22.54/22.65 ( (fun nat nat), suc ) 22.54/22.65 ( (fun nat nat), (fact_fact nat) ) 22.54/22.65 ( (fun nat nat), nat_size ) 22.54/22.65 ( (fun nat nat), (size_size nat) ) 22.54/22.65 ( (fun nat nat), fact ) 22.54/22.65 ( (filter nat), sequentially ) 22.54/22.65 ( (fun int (fun int rat)), fract ) 22.54/22.65 ( complex, ii ) 22.54/22.65 ( (fun int bool), zOdd ) 22.54/22.65 ( (fun int bool), zprime ) 22.54/22.65 ( (fun int bool), zEven ) 22.54/22.65 ( (fun int bool), nat_neg ) 22.54/22.65 ( (fun int bool), nat_is_nat ) 22.54/22.65 ( (fun int bool), (even_odd_even int) ) 22.54/22.65 ( (fun int bool), twoSqu1091635170sum2sq ) 22.54/22.65 ( (fun int (fun int int)), legacy_zgcd ) 22.54/22.65 ( (fun int (fun int int)), (gcd_gcd int) ) 22.54/22.65 ( (fun int (fun int int)), inv ) 22.54/22.65 ( (fun int (fun int int)), multInv ) 22.54/22.65 ( (fun int (fun int int)), legendre ) 22.54/22.65 ( (fun int (fun int int)), standardRes ) 22.54/22.65 ( (fun int (fun int int)), nat_tsub ) 22.54/22.65 ( (fun int (fun int int)), z3div ) 22.54/22.65 ( (fun int (fun int int)), z3mod ) 22.54/22.65 ( (fun int (fun int int)), int_lcm ) 22.54/22.65 ( (fun int (fun int int)), int_gcd ) 22.54/22.65 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.54/22.65 ( (fun bool bool), fNot ) 22.54/22.65 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.54/22.65 ( (fun bool (fun bool bool)), fconj ) 22.54/22.65 ( (fun bool (fun bool bool)), fdisj ) 22.54/22.65 ( (fun bool (fun bool bool)), fimplies ) 22.54/22.65 ( (fun int (fun int bool)), quadRes ) 22.54/22.65 ( (fun int (fun int bool)), d22set ) 22.54/22.65 ( (fun int (fun int bool)), norRRset ) 22.54/22.65 ( (fun int (fun int bool)), sRStar ) 22.54/22.65 ( (fun int (fun int bool)), sr ) 22.54/22.65 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.54/22.65 ( (fun nat bool), (even_odd_even nat) ) 22.54/22.65 ( (fun nat bool), prime ) 22.54/22.65 ( (fun real complex), cis ) 22.54/22.65 ( (fun nat (fun nat bool)), coprime ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.54/22.65 ( (fun (product_prod int int) bool), frac_1 ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.54/22.65 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.54/22.65 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.54/22.65 ( (fun (fun int bool) bool), nat_nat_set ) 22.54/22.65 ( (fun nat (fun real real)), root ) 22.54/22.65 ( (fun real (fun real real)), log ) 22.54/22.65 ( (fun real (fun real real)), powr ) 22.54/22.65 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.54/22.65 ( (fun complex complex), cnj ) 22.54/22.65 ( (fun complex complex), expi ) 22.54/22.65 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.54/22.65 ( (fun nat (fun nat nat)), nat_gcd ) 22.54/22.65 ( (fun nat (fun nat nat)), nat_lcm ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.54/22.65 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.54/22.65 ( (fun int (fun (fun int bool) bool)), resSet ) 22.54/22.65 ( (fun int nat), nat_1 ) 22.54/22.65 ( (fun int nat), phi ) 22.54/22.65 ( (fun complex real), re ) 22.54/22.65 ( (fun complex real), im ) 22.54/22.65 ( (fun complex real), arg ) 22.54/22.65 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.54/22.65 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.54/22.65 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.54/22.65 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.54/22.65 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.54/22.65 ( (fun (product_prod nat nat) bool), pred_nat ) 22.54/22.65 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.54/22.65 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.54/22.65 ( (fun (fun int bool) int), (the int) ) 22.54/22.65 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.54/22.65 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.54/22.65 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.54/22.65 ( (fun real (fun real complex)), rcis ) 22.54/22.65 ( (fun real (fun real complex)), complex_1 ) 22.54/22.65 ( (fun int (fun int (fun int bool))), zcong ) 22.54/22.65 ( (fun int (fun int (fun int bool))), wset ) 22.54/22.65 ( (fun int (fun int (fun int bool))), noXRRset ) 22.54/22.65 ( (fun int (fun int (fun int bool))), bnorRset ) 22.54/22.65 ( (fun int (fun int (fun int bool))), zcongm ) 22.54/22.65 ( (fun real nat), natceiling ) 22.54/22.65 ( (fun real nat), natfloor ) 22.54/22.65 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.54/22.65 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.54/22.65 ( (fun int real), (real_1 int) ) 22.54/22.65 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.54/22.65 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.54/22.65 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.54/22.65 ( (fun complex nat), (size_size complex) ) 22.54/22.65 ( (fun complex nat), complex_size ) 22.54/22.65 ( (fun (fun nat rat) bool), vanishes ) 22.54/22.65 ( (fun (product_prod int int) rat), frct ) 22.54/22.65 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.54/22.65 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.54/22.65 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.54/22.65 ( (fun rat real), ratreal ) 22.54/22.65 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.54/22.65 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.54/22.65 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.54/22.65 ( (fun rat (product_prod int int)), quotient_of ) 22.54/22.65 ( (fun int (fun nat nat)), nat_aux ) 22.54/22.65 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.54/22.65 ( (fun int (list int)), quickc666637781d_zero ) 22.54/22.65 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.54/22.65 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.54/22.65 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.54/22.65 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.54/22.65 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.54/22.65 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.54/22.65 ( (fun code_code_numeral int), code_int_of ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132796 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_132796))))) ) 22.54/22.65 ( int, (one_one nat) ) 22.54/22.65 ( real, (one_one nat) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((Xa $$unsorted) (Ya $$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) Xa) Ya)) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Xa) zOdd)))))) ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.54/22.65 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.54/22.65 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.65 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.54/22.65 ( y, v ) 22.54/22.65 ( y, w ) 22.54/22.65 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( sa, v ) 22.54/22.65 ( sa, w ) 22.54/22.65 ( x, v ) 22.54/22.65 ( x, w ) 22.54/22.65 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.65 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( r, v ) 22.54/22.65 ( r, w ) 22.54/22.65 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.54/22.65 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.54/22.65 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.54/22.65 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.54/22.65 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.54/22.65 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.65 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.65 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.65 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.65 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132817 $$unsorted) (BOUND_VARIABLE_132818 $$unsorted) (BOUND_VARIABLE_132819 $$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 (times_times X_a))) (or (not (linordered_semiring X_a)) (not (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_132817) BOUND_VARIABLE_132818)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_132819) BOUND_VARIABLE_132818)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_132818))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132817) BOUND_VARIABLE_132819))))))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.65 ) 22.54/22.65 (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)))) ) 22.54/22.65 ( rat ) 22.54/22.65 ( int ) 22.54/22.65 ( (fun int int) ) 22.54/22.65 ( nat ) 22.54/22.65 ( bool ) 22.54/22.65 ( real ) 22.54/22.65 ( (fun nat real) ) 22.54/22.65 ( (fun real real) ) 22.54/22.65 ( complex ) 22.54/22.65 ( (fun int bool) ) 22.54/22.65 ( (product_prod int int) ) 22.54/22.65 ( (fun (product_prod int int) int) ) 22.54/22.65 ( (fun int (fun int bool)) ) 22.54/22.65 ( (fun nat bool) ) 22.54/22.65 ( (fun (product_prod int int) bool) ) 22.54/22.65 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.54/22.65 ( (fun real bool) ) 22.54/22.65 ( quickcheck_code_int ) 22.54/22.65 ( code_code_numeral ) 22.54/22.65 ( (fun int (fun int (fun int bool))) ) 22.54/22.65 ( (fun int real) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_132856 $$unsorted) (BOUND_VARIABLE_132857 $$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_132857))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_132856) _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_132856) BOUND_VARIABLE_132857)) _let_2)))))) ) 22.54/22.65 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.54/22.65 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.54/22.65 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.54/22.65 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.54/22.65 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.54/22.65 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.65 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.54/22.65 ( int, y, v ) 22.54/22.65 ( int, y, w ) 22.54/22.65 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, sa, v ) 22.54/22.65 ( int, sa, w ) 22.54/22.65 ( int, x, v ) 22.54/22.65 ( int, x, w ) 22.54/22.65 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.65 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, r, v ) 22.54/22.65 ( int, r, w ) 22.54/22.65 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.54/22.65 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.54/22.65 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.54/22.65 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.65 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.65 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.65 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.65 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.54/22.65 ( 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)))))) ) 22.54/22.65 ( 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 ) 22.54/22.65 ( complex, ii, ii ) 22.54/22.65 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.54/22.65 ( 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 ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (zero_zero real)) (zero_zero X_a))) ) 22.54/22.65 ( rat ) 22.54/22.65 ( int ) 22.54/22.65 ( nat ) 22.54/22.65 ( real ) 22.54/22.65 ( complex ) 22.54/22.65 ( quickcheck_code_int ) 22.54/22.65 ( code_code_numeral ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((P_1 $$unsorted) (I $$unsorted)) (= (and (forall ((N_1 $$unsorted)) (or (not (= (ti int I) (hAPP nat int (semiring_1_of_nat int) N_1))) (hBOOL (hAPP nat bool P_1 N_1))) ) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) I) (zero_zero int)))) (hBOOL (hAPP nat bool P_1 (zero_zero nat))))) (hBOOL (hAPP nat bool P_1 (hAPP int nat nat_1 I)))) ) 22.54/22.65 ( (even_odd_even nat), (one_one int) ) 22.54/22.65 ( (even_odd_even nat), (zero_zero int) ) 22.54/22.65 ( (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.65 ( prime, (one_one int) ) 22.54/22.65 ( prime, (zero_zero int) ) 22.54/22.65 ( prime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.65 ) 22.54/22.65 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133095 $$unsorted) (BOUND_VARIABLE_133096 $$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_133095)) (hAPP real X_a _let_0 BOUND_VARIABLE_133096)) (hAPP real X_a _let_0 (hAPP real real (hAPP real (fun real real) (times_times real) BOUND_VARIABLE_133095) BOUND_VARIABLE_133096))))) ) 22.54/22.65 ( complex, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.54/22.65 ) 22.54/22.66 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP real real sin X)) (hAPP real real sin (hAPP real real (hAPP real (fun real real) (plus_plus real) X) pi))) ) 22.54/22.66 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((W $$unsorted)) (= (hAPP int rat (number_number_of rat) W) (hAPP int rat (hAPP int (fun int rat) fract W) (one_one int))) ) 22.54/22.66 ( (one_one int) ) 22.54/22.66 ( (zero_zero int) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133169 $$unsorted) (BOUND_VARIABLE_133170 $$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 (field_inverse_zero X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_133170) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_133169) _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_133170) BOUND_VARIABLE_133169)) _let_3))))))) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.54/22.66 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.54/22.66 ( 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) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun int int))) (not (= (hAPP int int (hAPP int _let_0 (plus_plus int) A_3) (hAPP int int (hAPP int _let_0 (times_times int) Ma) K_1)) (ti int B_2)))) )) (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong A_3) B_2) Ma)))) ) 22.54/22.66 ( (hAPP nat int (hAPP 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))) ) 22.54/22.66 ( (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((Wa $$unsorted) (Z $$unsorted)) (= (not (forall ((N_1 $$unsorted)) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) Wa) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1))) (ti int Z))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) Wa) Z))) ) 22.54/22.66 ( (one_one int), t ) 22.54/22.66 ( min, min ) 22.54/22.66 ( min, (zero_zero int) ) 22.54/22.66 ( (zero_zero int), pls ) 22.54/22.66 ( (zero_zero int), (one_one int) ) 22.54/22.66 ( (zero_zero int), min ) 22.54/22.66 ( (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))) ) 22.54/22.66 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133211 $$unsorted) (BOUND_VARIABLE_133212 $$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_133211) BOUND_VARIABLE_133212)) BOUND_VARIABLE_133211)))) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.54/22.66 ( int, y, v ) 22.54/22.66 ( int, y, w ) 22.54/22.66 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( int, sa, v ) 22.54/22.66 ( int, sa, w ) 22.54/22.66 ( int, x, v ) 22.54/22.66 ( int, x, w ) 22.54/22.66 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.54/22.66 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( int, r, v ) 22.54/22.66 ( int, r, w ) 22.54/22.66 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.54/22.66 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.54/22.66 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.54/22.66 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.54/22.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.54/22.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.54/22.66 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.54/22.66 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.66 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.54/22.66 ( 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)))))) ) 22.54/22.66 ( 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 ) 22.54/22.66 ( complex, ii, ii ) 22.54/22.66 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.54/22.66 ( 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 ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133254 $$unsorted) (BOUND_VARIABLE_133255 $$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_133254) BOUND_VARIABLE_133255)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133255) BOUND_VARIABLE_133254))))) ) 22.54/22.66 ( int, pls, min ) 22.54/22.66 ( int, pls, (zero_zero int) ) 22.54/22.66 ( int, (one_one int), (zero_zero int) ) 22.54/22.66 ( int, (one_one int), t ) 22.54/22.66 ( int, min, pls ) 22.54/22.66 ( int, min, min ) 22.54/22.66 ( int, min, (zero_zero int) ) 22.54/22.66 ( int, (zero_zero int), pls ) 22.54/22.66 ( int, (zero_zero int), (one_one int) ) 22.54/22.66 ( int, (zero_zero int), min ) 22.54/22.66 ( int, (zero_zero int), s ) 22.54/22.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (zero_zero int), skv_4 ) 22.54/22.66 ( int, (zero_zero int), skv_5 ) 22.54/22.66 ( int, s, (zero_zero int) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.54/22.66 ( int, t, (one_one int) ) 22.54/22.66 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( int, skv_4, (zero_zero int) ) 22.54/22.66 ( int, skv_5, (zero_zero int) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, pi, (zero_zero real) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.54/22.66 ( real, (hAPP real real (hAPP 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))) ) 22.54/22.66 ( real, (hAPP real real (hAPP 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) ) 22.54/22.66 ( real, (zero_zero real), pi ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (zero_zero real), skv_10 ) 22.54/22.66 ( real, (zero_zero real), skv_11 ) 22.54/22.66 ( real, (zero_zero real), skv_15 ) 22.54/22.66 ( real, (zero_zero real), skv_18 ) 22.54/22.66 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.66 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, skv_10, (zero_zero real) ) 22.54/22.66 ( real, skv_11, (zero_zero real) ) 22.54/22.66 ( real, skv_15, (zero_zero real) ) 22.54/22.66 ( real, skv_18, (zero_zero real) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (real_1 int))) (= (= (ti int Xa) (ti int Ya)) (= (hAPP int real _let_0 Ya) (hAPP int real _let_0 Xa)))) ) 22.54/22.66 ( pls, w ) 22.54/22.66 ( pls, y ) 22.54/22.66 ( min, s ) 22.54/22.66 ( min, m ) 22.54/22.66 ( s, m ) 22.54/22.66 ( s1, s1 ) 22.54/22.66 ( s1, v ) 22.54/22.66 ( m, min ) 22.54/22.66 ( m, m ) 22.54/22.66 ( t, m1 ) 22.54/22.66 ( v, s1 ) 22.54/22.66 ( v, r ) 22.54/22.66 ( w, y ) 22.54/22.66 ( y, pls ) 22.54/22.66 ( y, y ) 22.54/22.66 ( sa, t ) 22.54/22.66 ( sa, m1 ) 22.54/22.66 ( x, x ) 22.54/22.66 ( x, skv_14 ) 22.54/22.66 ( r, s1 ) 22.54/22.66 ( m1, sa ) 22.54/22.66 ( m1, m1 ) 22.54/22.66 ( skv_14, x ) 22.54/22.66 ( skv_14, skv_20 ) 22.54/22.66 ( skv_20, x ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133299 $$unsorted) (BOUND_VARIABLE_133300 $$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_133299) BOUND_VARIABLE_133300))) (not (= (ti X_a BOUND_VARIABLE_133299) (ti X_a BOUND_VARIABLE_133300)))) ) 22.54/22.66 ( int, (one_one int), t ) 22.54/22.66 ( int, min, min ) 22.54/22.66 ( int, min, (zero_zero int) ) 22.54/22.66 ( int, (zero_zero int), pls ) 22.54/22.66 ( int, (zero_zero int), (one_one int) ) 22.54/22.66 ( int, (zero_zero int), min ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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))) ) 22.54/22.66 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.54/22.66 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( nat, (zero_zero nat), n ) 22.54/22.66 ( nat, (zero_zero nat), tn ) 22.54/22.66 ( real, pi, (zero_zero real) ) 22.54/22.66 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (hAPP real real (hAPP 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))) ) 22.54/22.66 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (zero_zero real), pi ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (zero_zero real), skv_2 ) 22.54/22.66 ( real, (zero_zero real), skv_9 ) 22.54/22.66 ( real, (zero_zero real), skv_12 ) 22.54/22.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.66 ( 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) ) 22.54/22.66 ( 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 ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) I_1))) (or (not (hBOOL (hAPP nat bool _let_0 J_2))) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) J_2) M))))) ) 22.54/22.66 ( (one_one nat), (zero_zero nat), (one_one nat) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (tendsto nat real))) (let ((_let_6 (fun nat bool))) (let ((_let_7 (fun nat _let_6))) (let ((_let_8 (fun _let_6 real))) (let ((_let_9 (fun nat _let_1))) (let ((_let_10 (fun nat _let_2))) (let ((_let_11 (hAPP _let_0 _let_0 (hAPP _let_9 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_9 (hAPP (fun real _let_1) (fun _let_0 _let_9) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 A_3) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_0 bool (monoseq real) A_3))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 (hAPP _let_7 _let_0 (hAPP _let_8 (fun _let_7 _let_0) (combb _let_6 real nat) (hAPP _let_0 _let_8 (big_co1399186613setsum nat real) _let_11)) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb nat _let_6 nat) (hAPP nat _let_7 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (hAPP _let_10 _let_10 (combc nat nat nat) (hAPP _let_2 _let_10 (hAPP _let_10 (fun _let_2 _let_10) (combb nat _let_2 nat) (plus_plus nat)) (hAPP nat _let_2 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat))))) (hAPP _let_0 real (suminf real) _let_11)) sequentially))))))))))))))) ) 22.54/22.66 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X $$unsorted)) (= (hAPP real nat natceiling X) (hAPP int nat nat_1 (hAPP real int (archimedean_ceiling real) X))) ) 22.54/22.66 ( (one_one real) ) 22.54/22.66 ( (zero_zero real) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (= (hAPP int int bit0 (hAPP int int _let_0 K_4)) (hAPP int int _let_0 (hAPP int int bit0 K_4)))) ) 22.54/22.66 ( pls ) 22.54/22.66 ( (one_one int) ) 22.54/22.66 ( min ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133407 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (number_ring X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_133407)) (ring_1_Ints X_a))))) ) 22.54/22.66 ( int, pls ) 22.54/22.66 ( int, (hAPP int int bit1 pls) ) 22.54/22.66 ( int, min ) 22.54/22.66 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( nat, pls ) 22.54/22.66 ( nat, (hAPP int int bit1 pls) ) 22.54/22.66 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, min ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 22.54/22.66 ( complex, min ) 22.54/22.66 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( quickcheck_code_int, pls ) 22.54/22.66 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.54/22.66 ( quickcheck_code_int, (one_one int) ) 22.54/22.66 ( code_code_numeral, pls ) 22.54/22.66 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133423 $$unsorted) (BOUND_VARIABLE_133424 $$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_133423) BOUND_VARIABLE_133424))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_133423)) (hAPP X_a int _let_0 BOUND_VARIABLE_133424))))) ) 22.54/22.66 ( int, (one_one int), t ) 22.54/22.66 ( int, min, pls ) 22.54/22.66 ( int, min, min ) 22.54/22.66 ( int, (zero_zero int), pls ) 22.54/22.66 ( int, (zero_zero int), (one_one int) ) 22.54/22.66 ( int, (zero_zero int), min ) 22.54/22.66 ( int, (zero_zero int), s ) 22.54/22.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (zero_zero int), skv_4 ) 22.54/22.66 ( int, (zero_zero int), skv_5 ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.54/22.66 ( real, (hAPP real real (hAPP 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))) ) 22.54/22.66 ( real, (zero_zero real), pi ) 22.54/22.66 ( 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)))) ) 22.54/22.66 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.66 ( real, (zero_zero real), skv_10 ) 22.54/22.66 ( real, (zero_zero real), skv_11 ) 22.54/22.66 ( real, (zero_zero real), skv_15 ) 22.54/22.66 ( real, (zero_zero real), skv_18 ) 22.54/22.66 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.54/22.66 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133472 $$unsorted) (BOUND_VARIABLE_133473 $$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 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_133472)) BOUND_VARIABLE_133473)) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_133472) BOUND_VARIABLE_133473))))))) ) 22.54/22.66 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (uminus_uminus _let_0))) (= (= (ti _let_0 B_1) (ti _let_0 A_2)) (= (hAPP _let_0 _let_0 _let_1 A_2) (hAPP _let_0 _let_0 _let_1 B_1))))) ) 22.54/22.66 ( int, zOdd, zOdd ) 22.54/22.66 ( int, zOdd, zprime ) 22.54/22.66 ( int, zOdd, nat_is_nat ) 22.54/22.66 ( int, zprime, zOdd ) 22.54/22.66 ( int, zEven, nat_neg ) 22.54/22.66 ( int, nat_neg, twoSqu1091635170sum2sq ) 22.54/22.66 ( int, nat_is_nat, zprime ) 22.54/22.66 ( int, (even_odd_even int), (even_odd_even int) ) 22.54/22.66 ( int, twoSqu1091635170sum2sq, zEven ) 22.54/22.66 ( int, twoSqu1091635170sum2sq, nat_neg ) 22.54/22.66 ( int, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.54/22.66 ( nat, (even_odd_even nat), (even_odd_even nat) ) 22.54/22.66 ( nat, (even_odd_even nat), prime ) 22.54/22.66 ( nat, prime, (even_odd_even nat) ) 22.54/22.66 ( bool, fNot, fNot ) 22.54/22.66 ( (fun int bool), nat_nat_set, nat_nat_set ) 22.54/22.66 ( (product_prod int int), frac_1, frac_1 ) 22.54/22.66 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel, ratrel ) 22.54/22.66 ( (product_prod nat nat), pred_nat, pred_nat ) 22.54/22.66 ( (fun nat rat), vanishes, vanishes ) 22.54/22.66 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less, pair_leq ) 22.54/22.66 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq, pair_less ) 22.54/22.66 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq, pair_leq ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (div_div nat))) (let ((_let_3 (hAPP nat nat (hAPP nat _let_1 _let_2 M) N))) (let ((_let_4 (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N))) (and (or (not _let_4) (= _let_0 _let_3)) (or _let_4 (= _let_3 (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)) N))))))))))) ) 22.54/22.66 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( (zero_zero nat), n ) 22.54/22.66 ( (zero_zero nat), tn ) 22.54/22.66 ( (hAPP int nat nat_1 t), (one_one nat) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((Ya $$unsorted) (Xa $$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 Xa))) (not (hBOOL (hAPP int bool _let_1 Ya))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) Xa) Ya)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat nat_1 Xa)) (hAPP int nat nat_1 Ya))))))) ) 22.54/22.66 ( pls, (zero_zero int) ) 22.54/22.66 ( (one_one int), (zero_zero int) ) 22.54/22.66 ( min, min ) 22.54/22.66 ( min, (zero_zero int) ) 22.54/22.66 ( (zero_zero int), min ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.54/22.66 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.54/22.66 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.54/22.66 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.54/22.66 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.54/22.66 ( t, (one_one int) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133585 $$unsorted) (BOUND_VARIABLE_133586 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (minus_minus X_a))) (or (not (ab_group_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_133585)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_133586)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_133585) BOUND_VARIABLE_133586))))))) ) 22.54/22.66 ( 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) ) 22.54/22.66 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.66 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.66 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.66 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.54/22.66 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.54/22.66 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.54/22.66 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.54/22.66 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.54/22.66 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.54/22.66 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.54/22.66 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (= Y (hAPP complex real im (hAPP real complex (hAPP real (fun real complex) complex_1 X) Y))) ) 22.54/22.66 ( (one_one real), (zero_zero real) ) 22.54/22.66 ( (zero_zero real), (one_one real) ) 22.54/22.66 ( (zero_zero real), (zero_zero real) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X $$unsorted) (N $$unsorted) (M $$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))) (= (hAPP real real (hAPP nat _let_0 root M) (hAPP real real (hAPP nat _let_0 root N) X)) (hAPP real real (hAPP nat _let_0 root (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M) N)) X))))) ) 22.54/22.66 ( (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))) ) 22.54/22.66 ( (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))) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133640 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_133640) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_133640))) ) 22.54/22.66 ( int, pls ) 22.54/22.66 ( int, (hAPP int int bit1 pls) ) 22.54/22.66 ( int, min ) 22.54/22.66 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( nat, pls ) 22.54/22.66 ( nat, (hAPP int int bit1 pls) ) 22.54/22.66 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, (one_one int) ) 22.54/22.66 ( real, min ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, (zero_zero int) ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.54/22.66 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.54/22.66 ( 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)))))))) ) 22.54/22.66 ( complex, min ) 22.54/22.66 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.66 ( quickcheck_code_int, pls ) 22.54/22.66 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.54/22.66 ( quickcheck_code_int, (one_one int) ) 22.54/22.66 ( code_code_numeral, pls ) 22.54/22.66 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.54/22.66 ) 22.54/22.66 (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))) ) 22.54/22.66 ( int, int ) 22.54/22.66 ( int, (product_prod int int) ) 22.54/22.66 ( nat, nat ) 22.54/22.66 ( real, real ) 22.54/22.66 ( (product_prod int int), (product_prod int int) ) 22.54/22.66 ( quickcheck_code_int, quickcheck_code_int ) 22.54/22.66 ( code_code_numeral, code_code_numeral ) 22.54/22.66 ( (product_prod nat nat), (product_prod nat nat) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((P_4 $$unsorted)) (= (and (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) P_4)) (forall ((M_2 $$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 prime P_4))) ) 22.54/22.66 ( (zero_zero nat) ) 22.54/22.66 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.66 ( (hAPP nat nat suc (zero_zero nat)) ) 22.54/22.66 ) 22.54/22.66 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133687 $$unsorted) (BOUND_VARIABLE_133688 $$unsorted) (BOUND_VARIABLE_133689 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_133689)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_133689) BOUND_VARIABLE_133687)) BOUND_VARIABLE_133688)) BOUND_VARIABLE_133689) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133687) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_133688) BOUND_VARIABLE_133689))))))) ) 22.54/22.66 ( int, w, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), x ) 22.54/22.67 ( int, w, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.54/22.67 ( int, w, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), r ) 22.54/22.67 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.67 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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))) ) 22.54/22.67 ( 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)))) ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133718 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP int int (uminus_uminus int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_133718)) (hAPP X_a int (archimedean_ceiling X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_133718)))) ) 22.54/22.67 ( int, pls ) 22.54/22.67 ( int, (one_one int) ) 22.54/22.67 ( int, min ) 22.54/22.67 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.67 ( real, (one_one real) ) 22.54/22.67 ( 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) ) 22.54/22.67 ( complex, ii ) 22.54/22.67 ( complex, (one_one complex) ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133730 $$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_133730))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133730) _let_2))))))) ) 22.54/22.67 ( int, pls ) 22.54/22.67 ( int, (one_one int) ) 22.54/22.67 ( int, min ) 22.54/22.67 ( int, (zero_zero int) ) 22.54/22.67 ( int, s ) 22.54/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.54/22.67 ( int, t ) 22.54/22.67 ( int, m1 ) 22.54/22.67 ( int, skv_4 ) 22.54/22.67 ( int, skv_5 ) 22.54/22.67 ( nat, (zero_zero nat) ) 22.54/22.67 ( real, pi ) 22.54/22.67 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.67 ( real, (one_one real) ) 22.54/22.67 ( real, (zero_zero real) ) 22.54/22.67 ( 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) ) 22.54/22.67 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.67 ( 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))))) ) 22.54/22.67 ( 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)) ) 22.54/22.67 ( complex, ii ) 22.54/22.67 ( complex, (one_one complex) ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133815 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP X_a int (archimedean_ceiling X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_133815)) (ti int BOUND_VARIABLE_133815))) ) 22.54/22.67 ( real, (one_one int) ) 22.54/22.67 ( real, (zero_zero int) ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133834 $$unsorted) (BOUND_VARIABLE_133835 $$unsorted)) (or (not (monoid_mult X_a)) (not (linordered_ring X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_133835))) (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_133834) BOUND_VARIABLE_133835)))) ) 22.54/22.67 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.54/22.67 ) 22.54/22.67 (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))))) ) 22.54/22.67 ( rat ) 22.54/22.67 ( int ) 22.54/22.67 ( nat ) 22.54/22.67 ( real ) 22.54/22.67 ( complex ) 22.54/22.67 ( quickcheck_code_int ) 22.54/22.67 ( code_code_numeral ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((A_3 $$unsorted) (Xa $$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)) Xa))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) A_3) (hAPP real nat natfloor Xa))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (real_1 nat) A_3)) Xa)))))) ) 22.54/22.67 ( (zero_zero nat), pi ) 22.54/22.67 ( (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)))) ) 22.54/22.67 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.54/22.67 ( (zero_zero nat), skv_10 ) 22.54/22.67 ( (zero_zero nat), skv_11 ) 22.54/22.67 ( (zero_zero nat), skv_15 ) 22.54/22.67 ( (zero_zero nat), skv_18 ) 22.54/22.67 ) 22.54/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133898 $$unsorted) (BOUND_VARIABLE_133899 $$unsorted) (BOUND_VARIABLE_133900 $$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 (zero_zero X_a))) (let ((_let_4 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_133900))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_3) _let_4)))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_133898) _let_4))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) _let_3)))) (let ((_let_8 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133898))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (and (or (not _let_5) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_133899))) (or _let_5 (and (or _let_7 (hBOOL (hAPP X_a bool _let_8 _let_3))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_133899) _let_6)))))) (hBOOL (hAPP X_a bool _let_8 (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_133899) _let_4)))))))))))))) ) 22.54/22.67 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.54/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133947 $$unsorted) (BOUND_VARIABLE_133948 $$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_133948) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_133947))) (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_133948) BOUND_VARIABLE_133947)) _let_2)))))) ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.63/22.67 ( 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)))) ) 22.63/22.67 ( 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))) ) 22.63/22.67 ( 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)))) ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.63/22.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.63/22.67 ( 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) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133975 $$unsorted) (BOUND_VARIABLE_133976 $$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_133976))) (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_133976) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_133976) BOUND_VARIABLE_133975)))))) ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.63/22.67 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.63/22.67 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.63/22.67 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.63/22.67 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.63/22.67 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.63/22.67 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.63/22.67 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.63/22.67 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.63/22.67 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.63/22.67 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_133999 $$unsorted) (BOUND_VARIABLE_134000 $$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_133999))) (or (not (ring X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_134000)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_134000)))))) ) 22.63/22.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.63/22.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.63/22.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.63/22.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.63/22.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.63/22.67 ( int, y, v ) 22.63/22.67 ( int, y, w ) 22.63/22.67 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, sa, v ) 22.63/22.67 ( int, sa, w ) 22.63/22.67 ( int, x, v ) 22.63/22.67 ( int, x, w ) 22.63/22.67 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.63/22.67 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, r, v ) 22.63/22.67 ( int, r, w ) 22.63/22.67 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.63/22.67 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.63/22.67 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.63/22.67 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.63/22.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.63/22.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.63/22.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.63/22.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.63/22.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.63/22.67 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.63/22.67 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.63/22.67 ( 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)))))) ) 22.63/22.67 ( 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 ) 22.63/22.67 ( complex, ii, ii ) 22.63/22.67 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.63/22.67 ( 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 ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134023 $$unsorted)) (or (not (linorder X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_134023) BOUND_VARIABLE_134023) (ti X_a BOUND_VARIABLE_134023))) ) 22.63/22.67 ( int, pls ) 22.63/22.67 ( int, min ) 22.63/22.67 ( int, s ) 22.63/22.67 ( int, s1 ) 22.63/22.67 ( int, m ) 22.63/22.67 ( int, t ) 22.63/22.67 ( int, v ) 22.63/22.67 ( int, w ) 22.63/22.67 ( int, y ) 22.63/22.67 ( int, sa ) 22.63/22.67 ( int, x ) 22.63/22.67 ( int, r ) 22.63/22.67 ( int, m1 ) 22.63/22.67 ( int, skv_14 ) 22.63/22.67 ( int, skv_20 ) 22.63/22.67 ( (fun int int), bit1 ) 22.63/22.67 ( (fun int int), bit0 ) 22.63/22.67 ( (fun int int), succ ) 22.63/22.67 ( (fun int int), pred ) 22.63/22.67 ( (fun int int), (fact_fact int) ) 22.63/22.67 ( (fun int int), zfact ) 22.63/22.67 ( nat, n ) 22.63/22.67 ( nat, tn ) 22.63/22.67 ( bool, fTrue ) 22.63/22.67 ( bool, fFalse ) 22.63/22.67 ( real, pi ) 22.63/22.67 ( (fun nat real), (real_1 nat) ) 22.63/22.67 ( (fun nat real), cos_coeff ) 22.63/22.67 ( (fun nat real), sin_coeff ) 22.63/22.67 ( (fun real real), sin ) 22.63/22.67 ( (fun real real), cos ) 22.63/22.67 ( (fun real real), sqrt ) 22.63/22.67 ( (fun real real), tan ) 22.63/22.67 ( (fun real real), ln ) 22.63/22.67 ( (fun real real), arctan ) 22.63/22.67 ( (fun real real), arcsin ) 22.63/22.67 ( (fun real real), arccos ) 22.63/22.67 ( (fun nat nat), suc ) 22.63/22.67 ( (fun nat nat), (fact_fact nat) ) 22.63/22.67 ( (fun nat nat), nat_size ) 22.63/22.67 ( (fun nat nat), (size_size nat) ) 22.63/22.67 ( (fun nat nat), fact ) 22.63/22.67 ( (filter nat), sequentially ) 22.63/22.67 ( (fun int (fun int rat)), fract ) 22.63/22.67 ( complex, ii ) 22.63/22.67 ( (fun int bool), zOdd ) 22.63/22.67 ( (fun int bool), zprime ) 22.63/22.67 ( (fun int bool), zEven ) 22.63/22.67 ( (fun int bool), nat_neg ) 22.63/22.67 ( (fun int bool), nat_is_nat ) 22.63/22.67 ( (fun int bool), (even_odd_even int) ) 22.63/22.67 ( (fun int bool), twoSqu1091635170sum2sq ) 22.63/22.67 ( (fun int (fun int int)), legacy_zgcd ) 22.63/22.67 ( (fun int (fun int int)), (gcd_gcd int) ) 22.63/22.67 ( (fun int (fun int int)), inv ) 22.63/22.67 ( (fun int (fun int int)), multInv ) 22.63/22.67 ( (fun int (fun int int)), legendre ) 22.63/22.67 ( (fun int (fun int int)), standardRes ) 22.63/22.67 ( (fun int (fun int int)), nat_tsub ) 22.63/22.67 ( (fun int (fun int int)), z3div ) 22.63/22.67 ( (fun int (fun int int)), z3mod ) 22.63/22.67 ( (fun int (fun int int)), int_lcm ) 22.63/22.67 ( (fun int (fun int int)), int_gcd ) 22.63/22.67 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.63/22.67 ( (fun bool bool), fNot ) 22.63/22.67 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.63/22.67 ( (fun bool (fun bool bool)), fconj ) 22.63/22.67 ( (fun bool (fun bool bool)), fdisj ) 22.63/22.67 ( (fun bool (fun bool bool)), fimplies ) 22.63/22.67 ( (fun int (fun int bool)), quadRes ) 22.63/22.67 ( (fun int (fun int bool)), d22set ) 22.63/22.67 ( (fun int (fun int bool)), norRRset ) 22.63/22.67 ( (fun int (fun int bool)), sRStar ) 22.63/22.67 ( (fun int (fun int bool)), sr ) 22.63/22.67 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.63/22.67 ( (fun nat bool), (even_odd_even nat) ) 22.63/22.67 ( (fun nat bool), prime ) 22.63/22.67 ( (fun real complex), cis ) 22.63/22.67 ( (fun nat (fun nat bool)), coprime ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.63/22.67 ( (fun (product_prod int int) bool), frac_1 ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.63/22.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.63/22.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.63/22.67 ( (fun (fun int bool) bool), nat_nat_set ) 22.63/22.67 ( (fun nat (fun real real)), root ) 22.63/22.67 ( (fun real (fun real real)), log ) 22.63/22.67 ( (fun real (fun real real)), powr ) 22.63/22.67 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.63/22.67 ( (fun complex complex), cnj ) 22.63/22.67 ( (fun complex complex), expi ) 22.63/22.67 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.63/22.67 ( (fun nat (fun nat nat)), nat_gcd ) 22.63/22.67 ( (fun nat (fun nat nat)), nat_lcm ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.63/22.67 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.63/22.67 ( (fun int (fun (fun int bool) bool)), resSet ) 22.63/22.67 ( (fun int nat), nat_1 ) 22.63/22.67 ( (fun int nat), phi ) 22.63/22.67 ( (fun complex real), re ) 22.63/22.67 ( (fun complex real), im ) 22.63/22.67 ( (fun complex real), arg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.63/22.67 ( (fun (product_prod nat nat) bool), pred_nat ) 22.63/22.67 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.63/22.67 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.63/22.67 ( (fun (fun int bool) int), (the int) ) 22.63/22.67 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.63/22.67 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.63/22.67 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.63/22.67 ( (fun real (fun real complex)), rcis ) 22.63/22.67 ( (fun real (fun real complex)), complex_1 ) 22.63/22.67 ( (fun int (fun int (fun int bool))), zcong ) 22.63/22.67 ( (fun int (fun int (fun int bool))), wset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), noXRRset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), bnorRset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), zcongm ) 22.63/22.67 ( (fun real nat), natceiling ) 22.63/22.67 ( (fun real nat), natfloor ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.63/22.67 ( (fun int real), (real_1 int) ) 22.63/22.67 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.63/22.67 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.63/22.67 ( (fun complex nat), (size_size complex) ) 22.63/22.67 ( (fun complex nat), complex_size ) 22.63/22.67 ( (fun (fun nat rat) bool), vanishes ) 22.63/22.67 ( (fun (product_prod int int) rat), frct ) 22.63/22.67 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.63/22.67 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.63/22.67 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.63/22.67 ( (fun rat real), ratreal ) 22.63/22.67 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.63/22.67 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.63/22.67 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.63/22.67 ( (fun rat (product_prod int int)), quotient_of ) 22.63/22.67 ( (fun int (fun nat nat)), nat_aux ) 22.63/22.67 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.63/22.67 ( (fun int (list int)), quickc666637781d_zero ) 22.63/22.67 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.63/22.67 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.63/22.67 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.63/22.67 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.63/22.67 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.63/22.67 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.63/22.67 ( (fun code_code_numeral int), code_int_of ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) Y) _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)))))) ) 22.63/22.67 ( pi ) 22.63/22.67 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( (one_one real) ) 22.63/22.67 ( (zero_zero real) ) 22.63/22.67 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( (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))))) ) 22.63/22.67 ( (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)) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134047 $$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_134047))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134047) _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_134047))))))) ) 22.63/22.67 ( int, pls ) 22.63/22.67 ( int, (one_one int) ) 22.63/22.67 ( int, min ) 22.63/22.67 ( int, (zero_zero int) ) 22.63/22.67 ( int, s ) 22.63/22.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.63/22.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.67 ( int, t ) 22.63/22.67 ( int, m1 ) 22.63/22.67 ( int, skv_4 ) 22.63/22.67 ( int, skv_5 ) 22.63/22.67 ( nat, (zero_zero nat) ) 22.63/22.67 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.63/22.67 ( nat, n ) 22.63/22.67 ( nat, tn ) 22.63/22.67 ( real, pi ) 22.63/22.67 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( real, (one_one real) ) 22.63/22.67 ( real, (zero_zero real) ) 22.63/22.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( 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))))) ) 22.63/22.67 ( 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)) ) 22.63/22.67 ( real, skv_2 ) 22.63/22.67 ( real, skv_9 ) 22.63/22.67 ( real, skv_12 ) 22.63/22.67 ( complex, ii ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((L $$unsorted)) (= (= min (hAPP int int bit1 L)) (= min (ti int L))) ) 22.63/22.67 ( pls ) 22.63/22.67 ( (hAPP int int bit1 pls) ) 22.63/22.67 ( min ) 22.63/22.67 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.63/22.67 ( s ) 22.63/22.67 ( s1 ) 22.63/22.67 ( m ) 22.63/22.67 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.63/22.67 ( t ) 22.63/22.67 ( v ) 22.63/22.67 ( w ) 22.63/22.67 ( y ) 22.63/22.67 ( sa ) 22.63/22.67 ( x ) 22.63/22.67 ( r ) 22.63/22.67 ( m1 ) 22.63/22.67 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.63/22.67 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.63/22.67 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 22.63/22.67 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 22.63/22.67 ( skv_14 ) 22.63/22.67 ( skv_20 ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((Real1 $$unsorted) (Real2 $$unsorted) (Real1_2 $$unsorted) (Real2_2 $$unsorted)) (let ((_let_0 (fun real complex))) (= (= (hAPP real complex (hAPP real _let_0 complex_1 Real1_2) Real2_2) (hAPP real complex (hAPP real _let_0 complex_1 Real1) Real2)) (and (= Real2 Real2_2) (= Real1 Real1_2)))) ) 22.63/22.67 ( (one_one real), (zero_zero real), (zero_zero real), (one_one real) ) 22.63/22.67 ( (zero_zero real), (one_one real), (one_one real), (zero_zero real) ) 22.63/22.67 ( (zero_zero real), (one_one real), (zero_zero real), (one_one real) ) 22.63/22.67 ( (zero_zero real), (one_one real), (zero_zero real), (zero_zero real) ) 22.63/22.67 ( (zero_zero real), (zero_zero real), (one_one real), (zero_zero real) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (zero_zero real))) (or (= _let_0 Y) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y)))))) ) 22.63/22.67 ( (one_one real) ) 22.63/22.67 ( (zero_zero real) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (tendsto nat real))) (let ((_let_6 (fun nat bool))) (let ((_let_7 (fun nat _let_6))) (let ((_let_8 (fun _let_6 real))) (let ((_let_9 (fun nat _let_1))) (let ((_let_10 (hAPP _let_0 _let_0 (hAPP _let_9 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_9 (hAPP (fun real _let_1) (fun _let_0 _let_9) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 A_3) (zero_zero real)) sequentially))) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_3 N_1))) )) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_3 (hAPP nat nat suc N_1))) (hAPP nat real A_3 N_1))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 (hAPP _let_7 _let_0 (hAPP _let_8 (fun _let_7 _let_0) (combb _let_6 real nat) (hAPP _let_0 _let_8 (big_co1399186613setsum nat real) _let_10)) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb nat _let_6 nat) (hAPP nat _let_7 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_0 real (suminf real) _let_10)) sequentially)))))))))))))) ) 22.63/22.67 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134185 $$unsorted) (BOUND_VARIABLE_134186 $$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_134185)) (hAPP nat X_a _let_0 BOUND_VARIABLE_134186))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_134185) BOUND_VARIABLE_134186))))) ) 22.63/22.67 ( int, (zero_zero nat), (zero_zero nat) ) 22.63/22.67 ( int, (zero_zero nat), (one_one nat) ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134215 $$unsorted) (BOUND_VARIABLE_134222 $$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_134215)) (= (one_one real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_134215)))) (or (not (= _let_2 (ti X_a BOUND_VARIABLE_134222))) (= (zero_zero real) (hAPP X_a real _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_134222))))))))) ) 22.63/22.67 ( int, pls, pls ) 22.63/22.67 ( int, min, min ) 22.63/22.67 ( int, s, s ) 22.63/22.67 ( int, s1, s1 ) 22.63/22.67 ( int, m, m ) 22.63/22.67 ( int, t, t ) 22.63/22.67 ( int, v, v ) 22.63/22.67 ( int, w, w ) 22.63/22.67 ( int, y, y ) 22.63/22.67 ( int, sa, sa ) 22.63/22.67 ( int, x, x ) 22.63/22.67 ( int, r, r ) 22.63/22.67 ( int, m1, m1 ) 22.63/22.67 ( int, skv_14, skv_14 ) 22.63/22.67 ( int, skv_20, skv_20 ) 22.63/22.67 ( (fun int int), bit1, bit1 ) 22.63/22.67 ( (fun int int), bit0, bit0 ) 22.63/22.67 ( (fun int int), succ, succ ) 22.63/22.67 ( (fun int int), pred, pred ) 22.63/22.67 ( (fun int int), (fact_fact int), (fact_fact int) ) 22.63/22.67 ( (fun int int), zfact, zfact ) 22.63/22.67 ( nat, n, n ) 22.63/22.67 ( nat, tn, tn ) 22.63/22.67 ( bool, fTrue, fTrue ) 22.63/22.67 ( bool, fFalse, fFalse ) 22.63/22.67 ( real, pi, pi ) 22.63/22.67 ( (fun nat real), (real_1 nat), (real_1 nat) ) 22.63/22.67 ( (fun nat real), cos_coeff, cos_coeff ) 22.63/22.67 ( (fun nat real), sin_coeff, sin_coeff ) 22.63/22.67 ( (fun real real), sin, sin ) 22.63/22.67 ( (fun real real), cos, cos ) 22.63/22.67 ( (fun real real), sqrt, sqrt ) 22.63/22.67 ( (fun real real), tan, tan ) 22.63/22.67 ( (fun real real), ln, ln ) 22.63/22.67 ( (fun real real), arctan, arctan ) 22.63/22.67 ( (fun real real), arcsin, arcsin ) 22.63/22.67 ( (fun real real), arccos, arccos ) 22.63/22.67 ( (fun nat nat), suc, suc ) 22.63/22.67 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 22.63/22.67 ( (fun nat nat), nat_size, nat_size ) 22.63/22.67 ( (fun nat nat), (size_size nat), (size_size nat) ) 22.63/22.67 ( (fun nat nat), fact, fact ) 22.63/22.67 ( (filter nat), sequentially, sequentially ) 22.63/22.67 ( (fun int (fun int rat)), fract, fract ) 22.63/22.67 ( complex, ii, ii ) 22.63/22.67 ( (fun int bool), zOdd, zOdd ) 22.63/22.67 ( (fun int bool), zprime, zprime ) 22.63/22.67 ( (fun int bool), zEven, zEven ) 22.63/22.67 ( (fun int bool), nat_neg, nat_neg ) 22.63/22.67 ( (fun int bool), nat_is_nat, nat_is_nat ) 22.63/22.67 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 22.63/22.67 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.63/22.67 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 22.63/22.67 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 22.63/22.67 ( (fun int (fun int int)), inv, inv ) 22.63/22.67 ( (fun int (fun int int)), multInv, multInv ) 22.63/22.67 ( (fun int (fun int int)), legendre, legendre ) 22.63/22.67 ( (fun int (fun int int)), standardRes, standardRes ) 22.63/22.67 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 22.63/22.67 ( (fun int (fun int int)), z3div, z3div ) 22.63/22.67 ( (fun int (fun int int)), z3mod, z3mod ) 22.63/22.67 ( (fun int (fun int int)), int_lcm, int_lcm ) 22.63/22.67 ( (fun int (fun int int)), int_gcd, int_gcd ) 22.63/22.67 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.63/22.67 ( (fun bool bool), fNot, fNot ) 22.63/22.67 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 22.63/22.67 ( (fun bool (fun bool bool)), fconj, fconj ) 22.63/22.67 ( (fun bool (fun bool bool)), fdisj, fdisj ) 22.63/22.67 ( (fun bool (fun bool bool)), fimplies, fimplies ) 22.63/22.67 ( (fun int (fun int bool)), quadRes, quadRes ) 22.63/22.67 ( (fun int (fun int bool)), d22set, d22set ) 22.63/22.67 ( (fun int (fun int bool)), norRRset, norRRset ) 22.63/22.67 ( (fun int (fun int bool)), sRStar, sRStar ) 22.63/22.67 ( (fun int (fun int bool)), sr, sr ) 22.63/22.67 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 22.63/22.67 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 22.63/22.67 ( (fun nat bool), prime, prime ) 22.63/22.67 ( (fun real complex), cis, cis ) 22.63/22.67 ( (fun nat (fun nat bool)), coprime, coprime ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 22.63/22.67 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 22.63/22.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 22.63/22.67 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 22.63/22.67 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 22.63/22.67 ( (fun nat (fun real real)), root, root ) 22.63/22.67 ( (fun real (fun real real)), log, log ) 22.63/22.67 ( (fun real (fun real real)), powr, powr ) 22.63/22.67 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 22.63/22.67 ( (fun complex complex), cnj, cnj ) 22.63/22.67 ( (fun complex complex), expi, expi ) 22.63/22.67 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 22.63/22.67 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 22.63/22.67 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 22.63/22.67 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 22.63/22.67 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 22.63/22.67 ( (fun int nat), nat_1, nat_1 ) 22.63/22.67 ( (fun int nat), phi, phi ) 22.63/22.67 ( (fun complex real), re, re ) 22.63/22.67 ( (fun complex real), im, im ) 22.63/22.67 ( (fun complex real), arg, arg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 22.63/22.67 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 22.63/22.67 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 22.63/22.67 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 22.63/22.67 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 22.63/22.67 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 22.63/22.67 ( (fun (fun int bool) int), (the int), (the int) ) 22.63/22.67 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 22.63/22.67 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 22.63/22.67 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 22.63/22.67 ( (fun real (fun real complex)), rcis, rcis ) 22.63/22.67 ( (fun real (fun real complex)), complex_1, complex_1 ) 22.63/22.67 ( (fun int (fun int (fun int bool))), zcong, zcong ) 22.63/22.67 ( (fun int (fun int (fun int bool))), wset, wset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 22.63/22.67 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 22.63/22.67 ( (fun real nat), natceiling, natceiling ) 22.63/22.67 ( (fun real nat), natfloor, natfloor ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 22.63/22.67 ( (fun int real), (real_1 int), (real_1 int) ) 22.63/22.67 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 22.63/22.67 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 22.63/22.67 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 22.63/22.67 ( (fun complex nat), (size_size complex), (size_size complex) ) 22.63/22.67 ( (fun complex nat), complex_size, complex_size ) 22.63/22.67 ( (fun (fun nat rat) bool), vanishes, vanishes ) 22.63/22.67 ( (fun (product_prod int int) rat), frct, frct ) 22.63/22.67 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 22.63/22.67 ( (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 ) 22.63/22.67 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.63/22.67 ( (fun rat real), ratreal, ratreal ) 22.63/22.67 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 22.63/22.67 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 22.63/22.67 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 22.63/22.67 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 22.63/22.67 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 22.63/22.67 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 22.63/22.67 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 22.63/22.67 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 22.63/22.67 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.63/22.67 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 22.63/22.67 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 22.63/22.67 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 22.63/22.67 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 22.63/22.67 ( (fun code_code_numeral int), code_int_of, code_int_of ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134241 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_134241)) (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_134241))))) ) 22.63/22.67 ( int, pls ) 22.63/22.67 ( int, min ) 22.63/22.67 ( nat, pls ) 22.63/22.67 ( nat, (hAPP int int bit1 pls) ) 22.63/22.67 ( nat, min ) 22.63/22.67 ( quickcheck_code_int, pls ) 22.63/22.67 ( quickcheck_code_int, min ) 22.63/22.67 ( code_code_numeral, pls ) 22.63/22.67 ( code_code_numeral, min ) 22.63/22.67 ) 22.63/22.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134262 $$unsorted) (BOUND_VARIABLE_134263 $$unsorted) (BOUND_VARIABLE_134264 $$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_134264)) (= (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_134262) BOUND_VARIABLE_134264)) BOUND_VARIABLE_134263) (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_134262) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_134264) BOUND_VARIABLE_134263))) BOUND_VARIABLE_134264)))))) ) 22.63/22.68 ( int, y, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.63/22.68 ( int, y, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.63/22.68 ( int, x, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.63/22.68 ( int, x, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), v, y ) 22.63/22.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), v, sa ) 22.63/22.68 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ) 22.63/22.68 (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))) ) 22.63/22.68 ( (zero_zero nat) ) 22.63/22.68 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.63/22.68 ( (hAPP nat nat suc (zero_zero nat)) ) 22.63/22.68 ) 22.63/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134345 $$unsorted) (BOUND_VARIABLE_134346 $$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)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_134346))) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_134345)) BOUND_VARIABLE_134346) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_134345) BOUND_VARIABLE_134346))))))) ) 22.63/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.63/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.63/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.63/22.68 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.63/22.68 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.63/22.68 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.63/22.68 ( 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))))))))) ) 22.63/22.68 ( 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))) ) 22.63/22.68 ( 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))) ) 22.63/22.68 ( 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))) ) 22.63/22.68 ) 22.63/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134370 $$unsorted) (BOUND_VARIABLE_134371 $$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 BOUND_VARIABLE_134370) BOUND_VARIABLE_134371) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_134370)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_134371))))))) ) 22.63/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.63/22.68 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ( 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 ) 22.63/22.68 ( 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))), m1 ) 22.63/22.68 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.63/22.68 ( 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_21 ) 22.63/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.63/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.63/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.63/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.63/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.63/22.68 ( int, y, v ) 22.63/22.68 ( int, y, w ) 22.63/22.68 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ( int, sa, v ) 22.63/22.68 ( int, sa, w ) 22.63/22.68 ( int, x, v ) 22.63/22.68 ( int, x, w ) 22.63/22.68 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.63/22.68 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ( int, r, v ) 22.63/22.68 ( int, r, w ) 22.63/22.68 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.63/22.68 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.63/22.68 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.63/22.68 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.63/22.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.63/22.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.63/22.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.63/22.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.63/22.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.63/22.68 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.63/22.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.63/22.68 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.63/22.68 ( 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)))))) ) 22.63/22.68 ( 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 ) 22.63/22.68 ( complex, ii, ii ) 22.63/22.68 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.63/22.68 ( 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 ) 22.63/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134389 $$unsorted) (BOUND_VARIABLE_134390 $$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)) (= (or (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_134390)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134389) _let_2))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134390) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_134389)))) (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_134389) BOUND_VARIABLE_134390)) _let_2)))))))) ) 22.64/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.64/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.64/22.68 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.64/22.68 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( 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))))))))) ) 22.64/22.68 ( 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))) ) 22.64/22.68 ( 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))) ) 22.64/22.68 ( 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))) ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134424 $$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_134424))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_134424) (ti X_a BOUND_VARIABLE_134424))) ) 22.64/22.68 ( int, pls ) 22.64/22.68 ( int, (one_one int) ) 22.64/22.68 ( int, min ) 22.64/22.68 ( int, s ) 22.64/22.68 ( int, s1 ) 22.64/22.68 ( int, m ) 22.64/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.64/22.68 ( int, t ) 22.64/22.68 ( int, v ) 22.64/22.68 ( int, w ) 22.64/22.68 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.64/22.68 ( int, y ) 22.64/22.68 ( int, sa ) 22.64/22.68 ( int, x ) 22.64/22.68 ( int, r ) 22.64/22.68 ( int, m1 ) 22.64/22.68 ( int, skv_4 ) 22.64/22.68 ( int, skv_5 ) 22.64/22.68 ( int, skv_14 ) 22.64/22.68 ( int, skv_20 ) 22.64/22.68 ( (fun int int), bit1 ) 22.64/22.68 ( (fun int int), bit0 ) 22.64/22.68 ( (fun int int), succ ) 22.64/22.68 ( (fun int int), pred ) 22.64/22.68 ( (fun int int), (fact_fact int) ) 22.64/22.68 ( (fun int int), zfact ) 22.64/22.68 ( nat, n ) 22.64/22.68 ( nat, tn ) 22.64/22.68 ( bool, fTrue ) 22.64/22.68 ( bool, fFalse ) 22.64/22.68 ( real, pi ) 22.64/22.68 ( 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)))) ) 22.64/22.68 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( real, skv_10 ) 22.64/22.68 ( real, skv_11 ) 22.64/22.68 ( real, skv_15 ) 22.64/22.68 ( real, skv_18 ) 22.64/22.68 ( (fun nat real), (real_1 nat) ) 22.64/22.68 ( (fun nat real), cos_coeff ) 22.64/22.68 ( (fun nat real), sin_coeff ) 22.64/22.68 ( (fun real real), sin ) 22.64/22.68 ( (fun real real), cos ) 22.64/22.68 ( (fun real real), sqrt ) 22.64/22.68 ( (fun real real), tan ) 22.64/22.68 ( (fun real real), ln ) 22.64/22.68 ( (fun real real), arctan ) 22.64/22.68 ( (fun real real), arcsin ) 22.64/22.68 ( (fun real real), arccos ) 22.64/22.68 ( (fun nat nat), suc ) 22.64/22.68 ( (fun nat nat), (fact_fact nat) ) 22.64/22.68 ( (fun nat nat), nat_size ) 22.64/22.68 ( (fun nat nat), (size_size nat) ) 22.64/22.68 ( (fun nat nat), fact ) 22.64/22.68 ( (filter nat), sequentially ) 22.64/22.68 ( (fun int (fun int rat)), fract ) 22.64/22.68 ( complex, ii ) 22.64/22.68 ( (fun int bool), zOdd ) 22.64/22.68 ( (fun int bool), zprime ) 22.64/22.68 ( (fun int bool), zEven ) 22.64/22.68 ( (fun int bool), nat_neg ) 22.64/22.68 ( (fun int bool), nat_is_nat ) 22.64/22.68 ( (fun int bool), (even_odd_even int) ) 22.64/22.68 ( (fun int bool), twoSqu1091635170sum2sq ) 22.64/22.68 ( (fun int (fun int int)), legacy_zgcd ) 22.64/22.68 ( (fun int (fun int int)), (gcd_gcd int) ) 22.64/22.68 ( (fun int (fun int int)), inv ) 22.64/22.68 ( (fun int (fun int int)), multInv ) 22.64/22.68 ( (fun int (fun int int)), legendre ) 22.64/22.68 ( (fun int (fun int int)), standardRes ) 22.64/22.68 ( (fun int (fun int int)), nat_tsub ) 22.64/22.68 ( (fun int (fun int int)), z3div ) 22.64/22.68 ( (fun int (fun int int)), z3mod ) 22.64/22.68 ( (fun int (fun int int)), int_lcm ) 22.64/22.68 ( (fun int (fun int int)), int_gcd ) 22.64/22.68 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.64/22.68 ( (fun bool bool), fNot ) 22.64/22.68 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.64/22.68 ( (fun bool (fun bool bool)), fconj ) 22.64/22.68 ( (fun bool (fun bool bool)), fdisj ) 22.64/22.68 ( (fun bool (fun bool bool)), fimplies ) 22.64/22.68 ( (fun int (fun int bool)), quadRes ) 22.64/22.68 ( (fun int (fun int bool)), d22set ) 22.64/22.68 ( (fun int (fun int bool)), norRRset ) 22.64/22.68 ( (fun int (fun int bool)), sRStar ) 22.64/22.68 ( (fun int (fun int bool)), sr ) 22.64/22.68 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.64/22.68 ( (fun nat bool), (even_odd_even nat) ) 22.64/22.68 ( (fun nat bool), prime ) 22.64/22.68 ( (fun real complex), cis ) 22.64/22.68 ( (fun nat (fun nat bool)), coprime ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.64/22.68 ( (fun (product_prod int int) bool), frac_1 ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.64/22.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.64/22.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.64/22.68 ( (fun (fun int bool) bool), nat_nat_set ) 22.64/22.68 ( (fun nat (fun real real)), root ) 22.64/22.68 ( (fun real (fun real real)), log ) 22.64/22.68 ( (fun real (fun real real)), powr ) 22.64/22.68 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.64/22.68 ( (fun complex complex), cnj ) 22.64/22.68 ( (fun complex complex), expi ) 22.64/22.68 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.64/22.68 ( (fun nat (fun nat nat)), nat_gcd ) 22.64/22.68 ( (fun nat (fun nat nat)), nat_lcm ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.64/22.68 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.64/22.68 ( (fun int (fun (fun int bool) bool)), resSet ) 22.64/22.68 ( (fun int nat), nat_1 ) 22.64/22.68 ( (fun int nat), phi ) 22.64/22.68 ( (fun complex real), re ) 22.64/22.68 ( (fun complex real), im ) 22.64/22.68 ( (fun complex real), arg ) 22.64/22.68 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.64/22.68 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.64/22.68 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.64/22.68 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.64/22.68 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.64/22.68 ( (fun (product_prod nat nat) bool), pred_nat ) 22.64/22.68 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.64/22.68 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.64/22.68 ( (fun (fun int bool) int), (the int) ) 22.64/22.68 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.64/22.68 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.64/22.68 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.64/22.68 ( (fun real (fun real complex)), rcis ) 22.64/22.68 ( (fun real (fun real complex)), complex_1 ) 22.64/22.68 ( (fun int (fun int (fun int bool))), zcong ) 22.64/22.68 ( (fun int (fun int (fun int bool))), wset ) 22.64/22.68 ( (fun int (fun int (fun int bool))), noXRRset ) 22.64/22.68 ( (fun int (fun int (fun int bool))), bnorRset ) 22.64/22.68 ( (fun int (fun int (fun int bool))), zcongm ) 22.64/22.68 ( (fun real nat), natceiling ) 22.64/22.68 ( (fun real nat), natfloor ) 22.64/22.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.64/22.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.64/22.68 ( (fun int real), (real_1 int) ) 22.64/22.68 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.64/22.68 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.64/22.68 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.64/22.68 ( (fun complex nat), (size_size complex) ) 22.64/22.68 ( (fun complex nat), complex_size ) 22.64/22.68 ( (fun (fun nat rat) bool), vanishes ) 22.64/22.68 ( (fun (product_prod int int) rat), frct ) 22.64/22.68 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.64/22.68 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.64/22.68 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.64/22.68 ( (fun rat real), ratreal ) 22.64/22.68 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.64/22.68 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.64/22.68 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.64/22.68 ( (fun rat (product_prod int int)), quotient_of ) 22.64/22.68 ( (fun int (fun nat nat)), nat_aux ) 22.64/22.68 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.64/22.68 ( (fun int (list int)), quickc666637781d_zero ) 22.64/22.68 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.64/22.68 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.64/22.68 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.64/22.68 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.64/22.68 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.64/22.68 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.64/22.68 ( (fun code_code_numeral int), code_int_of ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134444 $$unsorted) (BOUND_VARIABLE_134445 $$unsorted) (BOUND_VARIABLE_134446 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134444) BOUND_VARIABLE_134445)) BOUND_VARIABLE_134446) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_134444) BOUND_VARIABLE_134446)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_134445) BOUND_VARIABLE_134446)))))))) ) 22.64/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.64/22.68 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134471 $$unsorted) (BOUND_VARIABLE_134472 $$unsorted) (BOUND_VARIABLE_134473 $$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_134473))) (= (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_134471) BOUND_VARIABLE_134473)) BOUND_VARIABLE_134472)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134471) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_134472) BOUND_VARIABLE_134473)))))))) ) 22.64/22.68 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.64/22.68 ( int, (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.64/22.68 ( 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))) ) 22.64/22.68 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.64/22.68 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.64/22.68 ) 22.64/22.68 (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)))))) ) 22.64/22.68 ( 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 ) 22.64/22.68 ( (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)))) ) 22.64/22.68 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 22.64/22.68 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 22.64/22.68 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.64/22.68 ( 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 ) 22.64/22.68 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134526 $$unsorted) (BOUND_VARIABLE_134527 $$unsorted) (BOUND_VARIABLE_134528 $$unsorted) (BOUND_VARIABLE_134529 $$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)))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134528) BOUND_VARIABLE_134529))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_134526) BOUND_VARIABLE_134527))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_134529))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_134526))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_134528) BOUND_VARIABLE_134526)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_134529) BOUND_VARIABLE_134527))))))))) ) 22.64/22.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134562 $$unsorted)) (or (not (linordered_field X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_134562)))))) ) 22.64/22.68 ( int, (one_one nat) ) 22.64/22.68 ( real, (one_one nat) ) 22.64/22.68 ) 22.64/22.68 (instantiation (forall ((X_a $$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)))) ) 22.64/22.68 ( rat ) 22.64/22.68 ( int ) 22.64/22.68 ( (fun int int) ) 22.64/22.68 ( nat ) 22.64/22.68 ( bool ) 22.64/22.68 ( real ) 22.64/22.68 ( (fun nat real) ) 22.64/22.68 ( (fun real real) ) 22.64/22.68 ( complex ) 22.64/22.68 ( (fun int bool) ) 22.64/22.68 ( (product_prod int int) ) 22.64/22.68 ( (fun (product_prod int int) int) ) 22.64/22.68 ( (fun int (fun int bool)) ) 22.64/22.68 ( (fun nat bool) ) 22.64/22.68 ( (fun (product_prod int int) bool) ) 22.64/22.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.64/22.68 ( (fun real bool) ) 22.64/22.68 ( code_code_numeral ) 22.64/22.68 ( (fun int (fun int (fun int bool))) ) 22.64/22.68 ( (fun int real) ) 22.64/22.68 ) 22.67/22.72 (instantiation (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (fun int _let_2))) (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_2 (ord_less int) _let_4) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_2 (hAPP int _let_3 zcong X) (zero_zero int)) P_5)) (not (hBOOL (hAPP int bool (hAPP int _let_2 quadRes P_5) X))) (hBOOL (hAPP int bool (hAPP int _let_2 (hAPP int _let_3 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) _let_1)) _let_4)))) _let_1) P_5)))))))) ) 22.67/22.72 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134602 $$unsorted) (BOUND_VARIABLE_134603 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_134603) (ti X_a BOUND_VARIABLE_134602)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_134602) (hAPP X_a X_a _let_0 BOUND_VARIABLE_134603))))) ) 22.67/22.72 ( int, pls, y ) 22.67/22.72 ( int, min, m ) 22.67/22.72 ( int, s, min ) 22.67/22.72 ( int, s1, s1 ) 22.67/22.72 ( int, s1, v ) 22.67/22.72 ( int, s1, r ) 22.67/22.72 ( int, m, min ) 22.67/22.72 ( int, m, s ) 22.67/22.72 ( int, m, m ) 22.67/22.72 ( int, t, sa ) 22.67/22.72 ( int, v, s1 ) 22.67/22.72 ( int, w, pls ) 22.67/22.72 ( int, y, pls ) 22.67/22.72 ( int, y, w ) 22.67/22.72 ( int, y, y ) 22.67/22.72 ( int, sa, m1 ) 22.67/22.72 ( int, x, x ) 22.67/22.72 ( int, x, skv_14 ) 22.67/22.72 ( int, x, skv_20 ) 22.67/22.72 ( int, r, v ) 22.67/22.72 ( int, m1, t ) 22.67/22.72 ( int, m1, sa ) 22.67/22.72 ( int, m1, m1 ) 22.67/22.72 ( int, skv_14, x ) 22.67/22.72 ( int, skv_20, skv_14 ) 22.67/22.72 ( (fun int int), bit1, (fact_fact int) ) 22.67/22.72 ( (fun int int), bit0, bit1 ) 22.67/22.72 ( (fun int int), bit0, bit0 ) 22.67/22.72 ( (fun int int), bit0, (fact_fact int) ) 22.67/22.72 ( (fun int int), succ, succ ) 22.67/22.72 ( (fun int int), succ, pred ) 22.67/22.72 ( (fun int int), succ, zfact ) 22.67/22.72 ( (fun int int), pred, zfact ) 22.67/22.72 ( (fun int int), (fact_fact int), bit0 ) 22.67/22.72 ( (fun int int), zfact, succ ) 22.67/22.72 ( nat, n, n ) 22.67/22.72 ( nat, n, tn ) 22.67/22.72 ( nat, tn, n ) 22.67/22.72 ( bool, fTrue, fTrue ) 22.67/22.72 ( bool, fTrue, fFalse ) 22.67/22.72 ( bool, fFalse, fTrue ) 22.67/22.72 ( real, pi, pi ) 22.67/22.72 ( (fun nat real), (real_1 nat), cos_coeff ) 22.67/22.72 ( (fun nat real), cos_coeff, sin_coeff ) 22.67/22.72 ( (fun nat real), sin_coeff, (real_1 nat) ) 22.67/22.72 ( (fun nat real), sin_coeff, cos_coeff ) 22.67/22.72 ( (fun nat real), sin_coeff, sin_coeff ) 22.67/22.72 ( (fun real real), sin, sin ) 22.67/22.72 ( (fun real real), sin, ln ) 22.67/22.72 ( (fun real real), sin, arctan ) 22.67/22.72 ( (fun real real), cos, tan ) 22.67/22.72 ( (fun real real), sqrt, arcsin ) 22.67/22.72 ( (fun real real), tan, cos ) 22.67/22.72 ( (fun real real), tan, tan ) 22.67/22.72 ( (fun real real), tan, arccos ) 22.67/22.72 ( (fun real real), ln, sin ) 22.67/22.72 ( (fun real real), arctan, ln ) 22.67/22.72 ( (fun real real), arcsin, sqrt ) 22.67/22.72 ( (fun real real), arcsin, arcsin ) 22.67/22.72 ( (fun real real), arccos, cos ) 22.67/22.72 ( (fun nat nat), suc, (size_size nat) ) 22.67/22.72 ( (fun nat nat), (fact_fact nat), fact ) 22.67/22.72 ( (fun nat nat), nat_size, suc ) 22.67/22.72 ( (fun nat nat), nat_size, nat_size ) 22.67/22.72 ( (fun nat nat), nat_size, (size_size nat) ) 22.67/22.72 ( (fun nat nat), (size_size nat), nat_size ) 22.67/22.72 ( (fun nat nat), fact, (fact_fact nat) ) 22.67/22.72 ( (fun nat nat), fact, fact ) 22.67/22.72 ( (filter nat), sequentially, sequentially ) 22.67/22.72 ( (fun int (fun int rat)), fract, fract ) 22.67/22.72 ( complex, ii, ii ) 22.67/22.72 ( (fun int bool), zOdd, zOdd ) 22.67/22.72 ( (fun int bool), zOdd, zprime ) 22.67/22.72 ( (fun int bool), zOdd, nat_is_nat ) 22.67/22.72 ( (fun int bool), zprime, zOdd ) 22.67/22.72 ( (fun int bool), zEven, nat_neg ) 22.67/22.72 ( (fun int bool), nat_neg, twoSqu1091635170sum2sq ) 22.67/22.72 ( (fun int bool), nat_is_nat, zprime ) 22.67/22.72 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 22.67/22.72 ( (fun int bool), twoSqu1091635170sum2sq, zEven ) 22.67/22.72 ( (fun int bool), twoSqu1091635170sum2sq, nat_neg ) 22.67/22.72 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.67/22.72 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 22.67/22.72 ( (fun int (fun int int)), legacy_zgcd, nat_tsub ) 22.67/22.72 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 22.67/22.72 ( (fun int (fun int int)), (gcd_gcd int), multInv ) 22.67/22.72 ( (fun int (fun int int)), (gcd_gcd int), standardRes ) 22.67/22.72 ( (fun int (fun int int)), inv, int_gcd ) 22.67/22.72 ( (fun int (fun int int)), multInv, (gcd_gcd int) ) 22.67/22.72 ( (fun int (fun int int)), legendre, int_lcm ) 22.67/22.72 ( (fun int (fun int int)), standardRes, multInv ) 22.67/22.72 ( (fun int (fun int int)), nat_tsub, legacy_zgcd ) 22.67/22.72 ( (fun int (fun int int)), z3div, inv ) 22.67/22.72 ( (fun int (fun int int)), z3mod, legendre ) 22.67/22.72 ( (fun int (fun int int)), int_lcm, legendre ) 22.67/22.72 ( (fun int (fun int int)), int_lcm, z3mod ) 22.67/22.72 ( (fun int (fun int int)), int_lcm, int_lcm ) 22.67/22.72 ( (fun int (fun int int)), int_gcd, inv ) 22.67/22.72 ( (fun int (fun int int)), int_gcd, z3div ) 22.67/22.72 ( (fun int (fun int int)), int_gcd, int_gcd ) 22.67/22.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.67/22.72 ( (fun bool bool), fNot, fNot ) 22.67/22.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 22.67/22.72 ( (fun bool (fun bool bool)), fconj, fdisj ) 22.67/22.72 ( (fun bool (fun bool bool)), fdisj, fconj ) 22.67/22.72 ( (fun bool (fun bool bool)), fdisj, fdisj ) 22.67/22.72 ( (fun bool (fun bool bool)), fdisj, fimplies ) 22.67/22.72 ( (fun bool (fun bool bool)), fimplies, fconj ) 22.67/22.72 ( (fun int (fun int bool)), quadRes, sRStar ) 22.67/22.72 ( (fun int (fun int bool)), d22set, quickc1265749348ro_rel ) 22.67/22.72 ( (fun int (fun int bool)), norRRset, quadRes ) 22.67/22.72 ( (fun int (fun int bool)), norRRset, norRRset ) 22.67/22.72 ( (fun int (fun int bool)), norRRset, sRStar ) 22.67/22.72 ( (fun int (fun int bool)), sRStar, norRRset ) 22.67/22.72 ( (fun int (fun int bool)), sr, d22set ) 22.67/22.72 ( (fun int (fun int bool)), sr, sr ) 22.67/22.72 ( (fun int (fun int bool)), sr, quickc1265749348ro_rel ) 22.67/22.72 ( (fun int (fun int bool)), quickc1265749348ro_rel, sr ) 22.67/22.72 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 22.67/22.72 ( (fun nat bool), (even_odd_even nat), prime ) 22.67/22.72 ( (fun nat bool), prime, (even_odd_even nat) ) 22.67/22.72 ( (fun real complex), cis, cis ) 22.67/22.72 ( (fun nat (fun nat bool)), coprime, coprime ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 22.67/22.72 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, posDivAlg_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, norm_frac_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, upto_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, lazy_small_lazy_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, negDivAlg_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, posDivAlg_rel ) 22.67/22.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 22.67/22.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than ) 22.67/22.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than2 ) 22.67/22.72 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 22.67/22.72 ( (fun nat (fun real real)), root, root ) 22.67/22.72 ( (fun real (fun real real)), log, powr ) 22.67/22.72 ( (fun real (fun real real)), powr, log ) 22.67/22.72 ( (fun real (fun real real)), powr, powr ) 22.67/22.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 22.67/22.72 ( (fun complex complex), cnj, expi ) 22.67/22.72 ( (fun complex complex), expi, cnj ) 22.67/22.72 ( (fun complex complex), expi, expi ) 22.67/22.72 ( (fun nat (fun nat nat)), (gcd_gcd nat), nat_lcm ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_gcd, (gcd_gcd nat) ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_gcd, nat_lcm ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_lcm, nat_gcd ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, negateSnd ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, normalize ) 22.67/22.72 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 22.67/22.72 ( (fun int (fun (fun int bool) bool)), rsetR, resSet ) 22.67/22.72 ( (fun int (fun (fun int bool) bool)), resSet, rsetR ) 22.67/22.72 ( (fun int nat), nat_1, phi ) 22.67/22.72 ( (fun int nat), phi, nat_1 ) 22.67/22.72 ( (fun int nat), phi, phi ) 22.67/22.72 ( (fun complex real), re, arg ) 22.67/22.72 ( (fun complex real), im, re ) 22.67/22.72 ( (fun complex real), arg, re ) 22.67/22.72 ( (fun complex real), arg, im ) 22.67/22.72 ( (fun complex real), arg, arg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), divmod_int, negDivAlg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), divmod_int, pdivmod ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), posDivAlg, norm_frac ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), negDivAlg, pdivmod ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), pdivmod, divmod_int ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), norm_frac, posDivAlg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 22.67/22.72 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 22.67/22.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 22.67/22.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 22.67/22.72 ( (fun (fun int bool) int), (the int), (the int) ) 22.67/22.72 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 22.67/22.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 22.67/22.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 22.67/22.72 ( (fun real (fun real complex)), rcis, rcis ) 22.67/22.72 ( (fun real (fun real complex)), rcis, complex_1 ) 22.67/22.72 ( (fun real (fun real complex)), complex_1, rcis ) 22.67/22.72 ( (fun int (fun int (fun int bool))), zcong, zcong ) 22.67/22.72 ( (fun int (fun int (fun int bool))), zcong, noXRRset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), wset, wset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), wset, bnorRset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), wset, zcongm ) 22.67/22.72 ( (fun int (fun int (fun int bool))), noXRRset, zcong ) 22.67/22.72 ( (fun int (fun int (fun int bool))), bnorRset, wset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), zcongm, bnorRset ) 22.67/22.72 ( (fun real nat), natceiling, natceiling ) 22.67/22.72 ( (fun real nat), natceiling, natfloor ) 22.67/22.72 ( (fun real nat), natfloor, natceiling ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_leq ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_less ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 22.67/22.72 ( (fun int real), (real_1 int), (real_1 int) ) 22.67/22.72 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 22.67/22.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 22.67/22.72 ( (fun complex nat), (size_size complex), (size_size complex) ) 22.67/22.72 ( (fun complex nat), (size_size complex), complex_size ) 22.67/22.72 ( (fun complex nat), complex_size, (size_size complex) ) 22.67/22.72 ( (fun (fun nat rat) bool), vanishes, vanishes ) 22.67/22.72 ( (fun (product_prod int int) rat), frct, frct ) 22.67/22.72 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 22.67/22.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda ) 22.67/22.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.67/22.72 ( (fun rat real), ratreal, ratreal ) 22.67/22.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 22.67/22.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 22.67/22.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 22.67/22.72 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 22.67/22.72 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 22.67/22.72 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 22.67/22.72 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 22.67/22.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 22.67/22.72 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.67/22.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 22.67/22.72 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 22.67/22.72 ( (fun code_code_numeral nat), code_c271388182l_size, (size_size code_code_numeral) ) 22.67/22.72 ( (fun code_code_numeral nat), (size_size code_code_numeral), code_c271388182l_size ) 22.67/22.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 22.67/22.72 ( (fun code_code_numeral int), code_int_of, code_int_of ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134674 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (hAPP int X_a _let_0 BOUND_VARIABLE_134674))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (zero_zero X_a)) _let_3)) _let_3) (hAPP int X_a _let_0 (hAPP int int bit0 BOUND_VARIABLE_134674)))))))) ) 22.67/22.72 ( int, pls ) 22.67/22.72 ( int, (hAPP int int bit1 pls) ) 22.67/22.72 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.67/22.72 ( nat, pls ) 22.67/22.72 ( nat, (hAPP int int bit1 pls) ) 22.67/22.72 ( real, (hAPP int int bit1 pls) ) 22.67/22.72 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.67/22.72 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.67/22.72 ( complex, (hAPP int int bit1 pls) ) 22.67/22.72 ( quickcheck_code_int, pls ) 22.67/22.72 ( code_code_numeral, pls ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_134703 $$unsorted) (BOUND_VARIABLE_134704 $$unsorted) (BOUND_VARIABLE_134705 $$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_134705)))) (let ((_let_3 (ti X_a BOUND_VARIABLE_134703))) (or (not (field_inverse_zero X_a)) (= (and (or (not _let_2) (= _let_0 _let_3)) (or _let_2 (= (ti X_a BOUND_VARIABLE_134704) (hAPP X_a X_a (hAPP X_a _let_1 (times_times X_a) BOUND_VARIABLE_134703) BOUND_VARIABLE_134705)))) (= _let_3 (hAPP X_a X_a (hAPP X_a _let_1 (inverse_divide X_a) BOUND_VARIABLE_134704) BOUND_VARIABLE_134705)))))))) ) 22.67/22.72 ( int, pls, pls, pls ) 22.67/22.72 ( int, min, min, min ) 22.67/22.72 ( int, s, s, s ) 22.67/22.72 ( int, s1, s1, s1 ) 22.67/22.72 ( int, m, m, m ) 22.67/22.72 ( int, t, t, t ) 22.67/22.72 ( int, v, v, v ) 22.67/22.72 ( int, w, w, w ) 22.67/22.72 ( int, y, y, y ) 22.67/22.72 ( int, sa, sa, sa ) 22.67/22.72 ( int, x, x, x ) 22.67/22.72 ( int, r, r, r ) 22.67/22.72 ( int, m1, m1, m1 ) 22.67/22.72 ( int, skv_14, skv_14, skv_14 ) 22.67/22.72 ( int, skv_20, skv_20, skv_20 ) 22.67/22.72 ( (fun int int), bit1, bit1, bit1 ) 22.67/22.72 ( (fun int int), bit0, bit0, bit0 ) 22.67/22.72 ( (fun int int), succ, succ, succ ) 22.67/22.72 ( (fun int int), pred, pred, pred ) 22.67/22.72 ( (fun int int), (fact_fact int), (fact_fact int), (fact_fact int) ) 22.67/22.72 ( (fun int int), zfact, zfact, zfact ) 22.67/22.72 ( nat, n, n, n ) 22.67/22.72 ( nat, tn, tn, tn ) 22.67/22.72 ( bool, fTrue, fTrue, fTrue ) 22.67/22.72 ( bool, fFalse, fFalse, fFalse ) 22.67/22.72 ( real, pi, pi, pi ) 22.67/22.72 ( (fun nat real), (real_1 nat), (real_1 nat), (real_1 nat) ) 22.67/22.72 ( (fun nat real), cos_coeff, cos_coeff, cos_coeff ) 22.67/22.72 ( (fun nat real), sin_coeff, sin_coeff, sin_coeff ) 22.67/22.72 ( (fun real real), sin, sin, sin ) 22.67/22.72 ( (fun real real), cos, cos, cos ) 22.67/22.72 ( (fun real real), sqrt, sqrt, sqrt ) 22.67/22.72 ( (fun real real), tan, tan, tan ) 22.67/22.72 ( (fun real real), ln, ln, ln ) 22.67/22.72 ( (fun real real), arctan, arctan, arctan ) 22.67/22.72 ( (fun real real), arcsin, arcsin, arcsin ) 22.67/22.72 ( (fun real real), arccos, arccos, arccos ) 22.67/22.72 ( (fun nat nat), suc, suc, suc ) 22.67/22.72 ( (fun nat nat), (fact_fact nat), (fact_fact nat), (fact_fact nat) ) 22.67/22.72 ( (fun nat nat), nat_size, nat_size, nat_size ) 22.67/22.72 ( (fun nat nat), (size_size nat), (size_size nat), (size_size nat) ) 22.67/22.72 ( (fun nat nat), fact, fact, fact ) 22.67/22.72 ( (filter nat), sequentially, sequentially, sequentially ) 22.67/22.72 ( (fun int (fun int rat)), fract, fract, fract ) 22.67/22.72 ( complex, ii, ii, ii ) 22.67/22.72 ( (fun int bool), zOdd, zOdd, zOdd ) 22.67/22.72 ( (fun int bool), zprime, zprime, zprime ) 22.67/22.72 ( (fun int bool), zEven, zEven, zEven ) 22.67/22.72 ( (fun int bool), nat_neg, nat_neg, nat_neg ) 22.67/22.72 ( (fun int bool), nat_is_nat, nat_is_nat, nat_is_nat ) 22.67/22.72 ( (fun int bool), (even_odd_even int), (even_odd_even int), (even_odd_even int) ) 22.67/22.72 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 22.67/22.72 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd, legacy_zgcd ) 22.67/22.72 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int), (gcd_gcd int) ) 22.67/22.72 ( (fun int (fun int int)), inv, inv, inv ) 22.67/22.72 ( (fun int (fun int int)), multInv, multInv, multInv ) 22.67/22.72 ( (fun int (fun int int)), legendre, legendre, legendre ) 22.67/22.72 ( (fun int (fun int int)), standardRes, standardRes, standardRes ) 22.67/22.72 ( (fun int (fun int int)), nat_tsub, nat_tsub, nat_tsub ) 22.67/22.72 ( (fun int (fun int int)), z3div, z3div, z3div ) 22.67/22.72 ( (fun int (fun int int)), z3mod, z3mod, z3mod ) 22.67/22.72 ( (fun int (fun int int)), int_lcm, int_lcm, int_lcm ) 22.67/22.72 ( (fun int (fun int int)), int_gcd, int_gcd, int_gcd ) 22.67/22.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 22.67/22.72 ( (fun bool bool), fNot, fNot, fNot ) 22.67/22.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset, is_RRset ) 22.67/22.72 ( (fun bool (fun bool bool)), fconj, fconj, fconj ) 22.67/22.72 ( (fun bool (fun bool bool)), fdisj, fdisj, fdisj ) 22.67/22.72 ( (fun bool (fun bool bool)), fimplies, fimplies, fimplies ) 22.67/22.72 ( (fun int (fun int bool)), quadRes, quadRes, quadRes ) 22.67/22.72 ( (fun int (fun int bool)), d22set, d22set, d22set ) 22.67/22.72 ( (fun int (fun int bool)), norRRset, norRRset, norRRset ) 22.67/22.72 ( (fun int (fun int bool)), sRStar, sRStar, sRStar ) 22.67/22.72 ( (fun int (fun int bool)), sr, sr, sr ) 22.67/22.72 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel, quickc1265749348ro_rel ) 22.67/22.72 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat), (even_odd_even nat) ) 22.67/22.72 ( (fun nat bool), prime, prime, prime ) 22.67/22.72 ( (fun real complex), cis, cis, cis ) 22.67/22.72 ( (fun nat (fun nat bool)), coprime, coprime, coprime ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel, ratrel ) 22.67/22.72 ( (fun (product_prod int int) bool), frac_1, frac_1, frac_1 ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel, upto_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel, posDivAlg_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel, negDivAlg_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel, lazy_small_lazy_rel ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel, norm_frac_rel ) 22.67/22.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2, int_ge_less_than2 ) 22.67/22.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than, int_ge_less_than ) 22.67/22.72 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set, nat_nat_set ) 22.67/22.72 ( (fun nat (fun real real)), root, root, root ) 22.67/22.72 ( (fun real (fun real real)), log, log, log ) 22.67/22.72 ( (fun real (fun real real)), powr, powr, powr ) 22.67/22.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd, xzgcd ) 22.67/22.72 ( (fun complex complex), cnj, cnj, cnj ) 22.67/22.72 ( (fun complex complex), expi, expi, expi ) 22.67/22.72 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat), (gcd_gcd nat) ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd, nat_gcd ) 22.67/22.72 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm, nat_lcm ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize, normalize ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd, negateSnd ) 22.67/22.72 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR, rsetR ) 22.67/22.72 ( (fun int (fun (fun int bool) bool)), resSet, resSet, resSet ) 22.67/22.72 ( (fun int nat), nat_1, nat_1, nat_1 ) 22.67/22.72 ( (fun int nat), phi, phi, phi ) 22.67/22.72 ( (fun complex real), re, re, re ) 22.67/22.72 ( (fun complex real), im, im, im ) 22.67/22.72 ( (fun complex real), arg, arg, arg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int, divmod_int ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg, posDivAlg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg, negDivAlg ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod, pdivmod ) 22.67/22.72 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac, norm_frac ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust, adjust ) 22.67/22.72 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat, pred_nat ) 22.67/22.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux, code_nat_of_aux ) 22.67/22.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral, code_S1047413653umeral ) 22.67/22.72 ( (fun (fun int bool) int), (the int), (the int), (the int) ) 22.67/22.72 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int, quickcheck_of_int ) 22.67/22.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat, divmod_nat ) 22.67/22.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral, code_d418564891umeral ) 22.67/22.72 ( (fun real (fun real complex)), rcis, rcis, rcis ) 22.67/22.72 ( (fun real (fun real complex)), complex_1, complex_1, complex_1 ) 22.67/22.72 ( (fun int (fun int (fun int bool))), zcong, zcong, zcong ) 22.67/22.72 ( (fun int (fun int (fun int bool))), wset, wset, wset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset, noXRRset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset, bnorRset ) 22.67/22.72 ( (fun int (fun int (fun int bool))), zcongm, zcongm, zcongm ) 22.67/22.72 ( (fun real nat), natceiling, natceiling, natceiling ) 22.67/22.72 ( (fun real nat), natfloor, natfloor, natfloor ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less, pair_less ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq, pair_leq ) 22.67/22.72 ( (fun int real), (real_1 int), (real_1 int), (real_1 int) ) 22.67/22.72 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of, quickcheck_int_of ) 22.67/22.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int, quickc495462417de_int ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel, nat_gcd_rel ) 22.67/22.72 ( (fun complex nat), (size_size complex), (size_size complex), (size_size complex) ) 22.67/22.72 ( (fun complex nat), complex_size, complex_size, complex_size ) 22.67/22.72 ( (fun (fun nat rat) bool), vanishes, vanishes, vanishes ) 22.67/22.72 ( (fun (product_prod int int) rat), frct, frct, frct ) 22.67/22.72 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS, setS ) 22.67/22.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda, xzgcda, xzgcda ) 22.67/22.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 22.67/22.72 ( (fun rat real), ratreal, ratreal, ratreal ) 22.67/22.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair, multInvPair ) 22.67/22.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR, rRset2norRR ) 22.67/22.72 ( (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 ) 22.67/22.72 ( (fun rat (product_prod int int)), quotient_of, quotient_of, quotient_of ) 22.67/22.72 ( (fun int (fun nat nat)), nat_aux, nat_aux, nat_aux ) 22.67/22.72 ( (fun nat (fun nat (product_prod int int))), bezw, bezw, bezw ) 22.67/22.72 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero, quickc666637781d_zero ) 22.67/22.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of, quickcheck_nat_of ) 22.67/22.72 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 22.67/22.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel, divmod_int_rel ) 22.67/22.72 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size, code_c271388182l_size ) 22.67/22.72 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral), (size_size code_code_numeral) ) 22.67/22.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel, divmod_nat_rel ) 22.67/22.72 ( (fun code_code_numeral int), code_int_of, code_int_of, code_int_of ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat (fact_fact nat) (hAPP int nat nat_1 X))) (hAPP int int (fact_fact int) X))) ) 22.67/22.72 ( pls ) 22.67/22.72 ( (one_one int) ) 22.67/22.72 ( min ) 22.67/22.72 ( (zero_zero int) ) 22.67/22.72 ( s ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.67/22.72 ( t ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.67/22.72 ( skv_4 ) 22.67/22.72 ( skv_5 ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero int))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) _let_0) X)) (= _let_0 (hAPP int int (fact_fact int) X)))) ) 22.67/22.72 ( pls ) 22.67/22.72 ( (one_one int) ) 22.67/22.72 ( min ) 22.67/22.72 ( (zero_zero int) ) 22.67/22.72 ( s ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.67/22.72 ( skv_4 ) 22.67/22.72 ( skv_5 ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted) (P_1 $$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_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) (zero_zero nat)) N_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 N_1) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) M_2) N_1)))) (hBOOL (hAPP nat bool (hAPP nat _let_0 P_1 M_2) N_1)))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 Ma) Na))) ) 22.67/22.72 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less nat) ) 22.67/22.72 ( (zero_zero nat), n, (ord_less nat) ) 22.67/22.72 ( (zero_zero nat), tn, (ord_less nat) ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((X_a $$unsorted)) (or (not (ord X_a)) (= (ord_min X_a) (hAPP (fun X_a (fun X_a bool)) (fun X_a (fun X_a X_a)) (min_1 X_a) (ord_less_eq X_a)))) ) 22.67/22.72 ( rat ) 22.67/22.72 ( int ) 22.67/22.72 ( (fun int int) ) 22.67/22.72 ( nat ) 22.67/22.72 ( bool ) 22.67/22.72 ( real ) 22.67/22.72 ( (fun nat real) ) 22.67/22.72 ( (fun real real) ) 22.67/22.72 ( (filter nat) ) 22.67/22.72 ( complex ) 22.67/22.72 ( (fun int bool) ) 22.67/22.72 ( (product_prod int int) ) 22.67/22.72 ( (fun (product_prod int int) int) ) 22.67/22.72 ( (fun int (fun int bool)) ) 22.67/22.72 ( (fun nat bool) ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.67/22.72 ( (fun (product_prod int int) bool) ) 22.67/22.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.67/22.72 ( (fun real bool) ) 22.67/22.72 ( quickcheck_code_int ) 22.67/22.72 ( code_code_numeral ) 22.67/22.72 ( (product_prod real real) ) 22.67/22.72 ( (filter real) ) 22.67/22.72 ( (product_prod nat nat) ) 22.67/22.72 ( (fun nat rat) ) 22.67/22.72 ( (fun int (fun int (fun int bool))) ) 22.67/22.72 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.67/22.72 ( (fun int real) ) 22.67/22.72 ) 22.67/22.72 (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)))))) ))) ))) ) 22.67/22.72 ( real ) 22.67/22.72 ( complex ) 22.67/22.72 ) 22.67/22.72 (instantiation (forall ((Xa $$unsorted) (Ya $$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) Xa) Ya)) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zEven)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Xa) zEven)))))) ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.67/22.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.67/22.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.67/22.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.67/22.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.67/22.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.67/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.70/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.70/22.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.70/22.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.70/22.72 ( y, v ) 22.70/22.72 ( y, w ) 22.70/22.72 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.72 ( sa, v ) 22.70/22.72 ( sa, w ) 22.70/22.72 ( x, v ) 22.70/22.72 ( x, w ) 22.70/22.72 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.72 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.72 ( r, v ) 22.70/22.72 ( r, w ) 22.70/22.72 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.70/22.73 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.70/22.73 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.70/22.73 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.70/22.73 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (fun int bool))) (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_2 _let_3 (zero_zero int)) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_2 _let_3 A_1) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_2 (hAPP int (fun int _let_2) zcong (hAPP int int (hAPP int _let_0 (times_times int) A_1) A_1)) _let_1) P_5))) (= _let_1 _let_4) (= _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) _let_1)))))))) ) 22.70/22.73 ( (one_one int), t ) 22.70/22.73 ( min, min ) 22.70/22.73 ( min, (zero_zero int) ) 22.70/22.73 ( (zero_zero int), pls ) 22.70/22.73 ( (zero_zero int), (one_one int) ) 22.70/22.73 ( (zero_zero int), min ) 22.70/22.73 ( (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))) ) 22.70/22.73 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (div_div nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) N)) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (one_one nat))) _let_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 N) _let_1))))))) ) 22.70/22.73 ( (zero_zero nat) ) 22.70/22.73 ( (one_one nat) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (real_1 nat))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP nat real _let_0 N)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) (hAPP nat real _let_0 (hAPP nat nat suc N))))) (= N (hAPP int nat nat_1 (hAPP real int (archim2085082626_floor real) X))))))) ) 22.70/22.73 ( (zero_zero nat), pi ) 22.70/22.73 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (zero_zero nat), skv_2 ) 22.70/22.73 ( (zero_zero nat), skv_9 ) 22.70/22.73 ( (zero_zero nat), skv_12 ) 22.70/22.73 ( (one_one nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((I_1 $$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)))) ) 22.70/22.73 ( pls ) 22.70/22.73 ( min ) 22.70/22.73 ( s ) 22.70/22.73 ( s1 ) 22.70/22.73 ( m ) 22.70/22.73 ( t ) 22.70/22.73 ( v ) 22.70/22.73 ( w ) 22.70/22.73 ( y ) 22.70/22.73 ( sa ) 22.70/22.73 ( x ) 22.70/22.73 ( r ) 22.70/22.73 ( m1 ) 22.70/22.73 ( skv_14 ) 22.70/22.73 ( skv_20 ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((I_1 $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (sgn_sgn int) I_1))) (let ((_let_2 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) I_1)))) (or (= (zero_zero int) (ti int I_1)) (and (or (not _let_2) (= _let_0 _let_1)) (or _let_2 (= (hAPP int int (uminus_uminus int) _let_0) _let_1))))))) ) 22.70/22.73 ( pls ) 22.70/22.73 ( (one_one int) ) 22.70/22.73 ( min ) 22.70/22.73 ( s ) 22.70/22.73 ( s1 ) 22.70/22.73 ( m ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( t ) 22.70/22.73 ( v ) 22.70/22.73 ( w ) 22.70/22.73 ( y ) 22.70/22.73 ( sa ) 22.70/22.73 ( x ) 22.70/22.73 ( r ) 22.70/22.73 ( m1 ) 22.70/22.73 ( skv_14 ) 22.70/22.73 ( skv_20 ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135013 $$unsorted) (BOUND_VARIABLE_135014 $$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_eq X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_135013)) (hAPP nat X_a _let_0 BOUND_VARIABLE_135014))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_135013) BOUND_VARIABLE_135014))))) ) 22.70/22.73 ( int, (zero_zero nat), (zero_zero nat) ) 22.70/22.73 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.73 ( int, (zero_zero nat), (one_one nat) ) 22.70/22.73 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135078 $$unsorted) (BOUND_VARIABLE_135079 $$unsorted) (BOUND_VARIABLE_135080 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_135078))) (or (not (linord893533164strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_135079) BOUND_VARIABLE_135080))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_135078))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_135079)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_135080))))))) ) 22.70/22.73 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135114 $$unsorted) (BOUND_VARIABLE_135115 $$unsorted) (BOUND_VARIABLE_135116 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_135115))) (or (not (ord X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_135116))) (not (= (ti X_a BOUND_VARIABLE_135116) (ti X_a BOUND_VARIABLE_135114))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_135114)))) ) 22.70/22.73 ( int, pls, (zero_zero int), pls ) 22.70/22.73 ( int, min, min, min ) 22.70/22.73 ( int, s, min, (zero_zero int) ) 22.70/22.73 ( int, s1, (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))) ) 22.70/22.73 ( int, m, 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))) ) 22.70/22.73 ( int, t, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ( int, v, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( int, w, (zero_zero int), min ) 22.70/22.73 ( int, y, 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))) ) 22.70/22.73 ( int, sa, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( int, x, 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))) ) 22.70/22.73 ( int, r, (zero_zero int), (one_one int) ) 22.70/22.73 ( int, m1, (one_one int), t ) 22.70/22.73 ( int, skv_14, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ( nat, n, (zero_zero nat), n ) 22.70/22.73 ( nat, tn, (zero_zero nat), tn ) 22.70/22.73 ( real, pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135140 $$unsorted) (BOUND_VARIABLE_135141 $$unsorted) (BOUND_VARIABLE_135142 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135140))) (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_135141) BOUND_VARIABLE_135142)) (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_135141)) (hAPP nat X_a _let_0 BOUND_VARIABLE_135142))))) ) 22.70/22.73 ( int, s, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, s1, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, v, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, w, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, y, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, x, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (one_one nat), (one_one nat) ) 22.70/22.73 ( int, skv_6, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, skv_7, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, skv_16, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, skv_23, (one_one nat), (one_one nat) ) 22.70/22.73 ( int, skv_24, (one_one nat), (one_one nat) ) 22.70/22.73 ( complex, ii, (one_one nat), (one_one nat) ) 22.70/22.73 ) 22.70/22.73 (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))))))) ) 22.70/22.73 ( (one_one int), t ) 22.70/22.73 ( min, min ) 22.70/22.73 ( min, (zero_zero int) ) 22.70/22.73 ( (zero_zero int), pls ) 22.70/22.73 ( (zero_zero int), (one_one int) ) 22.70/22.73 ( (zero_zero int), min ) 22.70/22.73 ( (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))) ) 22.70/22.73 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real ln X)))))) ) 22.70/22.73 ( (one_one real) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135199 $$unsorted)) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_135199) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_135199) (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_135199)))) ) 22.70/22.73 ( rat, (zero_zero rat) ) 22.70/22.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( 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))) ) 22.70/22.73 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( int, v ) 22.70/22.73 ( int, w ) 22.70/22.73 ( int, y ) 22.70/22.73 ( int, sa ) 22.70/22.73 ( int, x ) 22.70/22.73 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.70/22.73 ( int, r ) 22.70/22.73 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.73 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.73 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( int, skv_13 ) 22.70/22.73 ( int, skv_14 ) 22.70/22.73 ( int, skv_19 ) 22.70/22.73 ( int, skv_20 ) 22.70/22.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.73 ( real, (zero_zero real) ) 22.70/22.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( 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))))) ) 22.70/22.73 ( complex, ii ) 22.70/22.73 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.73 ( 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)) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_135218 $$unsorted) (BOUND_VARIABLE_135219 $$unsorted) (BOUND_VARIABLE_135220 $$unsorted)) (let ((_let_0 (fun X_b X_b))) (let ((_let_1 (plus_plus X_b))) (let ((_let_2 (hAPP X_b _let_0 (times_times X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_135218)))) (or (not (number X_b)) (not (semiring X_b)) (= (hAPP X_b X_b (hAPP X_b _let_0 _let_1 (hAPP X_b X_b _let_2 BOUND_VARIABLE_135219)) (hAPP X_b X_b _let_2 BOUND_VARIABLE_135220)) (hAPP X_b X_b _let_2 (hAPP X_b X_b (hAPP X_b _let_0 _let_1 BOUND_VARIABLE_135219) BOUND_VARIABLE_135220))))))) ) 22.70/22.73 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((N $$unsorted)) (or (= (zero_zero nat) N) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) coprime (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) N) (one_one nat))) N))) ) 22.70/22.73 ( (hAPP int nat nat_1 t) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less int) (zero_zero int)))) (let ((_let_2 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 (zero_zero int)) A_3))) (= (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int (fun int int) (div_div int) A_3) B_2))) (and (hBOOL (hAPP int bool _let_1 B_2)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B_2) A_3)))))))) ) 22.70/22.73 ( (one_one int), t ) 22.70/22.73 ( min, pls ) 22.70/22.73 ( min, min ) 22.70/22.73 ( (zero_zero int), pls ) 22.70/22.73 ( (zero_zero int), (one_one int) ) 22.70/22.73 ( (zero_zero int), min ) 22.70/22.73 ( (zero_zero int), s ) 22.70/22.73 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.73 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.73 ( (zero_zero int), skv_4 ) 22.70/22.73 ( (zero_zero int), skv_5 ) 22.70/22.73 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (bseq X_a))) (or (not (real_normed_vector X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 22.70/22.73 ( rat ) 22.70/22.73 ( int ) 22.70/22.73 ( (fun int int) ) 22.70/22.73 ( nat ) 22.70/22.73 ( bool ) 22.70/22.73 ( real ) 22.70/22.73 ( (fun real real) ) 22.70/22.73 ( (fun nat nat) ) 22.70/22.73 ( complex ) 22.70/22.73 ( (product_prod int int) ) 22.70/22.73 ( (fun bool bool) ) 22.70/22.73 ( (fun nat bool) ) 22.70/22.73 ( (fun nat (fun nat bool)) ) 22.70/22.73 ( (fun nat (product_prod int int)) ) 22.70/22.73 ( (product_prod real real) ) 22.70/22.73 ( (product_prod nat nat) ) 22.70/22.73 ( (fun (product_prod nat nat) bool) ) 22.70/22.73 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.70/22.73 ( (fun nat (product_prod nat nat)) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_135482 $$unsorted) (BOUND_VARIABLE_135483 $$unsorted) (BOUND_VARIABLE_135484 $$unsorted) (BOUND_VARIABLE_135485 $$unsorted) (BOUND_VARIABLE_135486 $$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_135485))) (or (not (topological_space X_b)) (not (metric_space X_a)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_135486))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_135485)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_1) BOUND_VARIABLE_135485)) BOUND_VARIABLE_135486))) (= (hAPP X_a X_b BOUND_VARIABLE_135483 X_1) (hAPP X_a X_b BOUND_VARIABLE_135484 X_1))) )) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_135484) BOUND_VARIABLE_135482) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_135483) BOUND_VARIABLE_135482) _let_5))))))))) ) 22.70/22.73 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (number_number_of real))) (let ((_let_3 (fun real real))) (let ((_let_4 (fun nat nat))) (let ((_let_5 (one_one real))) (let ((_let_6 (fun real bool))) (let ((_let_7 (ord_less real))) (let ((_let_8 (fun nat _let_3))) (let ((_let_9 (fun _let_0 _let_0))) (let ((_let_10 (combs nat real real))) (let ((_let_11 (hAPP (fun real _let_3) (fun _let_0 _let_8) (combb real _let_3 nat) (times_times real)))) (let ((_let_12 (fun _let_4 _let_0))) (let ((_let_13 (combb nat real nat))) (let ((_let_14 (fun nat _let_4))) (or (not (hBOOL (hAPP real bool (hAPP real _let_6 _let_7 (zero_zero real)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_6 _let_7 Xa) (hAPP int real _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_8 _let_9 _let_10 (hAPP _let_0 _let_8 _let_11 (hAPP _let_0 _let_0 (hAPP _let_8 _let_9 _let_10 (hAPP _let_0 _let_8 _let_11 (hAPP real _let_0 _let_1 (hAPP int real _let_2 min)))) (hAPP _let_0 _let_0 (hAPP _let_3 _let_9 (combb real real nat) (hAPP real _let_3 (inverse_divide real) _let_5)) (hAPP _let_4 _let_0 (hAPP _let_0 _let_12 _let_13 (real_1 nat)) (hAPP nat _let_4 (hAPP _let_14 _let_14 (combc nat nat nat) (plus_plus nat)) (one_one nat))))))) (hAPP _let_4 _let_0 (hAPP _let_0 _let_12 _let_13 (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_3 (minus_minus real) Xa) _let_5))) suc))) (hAPP real real ln Xa)))))))))))))))))) ) 22.70/22.73 ( pi ) 22.70/22.73 ( (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)))) ) 22.70/22.73 ( (one_one real) ) 22.70/22.73 ( (zero_zero real) ) 22.70/22.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (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))))) ) 22.70/22.73 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.70/22.73 ( (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)) ) 22.70/22.73 ( skv_2 ) 22.70/22.73 ( skv_9 ) 22.70/22.73 ( skv_12 ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP nat real (real_1 nat) A_1))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natfloor X)) A_1))) ) 22.70/22.73 ( (one_one nat), (one_one real) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (gcd_gcd int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N)) N) (hAPP int int (hAPP int _let_0 _let_1 M) N)))) ) 22.70/22.73 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.70/22.73 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.70/22.73 ( (hAPP nat int (hAPP 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) ) 22.70/22.73 ( (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) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.73 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.70/22.73 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.73 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.73 ) 22.70/22.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135728 $$unsorted) (BOUND_VARIABLE_135729 $$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_135729))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135729) BOUND_VARIABLE_135728))))) ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.70/22.73 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.70/22.73 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.70/22.73 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.70/22.73 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.70/22.74 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.70/22.74 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.70/22.74 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.70/22.74 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.70/22.74 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.70/22.74 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((D_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun int _let_0))) (let ((_let_6 (fun _let_1 bool))) (= (hAPP int _let_6 int_ge_less_than2 D_1) (hAPP _let_6 _let_6 (collect _let_1) (hAPP _let_5 _let_6 (product_prod_case int int bool) (hAPP _let_5 _let_5 (hAPP _let_4 (fun _let_5 _let_5) (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_eq int) D_1)))) (ord_less int)))))))))))) ) 22.70/22.74 ( (one_one int) ) 22.70/22.74 ( min ) 22.70/22.74 ( (zero_zero int) ) 22.70/22.74 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.70/22.74 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.70/22.74 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.70/22.74 ( (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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X $$unsorted) (Y $$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 X)) (hAPP real real cos Y))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin X)) (hAPP real real sin Y))) (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y))))) ) 22.70/22.74 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135782 $$unsorted) (BOUND_VARIABLE_135783 $$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_135782) BOUND_VARIABLE_135783))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_135782)) BOUND_VARIABLE_135783))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_135782)) BOUND_VARIABLE_135783))))) ) 22.70/22.74 ( int, pls, pls ) 22.70/22.74 ( int, pls, (one_one int) ) 22.70/22.74 ( int, pls, min ) 22.70/22.74 ( int, pls, s ) 22.70/22.74 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, pls, skv_4 ) 22.70/22.74 ( int, pls, skv_5 ) 22.70/22.74 ( int, (one_one int), pls ) 22.70/22.74 ( int, (one_one int), min ) 22.70/22.74 ( int, (one_one int), t ) 22.70/22.74 ( int, min, pls ) 22.70/22.74 ( int, min, min ) 22.70/22.74 ( int, (zero_zero int), pls ) 22.70/22.74 ( int, (zero_zero int), (one_one int) ) 22.70/22.74 ( int, (zero_zero int), min ) 22.70/22.74 ( int, (zero_zero int), s ) 22.70/22.74 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, (zero_zero int), skv_4 ) 22.70/22.74 ( int, (zero_zero int), skv_5 ) 22.70/22.74 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.74 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( real, (zero_zero real), pi ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( real, (zero_zero real), skv_10 ) 22.70/22.74 ( real, (zero_zero real), skv_11 ) 22.70/22.74 ( real, (zero_zero real), skv_15 ) 22.70/22.74 ( real, (zero_zero real), skv_18 ) 22.70/22.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.74 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (= A_3 B_2) (= (hAPP rat _let_0 quotient_of B_2) (hAPP rat _let_0 quotient_of A_3)))) ) 22.70/22.74 ( (one_one rat), (zero_zero rat) ) 22.70/22.74 ( (zero_zero rat), (one_one rat) ) 22.70/22.74 ( (zero_zero rat), (zero_zero rat) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135824 $$unsorted) (BOUND_VARIABLE_135825 $$unsorted) (BOUND_VARIABLE_135826 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_135826))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_135826))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_135824)) (hAPP nat X_a _let_2 BOUND_VARIABLE_135825)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_135824) BOUND_VARIABLE_135825)))))) ) 22.70/22.74 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135849 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_135849) BOUND_VARIABLE_135849))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$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)))) ) 22.70/22.74 ( rat ) 22.70/22.74 ( int ) 22.70/22.74 ( nat ) 22.70/22.74 ( bool ) 22.70/22.74 ( real ) 22.70/22.74 ( (filter nat) ) 22.70/22.74 ( (fun int bool) ) 22.70/22.74 ( (product_prod int int) ) 22.70/22.74 ( (fun nat bool) ) 22.70/22.74 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.70/22.74 ( quickcheck_code_int ) 22.70/22.74 ( code_code_numeral ) 22.70/22.74 ( (product_prod real real) ) 22.70/22.74 ( (filter real) ) 22.70/22.74 ( (product_prod nat nat) ) 22.70/22.74 ( (fun nat rat) ) 22.70/22.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_0 (product_prod nat nat))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) nat_gcd_rel) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (product_Pair nat nat) A0) A1)))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_2 (fun nat bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP (fun _let_0 _let_1) _let_1 (accp _let_0) nat_gcd_rel) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (product_Pair nat nat) X_1) Y_1)))) (and (not (= (zero_zero nat) Y_1)) (not (hBOOL (hAPP nat bool (hAPP nat _let_2 P_1 Y_1) (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X_1) Y_1))))) (hBOOL (hAPP nat bool (hAPP nat _let_2 P_1 X_1) Y_1)))) )) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) P_1 A0) A1))))) ) 22.70/22.74 ( (ord_less nat), (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( (ord_less nat), (zero_zero nat), n ) 22.70/22.74 ( (ord_less nat), (zero_zero nat), tn ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$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)))) ) 22.70/22.74 ( rat ) 22.70/22.74 ( int ) 22.70/22.74 ( nat ) 22.70/22.74 ( real ) 22.70/22.74 ( complex ) 22.70/22.74 ( (fun real bool) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_135897 $$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_135897) (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_135897))) ) 22.70/22.74 ( rat, (zero_zero rat) ) 22.70/22.74 ( int, (one_one int) ) 22.70/22.74 ( int, min ) 22.70/22.74 ( int, (zero_zero int) ) 22.70/22.74 ( int, s ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, t ) 22.70/22.74 ( int, m1 ) 22.70/22.74 ( int, skv_4 ) 22.70/22.74 ( int, skv_5 ) 22.70/22.74 ( nat, (zero_zero nat) ) 22.70/22.74 ( real, pi ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( real, (one_one real) ) 22.70/22.74 ( real, (zero_zero real) ) 22.70/22.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( 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))))) ) 22.70/22.74 ( 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)) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X $$unsorted) (Y $$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) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real sqrt X)) (hAPP real real sqrt Y)))))) ) 22.70/22.74 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136026 $$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_136026) BOUND_VARIABLE_136026)) _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_136026) _let_2)) (hAPP X_a X_a (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_136026) _let_2)))))))) ) 22.70/22.74 ( int, (one_one int) ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( 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) ) 22.70/22.74 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.70/22.74 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.70/22.74 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( nat, (one_one nat) ) 22.70/22.74 ( complex, ii ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136063 $$unsorted) (BOUND_VARIABLE_136064 $$unsorted) (BOUND_VARIABLE_136065 $$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_136064))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136065) sequentially))) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136063) sequentially))) (= (ti X_a BOUND_VARIABLE_136063) (ti X_a BOUND_VARIABLE_136065))))) ) 22.70/22.74 ( real, (zero_zero real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (Y_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (= (ti _let_0 Y_2) (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_2))) ) 22.70/22.74 ( int, zOdd ) 22.70/22.74 ( int, zprime ) 22.70/22.74 ( int, zEven ) 22.70/22.74 ( int, nat_neg ) 22.70/22.74 ( int, nat_is_nat ) 22.70/22.74 ( int, (even_odd_even int) ) 22.70/22.74 ( int, twoSqu1091635170sum2sq ) 22.70/22.74 ( nat, (even_odd_even nat) ) 22.70/22.74 ( nat, prime ) 22.70/22.74 ( bool, fNot ) 22.70/22.74 ( (fun int bool), nat_nat_set ) 22.70/22.74 ( (product_prod int int), frac_1 ) 22.70/22.74 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), ratrel ) 22.70/22.74 ( (product_prod nat nat), pred_nat ) 22.70/22.74 ( (fun nat rat), vanishes ) 22.70/22.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_less ) 22.70/22.74 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), pair_leq ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136099 $$unsorted) (BOUND_VARIABLE_136100 $$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_136100))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136099) _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_136100) BOUND_VARIABLE_136099)) _let_2)))))) ) 22.70/22.74 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.70/22.74 ( 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))) ) 22.70/22.74 ( int, v, y ) 22.70/22.74 ( int, v, sa ) 22.70/22.74 ( int, v, x ) 22.70/22.74 ( int, v, r ) 22.70/22.74 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.74 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.74 ( int, w, y ) 22.70/22.74 ( int, w, sa ) 22.70/22.74 ( int, w, x ) 22.70/22.74 ( int, w, r ) 22.70/22.74 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.74 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.74 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.70/22.74 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.74 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( int, skv_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))) ) 22.70/22.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( 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))))) ) 22.70/22.74 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( complex, ii, ii ) 22.70/22.74 ( 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)) ) 22.70/22.74 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ) 22.70/22.74 (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)))) ) 22.70/22.74 ( rat ) 22.70/22.74 ( int ) 22.70/22.74 ( (fun int int) ) 22.70/22.74 ( nat ) 22.70/22.74 ( bool ) 22.70/22.74 ( real ) 22.70/22.74 ( (fun nat real) ) 22.70/22.74 ( (fun real real) ) 22.70/22.74 ( complex ) 22.70/22.74 ( (fun int bool) ) 22.70/22.74 ( (product_prod int int) ) 22.70/22.74 ( (fun (product_prod int int) int) ) 22.70/22.74 ( (fun int (fun int bool)) ) 22.70/22.74 ( (fun nat bool) ) 22.70/22.74 ( (fun (product_prod int int) bool) ) 22.70/22.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.70/22.74 ( (fun real bool) ) 22.70/22.74 ( quickcheck_code_int ) 22.70/22.74 ( code_code_numeral ) 22.70/22.74 ( (fun int (fun int (fun int bool))) ) 22.70/22.74 ( (fun int real) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ordere142940540dd_abs X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 22.70/22.74 ( rat ) 22.70/22.74 ( int ) 22.70/22.74 ( nat ) 22.70/22.74 ( real ) 22.70/22.74 ( complex ) 22.70/22.74 ( quickcheck_code_int ) 22.70/22.74 ( code_code_numeral ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136192 $$unsorted) (BOUND_VARIABLE_136193 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (linorder X_a)) (= (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136193) BOUND_VARIABLE_136192)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136192) BOUND_VARIABLE_136193))) (not (= (ti X_a BOUND_VARIABLE_136192) (ti X_a BOUND_VARIABLE_136193))))))) ) 22.70/22.74 ( int, pls, (zero_zero int) ) 22.70/22.74 ( int, (one_one int), (zero_zero int) ) 22.70/22.74 ( int, (one_one int), t ) 22.70/22.74 ( int, min, min ) 22.70/22.74 ( int, min, (zero_zero int) ) 22.70/22.74 ( int, (zero_zero int), pls ) 22.70/22.74 ( int, (zero_zero int), (one_one int) ) 22.70/22.74 ( int, (zero_zero int), min ) 22.70/22.74 ( 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))) ) 22.70/22.74 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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))) ) 22.70/22.74 ( 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))), (zero_zero int) ) 22.70/22.74 ( 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))), s ) 22.70/22.74 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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))), t ) 22.70/22.74 ( 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))), skv_4 ) 22.70/22.74 ( 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))), skv_5 ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.70/22.74 ( int, t, (one_one int) ) 22.70/22.74 ( 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))) ) 22.70/22.74 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.74 ( 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))) ) 22.70/22.74 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.74 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( nat, (zero_zero nat), n ) 22.70/22.74 ( nat, (zero_zero nat), tn ) 22.70/22.74 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.70/22.74 ( nat, n, (zero_zero nat) ) 22.70/22.74 ( nat, tn, (zero_zero nat) ) 22.70/22.74 ( real, pi, (zero_zero real) ) 22.70/22.74 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( 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)) ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( 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)))), (zero_zero real) ) 22.70/22.74 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( real, (zero_zero real), pi ) 22.70/22.74 ( 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)))) ) 22.70/22.74 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( 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))))) ) 22.70/22.74 ( real, (zero_zero real), skv_2 ) 22.70/22.74 ( real, (zero_zero real), skv_9 ) 22.70/22.74 ( real, (zero_zero real), skv_12 ) 22.70/22.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.70/22.74 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.74 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.70/22.74 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.74 ( 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) ) 22.70/22.74 ( 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 ) 22.70/22.74 ( real, skv_2, (zero_zero real) ) 22.70/22.74 ( real, skv_9, (zero_zero real) ) 22.70/22.74 ( real, skv_12, (zero_zero real) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real (hAPP real (fun real real) (inverse_divide real) X) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= X (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_0) _let_0))) ) 22.70/22.74 ( pi ) 22.70/22.74 ( (one_one real) ) 22.70/22.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) X))) (not (= _let_0 (hAPP real real sqrt X))))) ) 22.70/22.74 ( pi ) 22.70/22.74 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.74 ( (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)))) ) 22.70/22.74 ( (one_one real) ) 22.70/22.74 ( (zero_zero real) ) 22.70/22.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.74 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.74 ( skv_2 ) 22.70/22.74 ( skv_9 ) 22.70/22.74 ( skv_12 ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (gcd_gcd nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N) (hAPP nat nat (hAPP nat _let_0 _let_1 M) N))))) ) 22.70/22.74 ( (one_one nat), (hAPP int nat nat_1 t) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136239 $$unsorted) (BOUND_VARIABLE_136240 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (minus_minus X_a))) (let ((_let_4 (zero_zero X_a))) (let ((_let_5 (hAPP X_a X_a _let_2 BOUND_VARIABLE_136240))) (let ((_let_6 (hAPP X_a X_a _let_2 BOUND_VARIABLE_136239))) (or (not (division_ring X_a)) (= _let_4 (ti X_a BOUND_VARIABLE_136240)) (= _let_4 (ti X_a BOUND_VARIABLE_136239)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_3 _let_5) _let_6) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_5) (hAPP X_a X_a (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_136239) BOUND_VARIABLE_136240))) _let_6)))))))))) ) 22.70/22.74 ( 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) ) 22.70/22.74 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.70/22.74 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.70/22.74 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.70/22.74 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.74 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.74 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.70/22.74 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.70/22.74 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.70/22.74 ) 22.70/22.74 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int int (number_number_of int) min))) (= (hAPP int _let_0 (hAPP int _let_1 (product_Pair int int) _let_2) (hAPP int int (hAPP int (fun int int) (minus_minus int) B) (one_one int))) (hAPP int _let_0 (hAPP int _let_1 negDivAlg _let_2) B))))) ) 22.70/22.74 ( (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)))) ) 22.70/22.74 ( y ) 22.70/22.74 ( x ) 22.70/22.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.70/22.74 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.70/22.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.70/22.74 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.70/22.74 ( (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))) m1))) ) 22.70/22.75 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.70/22.75 ) 22.70/22.75 (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 $$unsorted) (D_2 $$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 (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd C_4) D_2))) (not (= (ti int B) (hAPP int int _let_1 D_2))) (not (= (ti int A_1) (hAPP int int _let_1 C_4)))))) )))) ) 22.70/22.75 ( pls, pls ) 22.70/22.75 ( min, min ) 22.70/22.75 ( s, s ) 22.70/22.75 ( s1, s1 ) 22.70/22.75 ( m, m ) 22.70/22.75 ( t, t ) 22.70/22.75 ( v, v ) 22.70/22.75 ( w, w ) 22.70/22.75 ( y, y ) 22.70/22.75 ( sa, sa ) 22.70/22.75 ( x, x ) 22.70/22.75 ( r, r ) 22.70/22.75 ( m1, m1 ) 22.70/22.75 ( skv_14, skv_14 ) 22.70/22.75 ( skv_20, skv_20 ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136300 $$unsorted) (BOUND_VARIABLE_136301 $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power 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_1) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_136300) _let_0)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_136301) _let_0)))) (or (not (= _let_1 (ti X_a BOUND_VARIABLE_136301))) (not (= _let_1 (ti X_a BOUND_VARIABLE_136300)))))))))) ) 22.70/22.75 ( int, v, w ) 22.70/22.75 ( int, x, y ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.70/22.75 ( int, skv_6, skv_7 ) 22.70/22.75 ( int, skv_23, skv_24 ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fEx X_a))) (= _let_0 (ti (fun (fun X_a bool) bool) _let_0))) ) 22.70/22.75 ( int ) 22.70/22.75 ( nat ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (monoseq X_a))) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 22.70/22.75 ( rat ) 22.70/22.75 ( int ) 22.70/22.75 ( (fun int int) ) 22.70/22.75 ( nat ) 22.70/22.75 ( bool ) 22.70/22.75 ( real ) 22.70/22.75 ( (fun real real) ) 22.70/22.75 ( (fun nat nat) ) 22.70/22.75 ( complex ) 22.70/22.75 ( (product_prod int int) ) 22.70/22.75 ( (fun bool bool) ) 22.70/22.75 ( (fun nat bool) ) 22.70/22.75 ( (fun nat (fun nat bool)) ) 22.70/22.75 ( quickcheck_code_int ) 22.70/22.75 ( code_code_numeral ) 22.70/22.75 ( (fun nat (product_prod int int)) ) 22.70/22.75 ( (product_prod real real) ) 22.70/22.75 ( (product_prod nat nat) ) 22.70/22.75 ( (fun (product_prod nat nat) bool) ) 22.70/22.75 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.70/22.75 ( (fun nat (product_prod nat nat)) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136336 $$unsorted) (BOUND_VARIABLE_136337 $$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_136336))) (or (not (linordered_field X_a)) (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_136337))) (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_136336) BOUND_VARIABLE_136337)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2))))))))) ) 22.70/22.75 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.70/22.75 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.70/22.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.75 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.70/22.75 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.70/22.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( nat, (one_one nat), (one_one nat) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X)) (hAPP real real _let_2 Y))))))) ) 22.70/22.75 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136428 $$unsorted) (BOUND_VARIABLE_136429 $$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_136428) BOUND_VARIABLE_136429)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_136428)) BOUND_VARIABLE_136429)))))) ) 22.70/22.75 ( 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))), (hAPP 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)) ) 22.70/22.75 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136545 $$unsorted) (BOUND_VARIABLE_136546 $$unsorted) (BOUND_VARIABLE_136547 $$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_136546) BOUND_VARIABLE_136547))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136547) BOUND_VARIABLE_136545))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136546) BOUND_VARIABLE_136545))))) ) 22.70/22.75 ( int, min, min, min ) 22.70/22.75 ( int, (zero_zero int), (zero_zero int), min ) 22.70/22.75 ( 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))), (one_one int), t ) 22.70/22.75 ( 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))), (zero_zero int), pls ) 22.70/22.75 ( 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))), (zero_zero int), s ) 22.70/22.75 ( 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))), (zero_zero int), skv_4 ) 22.70/22.75 ( 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))), (zero_zero int), skv_5 ) 22.70/22.75 ( 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))), (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), min, pls ) 22.70/22.75 ( int, t, (zero_zero int), (one_one int) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( real, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.75 ( 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 ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((Ya $$unsorted) (Xa $$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 Xa))) (not (hBOOL (hAPP int bool _let_1 Ya))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) (hAPP int nat nat_1 Xa)) (hAPP int nat nat_1 Ya))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Xa) Ya)))))) ) 22.70/22.75 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136600 $$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) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_136600)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP int int bit1 pls)) BOUND_VARIABLE_136600))))) ) 22.70/22.75 ( int, pls ) 22.70/22.75 ( nat, (hAPP int int bit1 pls) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (= (ti X_a A_1) (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)))) ) 22.70/22.75 ( int, int, (one_one int), (one_one int) ) 22.70/22.75 ( int, int, (zero_zero int), (one_one int) ) 22.70/22.75 ( int, int, s, (one_one int) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136652 $$unsorted) (BOUND_VARIABLE_136653 $$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_136652) BOUND_VARIABLE_136653)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_136652)) BOUND_VARIABLE_136653)))))) ) 22.70/22.75 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( 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))))))))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 A_3))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool P_1 X_1))) (= (ti X_a A_3) (ti X_a X_1))) )) (= (ti X_a A_3) (hAPP (fun X_a bool) X_a (hilbert_Eps X_a) P_1))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 22.70/22.75 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) min), min ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 22.70/22.75 ( int, nat_neg, (one_one int) ) 22.70/22.75 ( int, nat_neg, (zero_zero int) ) 22.70/22.75 ( int, nat_neg, (hAPP int int (number_number_of int) min) ) 22.70/22.75 ( int, nat_is_nat, (one_one int) ) 22.70/22.75 ( int, nat_is_nat, (zero_zero int) ) 22.70/22.75 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 22.70/22.75 ( int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 22.70/22.75 ( int, (even_odd_even int), (one_one int) ) 22.70/22.75 ( int, (even_odd_even int), (zero_zero int) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) pls), min ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 22.70/22.75 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( 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) (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)) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.75 ( int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( nat, (even_odd_even nat), (zero_zero nat) ) 22.70/22.75 ( nat, (even_odd_even nat), (one_one nat) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 22.70/22.75 ( nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 22.70/22.75 ( nat, prime, (zero_zero nat) ) 22.70/22.75 ( nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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) ) 22.70/22.75 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 22.70/22.75 ( 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 ) 22.70/22.75 ( 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 ) 22.70/22.75 ( 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) ) 22.70/22.75 ( real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 22.70/22.75 ( (filter nat), (trivial_limit nat), sequentially ) 22.70/22.75 ( (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)) ) 22.70/22.75 ( (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 22.70/22.75 ( (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.70/22.75 ( (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) ) 22.70/22.75 ( (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))))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) (hAPP nat nat suc N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat suc M)) N)))) ) 22.70/22.75 ( (zero_zero nat), (one_one nat) ) 22.70/22.75 ( (one_one nat), (zero_zero nat) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136695 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_136695) pls)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_136695)) (zero_zero X_a))))) ) 22.70/22.75 ( int, pls ) 22.70/22.75 ( int, (hAPP int int bit1 pls) ) 22.70/22.75 ( int, min ) 22.70/22.75 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.75 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.75 ( nat, pls ) 22.70/22.75 ( nat, (hAPP int int bit1 pls) ) 22.70/22.75 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.75 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.75 ( real, min ) 22.70/22.75 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.75 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.75 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.75 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 22.70/22.75 ( complex, min ) 22.70/22.75 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.75 ( quickcheck_code_int, pls ) 22.70/22.75 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.70/22.75 ( quickcheck_code_int, (one_one int) ) 22.70/22.75 ( code_code_numeral, pls ) 22.70/22.75 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136714 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (comm_ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP X_a X_a _let_0 (one_one X_a))) BOUND_VARIABLE_136714) (hAPP X_a X_a _let_0 BOUND_VARIABLE_136714)))) ) 22.70/22.75 ( int, pls ) 22.70/22.75 ( int, (one_one int) ) 22.70/22.75 ( int, min ) 22.70/22.75 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( real, (one_one real) ) 22.70/22.75 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.70/22.75 ( complex, ii ) 22.70/22.75 ( complex, (one_one complex) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136748 $$unsorted)) (or (not (ab_group_add X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_136748)) BOUND_VARIABLE_136748))) ) 22.70/22.75 ( int, pls ) 22.70/22.75 ( int, (one_one int) ) 22.70/22.75 ( int, min ) 22.70/22.75 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( real, (one_one real) ) 22.70/22.75 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.70/22.75 ( complex, ii ) 22.70/22.75 ( complex, (one_one complex) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136769 $$unsorted) (BOUND_VARIABLE_136770 $$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_136770) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_136769) _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_136770) BOUND_VARIABLE_136769))))))) ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( 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))) ) 22.70/22.75 ( 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)))) ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.70/22.75 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.70/22.75 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.70/22.75 ( 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) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 Xa) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (deriv real) arccos) Xa) (hAPP real real (inverse_inverse real) (hAPP real real (uminus_uminus real) (hAPP real real sqrt (hAPP real real (hAPP real _let_0 (minus_minus real) _let_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) Xa) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))))) ) 22.70/22.75 ( (hAPP int real (number_number_of real) min) ) 22.70/22.75 ( pi ) 22.70/22.75 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( (one_one real) ) 22.70/22.75 ( (zero_zero real) ) 22.70/22.75 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.70/22.75 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.75 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136846 $$unsorted) (BOUND_VARIABLE_136847 $$unsorted) (BOUND_VARIABLE_136848 $$unsorted) (BOUND_VARIABLE_136849 $$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_136849)) (= _let_0 (ti X_a BOUND_VARIABLE_136848)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_136849) BOUND_VARIABLE_136847))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_136848) BOUND_VARIABLE_136846))) (= (= (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_136847) BOUND_VARIABLE_136848) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_136849) BOUND_VARIABLE_136846)) (= (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_136846) BOUND_VARIABLE_136848) (hAPP X_a X_a (hAPP X_a _let_3 _let_5 BOUND_VARIABLE_136847) BOUND_VARIABLE_136849)))))))))) ) 22.70/22.75 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.75 ( int, (hAPP 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)), (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_136890 $$unsorted)) (or (not (ordere142940540dd_abs 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 (abs_abs X_a) BOUND_VARIABLE_136890)))) ) 22.70/22.75 ( int, v ) 22.70/22.75 ( int, w ) 22.70/22.75 ( int, skv_14 ) 22.70/22.75 ( int, skv_20 ) 22.70/22.75 ) 22.70/22.75 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (ord_gr676655987ssThan X_a))) (or (not (ordered_ab_group_add X_a)) (= _let_0 (ti (fun X_a (fun X_a (fun X_a bool))) _let_0)))) ) 22.70/22.75 ( rat ) 22.70/22.75 ( int ) 22.70/22.75 ( nat ) 22.70/22.75 ( bool ) 22.70/22.75 ( real ) 22.70/22.75 ( (filter nat) ) 22.70/22.75 ( (fun int bool) ) 22.70/22.75 ( (product_prod int int) ) 22.70/22.75 ( (fun nat bool) ) 22.70/22.75 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.70/22.75 ( (product_prod real real) ) 22.70/22.75 ( (filter real) ) 22.70/22.75 ( (product_prod nat nat) ) 22.70/22.75 ( (fun nat rat) ) 22.70/22.75 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.70/22.75 ) 22.70/22.76 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (not (hBOOL (hAPP int bool nat_is_nat Y))) (hBOOL (hAPP int bool nat_is_nat (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y)))) ) 22.70/22.76 ( (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)))) ) 22.70/22.76 ( (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) ) 22.70/22.76 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.70/22.76 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.70/22.76 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.70/22.76 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.70/22.76 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.70/22.76 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (product_Pair int int))) (let ((_let_5 (hAPP int _let_0 _let_1 A_1))) (let ((_let_6 (hAPP int _let_0 _let_1 B))) (= (hAPP _let_2 int twoSqu1094008024sum2sq (hAPP int _let_2 (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_5 P_5)) (hAPP int int _let_6 Q_3))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_5 Q_3)) (hAPP int int _let_6 P_5)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP _let_2 int twoSqu1094008024sum2sq (hAPP int _let_2 (hAPP int _let_3 _let_4 A_1) B))) (hAPP _let_2 int twoSqu1094008024sum2sq (hAPP int _let_2 (hAPP int _let_3 _let_4 P_5) Q_3))))))))))) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.70/22.76 ( x, y, v, w ) 22.70/22.76 ( r, sa, v, w ) 22.70/22.76 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v, w ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) U) (hAPP nat nat suc L)) (hAPP _let_0 nat (finite_card nat) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_gr676655987ssThan nat) L) U)))) ) 22.70/22.76 ( (zero_zero nat), (hAPP int nat nat_1 t) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (product_prod X_a X_b))) (let ((_let_2 (fun _let_1 bool))) (let ((_let_3 (fun X_b bool))) (let ((_let_4 (fun X_a _let_3))) (let ((_let_5 (fun _let_3 _let_3))) (let ((_let_6 (fun X_a _let_5))) (let ((_let_7 (fun X_a _let_0))) (let ((_let_8 (fun X_a bool))) (= (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) Xa) Ya) (hAPP _let_2 _let_1 (the _let_1) (hAPP _let_4 _let_2 (product_prod_case X_a X_b bool) (hAPP _let_3 _let_4 (hAPP _let_6 (fun _let_3 _let_4) (combc X_a _let_3 _let_3) (hAPP _let_7 _let_6 (hAPP (fun _let_0 _let_5) (fun _let_7 _let_6) (combb _let_0 _let_5 X_a) (combb bool bool X_b)) (hAPP _let_8 _let_7 (hAPP (fun bool _let_0) (fun _let_8 _let_7) (combb bool _let_0 X_a) fconj) (hAPP X_a _let_8 (fequal X_a) Xa)))) (hAPP X_b _let_3 (fequal X_b) Ya)))))))))))))) ) 22.70/22.76 ( int, int, (one_one int), (one_one int) ) 22.70/22.76 ( int, int, (zero_zero int), (one_one int) ) 22.70/22.76 ( int, int, s, (one_one int) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((K_4 $$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)))))) ) 22.70/22.76 ( 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))) ) 22.70/22.76 ( (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)))) ) 22.70/22.76 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_10 ) 22.70/22.76 ( (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) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137011 $$unsorted) (BOUND_VARIABLE_137012 $$unsorted) (BOUND_VARIABLE_137013 $$unsorted) (BOUND_VARIABLE_137014 $$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_137011) BOUND_VARIABLE_137012) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137013) BOUND_VARIABLE_137014))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_137013) BOUND_VARIABLE_137014)) (hBOOL (hAPP X_a bool (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_137011) BOUND_VARIABLE_137012)))))))) ) 22.70/22.76 ( 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), (hAPP nat int (hAPP 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) ) 22.70/22.76 ( 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), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.70/22.76 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP nat int (hAPP 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) ) 22.70/22.76 ( int, x, (let ((_let_0 (fun int int))) (hAPP 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pls)))))) ) 22.70/22.76 ( nat, (hAPP int nat nat_1 t), (one_one nat), (hAPP int nat nat_1 t), (one_one nat) ) 22.70/22.76 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.70/22.76 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral), (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137041 $$unsorted)) (or (not (division_ring X_a)) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_137041) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) BOUND_VARIABLE_137041))) ) 22.70/22.76 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.76 ( real, (zero_zero real) ) 22.70/22.76 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 22.70/22.76 ( complex, ii ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$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))))) ) 22.70/22.76 ( rat ) 22.70/22.76 ( int ) 22.70/22.76 ( nat ) 22.70/22.76 ( real ) 22.70/22.76 ( complex ) 22.70/22.76 ( quickcheck_code_int ) 22.70/22.76 ( code_code_numeral ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((N $$unsorted) (P_5 $$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)) (= (one_one int) (hAPP int int (hAPP int (fun int int) legacy_zgcd N) P_5))) ) 22.70/22.76 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.76 ( (hAPP 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 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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) ) 22.70/22.76 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.70/22.76 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.70/22.76 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.70/22.76 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.76 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.70/22.76 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.70/22.76 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) P_5))) ) 22.70/22.76 ( (zero_zero nat) ) 22.70/22.76 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.76 ( (hAPP nat nat suc (zero_zero nat)) ) 22.70/22.76 ( n ) 22.70/22.76 ( tn ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137106 $$unsorted)) (or (not (real_vector X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_137106) (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP int real (number_number_of real) min)) BOUND_VARIABLE_137106))) ) 22.70/22.76 ( int, pls ) 22.70/22.76 ( int, (one_one int) ) 22.70/22.76 ( int, min ) 22.70/22.76 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (one_one real) ) 22.70/22.76 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.70/22.76 ( complex, ii ) 22.70/22.76 ( complex, (one_one complex) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$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)))) ) 22.70/22.76 ( rat ) 22.70/22.76 ( int ) 22.70/22.76 ( (fun int int) ) 22.70/22.76 ( nat ) 22.70/22.76 ( bool ) 22.70/22.76 ( real ) 22.70/22.76 ( (fun nat real) ) 22.70/22.76 ( (fun real real) ) 22.70/22.76 ( (fun nat nat) ) 22.70/22.76 ( (fun int rat) ) 22.70/22.76 ( complex ) 22.70/22.76 ( (fun int bool) ) 22.70/22.76 ( (product_prod int int) ) 22.70/22.76 ( (fun (product_prod int int) int) ) 22.70/22.76 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.70/22.76 ( (fun nat int) ) 22.70/22.76 ( (fun bool bool) ) 22.70/22.76 ( (fun int (fun bool bool)) ) 22.70/22.76 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.70/22.76 ( (fun int (fun int bool)) ) 22.70/22.76 ( (fun nat bool) ) 22.70/22.76 ( (fun (product_prod int int) bool) ) 22.70/22.76 ( (fun int (fun (product_prod int int) bool)) ) 22.70/22.76 ( quickcheck_code_int ) 22.70/22.76 ( (fun (fun int bool) bool) ) 22.70/22.76 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.70/22.76 ( (product_prod int (product_prod int int)) ) 22.70/22.76 ( (fun int (product_prod int (product_prod int int))) ) 22.70/22.76 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 22.70/22.76 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.70/22.76 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.70/22.76 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.70/22.76 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.70/22.76 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.70/22.76 ( (fun nat (fun bool bool)) ) 22.70/22.76 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.70/22.76 ( (fun int (product_prod int int)) ) 22.70/22.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.70/22.76 ( (fun int (fun (fun int bool) bool)) ) 22.70/22.76 ( (fun (fun int int) (fun int bool)) ) 22.70/22.76 ( (list int) ) 22.70/22.76 ( (fun int (fun int (fun int bool))) ) 22.70/22.76 ( (fun int real) ) 22.70/22.76 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137155 $$unsorted) (BOUND_VARIABLE_137156 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_137155)) BOUND_VARIABLE_137156)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_137155) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_137156))))) ) 22.70/22.76 ( real, (zero_zero int), pi ) 22.70/22.76 ( real, (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (zero_zero int), skv_10 ) 22.70/22.76 ( real, (zero_zero int), skv_11 ) 22.70/22.76 ( real, (zero_zero int), skv_15 ) 22.70/22.76 ( real, (zero_zero int), skv_18 ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137184 $$unsorted) (BOUND_VARIABLE_137185 $$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_137184))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_137185)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_137185)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_137185)))))) ) 22.70/22.76 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.76 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.76 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.76 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.76 ( 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))))))))) ) 22.70/22.76 ( 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))) ) 22.70/22.76 ( 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))) ) 22.70/22.76 ( 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))) ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_137295 $$unsorted) (BOUND_VARIABLE_137296 $$unsorted) (BOUND_VARIABLE_137297 $$unsorted) (BOUND_VARIABLE_137298 $$unsorted) (BOUND_VARIABLE_137299 $$unsorted) (BOUND_VARIABLE_137300 $$unsorted)) (let ((_let_0 (filter X_b))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_b X_c))) (let ((_let_3 (filter X_a))) (let ((_let_4 (fun _let_3 bool))) (let ((_let_5 (fun X_a X_c))) (let ((_let_6 (fun X_a X_b))) (let ((_let_7 (hAPP X_a _let_3 (at X_a) BOUND_VARIABLE_137299))) (or (not (real_normed_vector X_a)) (not (topological_space X_b)) (not (topological_space X_c)) (not (hBOOL (hAPP _let_3 bool (hAPP X_b _let_4 (hAPP _let_6 (fun X_b _let_4) (tendsto X_a X_b) BOUND_VARIABLE_137297) BOUND_VARIABLE_137298) _let_7))) (not (hBOOL (hAPP _let_0 bool (hAPP X_c _let_1 (hAPP _let_2 (fun X_c _let_1) (tendsto X_b X_c) BOUND_VARIABLE_137295) BOUND_VARIABLE_137296) (hAPP X_b _let_0 (at X_b) BOUND_VARIABLE_137298)))) (hBOOL (hAPP _let_3 bool (hAPP X_c _let_4 (hAPP _let_5 (fun X_c _let_4) (tendsto X_a X_c) (hAPP _let_6 _let_5 (hAPP _let_2 (fun _let_6 _let_5) (combb X_b X_c X_a) BOUND_VARIABLE_137295) BOUND_VARIABLE_137297)) BOUND_VARIABLE_137296) _let_7)) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_137299)) (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_1) BOUND_VARIABLE_137299))) BOUND_VARIABLE_137300))) (not (= (hAPP X_a X_b BOUND_VARIABLE_137297 X_1) (ti X_b BOUND_VARIABLE_137298)))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_137300)))))))))))) ) 22.70/22.76 ( 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)))), pi ) 22.70/22.76 ) 22.70/22.76 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (linord1117847801e_zero X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.76 ( rat ) 22.70/22.76 ( int ) 22.70/22.76 ( (fun int int) ) 22.70/22.76 ( nat ) 22.70/22.76 ( bool ) 22.70/22.76 ( real ) 22.70/22.76 ( (fun nat real) ) 22.70/22.76 ( (fun real real) ) 22.70/22.76 ( (filter nat) ) 22.70/22.76 ( complex ) 22.70/22.76 ( (fun int bool) ) 22.70/22.76 ( (product_prod int int) ) 22.70/22.76 ( (fun (product_prod int int) int) ) 22.70/22.76 ( (fun int (fun int bool)) ) 22.70/22.76 ( (fun nat bool) ) 22.70/22.76 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.70/22.76 ( (fun (product_prod int int) bool) ) 22.70/22.76 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.70/22.76 ( (fun real bool) ) 22.70/22.76 ( quickcheck_code_int ) 22.70/22.76 ( code_code_numeral ) 22.70/22.76 ( (product_prod real real) ) 22.70/22.76 ( (filter real) ) 22.70/22.76 ( (product_prod nat nat) ) 22.70/22.76 ( (fun nat rat) ) 22.70/22.76 ( (fun int (fun int (fun int bool))) ) 22.70/22.76 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.70/22.76 ( (fun int real) ) 22.70/22.76 ) 22.70/22.77 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_1) C_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 B) C_1))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 A_1) B)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) A_1)))))) ) 22.70/22.77 ( (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))) ) 22.70/22.77 ( min, (zero_zero int), (one_one int) ) 22.70/22.77 ( (zero_zero 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))) ) 22.70/22.77 ( s, (one_one int), t ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), min, (zero_zero int) ) 22.70/22.77 ( t, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( m1, min, min ) 22.70/22.77 ( skv_4, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( skv_5, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int bit0 K_4)) L_4) (hAPP int int bit0 (hAPP int int (hAPP int _let_0 _let_1 K_4) L_4))))) ) 22.70/22.77 ( pls, (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))) m1))) ) 22.70/22.77 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.77 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.77 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.70/22.77 ( pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.70/22.77 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137453 $$unsorted) (BOUND_VARIABLE_137454 $$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_137453) BOUND_VARIABLE_137454))) (or (not (monoid_mult X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137453) _let_2) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_137453)))))) ) 22.70/22.77 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real real (hAPP 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_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (uminus_uminus real) _let_0)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) (hAPP real real cos X))))))) ) 22.70/22.77 ( pi ) 22.70/22.77 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (zero_zero real) ) 22.70/22.77 ( (hAPP real 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))))) ) 22.70/22.77 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.70/22.77 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (hAPP real real (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))))) ) 22.70/22.77 ( (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)))) ) 22.70/22.77 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.70/22.77 ( skv_10 ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fact_fact nat))) (let ((_let_1 (hAPP nat nat suc X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) _let_1) (hAPP nat nat _let_0 X)) (hAPP nat nat _let_0 _let_1)))) ) 22.70/22.77 ( (zero_zero nat) ) 22.70/22.77 ( (hAPP nat nat suc (zero_zero nat)) ) 22.70/22.77 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((N $$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))) (= (hAPP int int _let_1 N) (hAPP int int (hAPP int _let_0 (times_times int) N) (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (minus_minus int) N) (one_one int)))))))) ) 22.70/22.77 ( pls ) 22.70/22.77 ( (one_one int) ) 22.70/22.77 ( min ) 22.70/22.77 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( y ) 22.70/22.77 ( sa ) 22.70/22.77 ( x ) 22.70/22.77 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.70/22.77 ( r ) 22.70/22.77 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.77 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.77 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.70/22.77 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.70/22.77 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (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))) m1))) ) 22.70/22.77 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.70/22.77 ( skv_13 ) 22.70/22.77 ( skv_19 ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137531 $$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_137531))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_137531))))) ) 22.70/22.77 ( real, (zero_zero real) ) 22.70/22.77 ( complex, ii ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) A_3) B_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_2) (hAPP int _let_0 d22set A_3)))))) ) 22.70/22.77 ( (one_one int), t ) 22.70/22.77 ( min, min ) 22.70/22.77 ( min, (zero_zero int) ) 22.70/22.77 ( (zero_zero int), pls ) 22.70/22.77 ( (zero_zero int), (one_one int) ) 22.70/22.77 ( (zero_zero int), min ) 22.70/22.77 ( (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))) ) 22.70/22.77 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) Z_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1))) ) 22.70/22.77 ( (one_one nat) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (uminus_uminus int))) (= (hAPP int int _let_0 (hAPP int int _let_0 Z_1)) (ti int Z_1))) ) 22.70/22.77 ( pls ) 22.70/22.77 ( (one_one int) ) 22.70/22.77 ( min ) 22.70/22.77 ( s ) 22.70/22.77 ( s1 ) 22.70/22.77 ( m ) 22.70/22.77 ( t ) 22.70/22.77 ( v ) 22.70/22.77 ( w ) 22.70/22.77 ( y ) 22.70/22.77 ( sa ) 22.70/22.77 ( x ) 22.70/22.77 ( r ) 22.70/22.77 ( m1 ) 22.70/22.77 ( skv_14 ) 22.70/22.77 ( skv_20 ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137716 $$unsorted) (BOUND_VARIABLE_137717 $$unsorted) (BOUND_VARIABLE_137718 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_137717))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_137718))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_137716))) (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_137718) BOUND_VARIABLE_137716))))) ) 22.70/22.77 ( 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)))) ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((Ma $$unsorted) (Xa $$unsorted)) (= (not (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun int bool))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int (fun int _let_0) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) Y_1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) Xa) Ma)))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes Ma) Xa))) ) 22.70/22.77 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (number_number_of int) min) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (inverse_divide real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (fun real complex))) (let ((_let_6 (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 A_1) _let_4)) (hAPP nat real (hAPP real _let_0 _let_1 B) _let_4)))) (= (hAPP real complex (hAPP real _let_5 complex_1 (hAPP real real (hAPP real _let_2 _let_3 A_1) _let_6)) (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (uminus_uminus real) B)) _let_6)) (hAPP complex complex (inverse_inverse complex) (hAPP real complex (hAPP real _let_5 complex_1 A_1) B)))))))))) ) 22.70/22.77 ( (zero_zero real), (one_one real) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137801 $$unsorted)) (or (not (linordered_semidom X_a)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_137801)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_137801))))) ) 22.70/22.77 ( int, (zero_zero nat) ) 22.70/22.77 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (one_one nat) ) 22.70/22.77 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, n ) 22.70/22.77 ( real, (zero_zero nat) ) 22.70/22.77 ( real, (one_one nat) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137880 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_137880) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_137880) (hAPP int X_a (number_number_of X_a) min)))) ) 22.70/22.77 ( int, pls ) 22.70/22.77 ( int, (one_one int) ) 22.70/22.77 ( int, min ) 22.70/22.77 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( int, y ) 22.70/22.77 ( int, sa ) 22.70/22.77 ( int, x ) 22.70/22.77 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.70/22.77 ( int, r ) 22.70/22.77 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.77 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( int, skv_13 ) 22.70/22.77 ( int, skv_19 ) 22.70/22.77 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( real, (one_one real) ) 22.70/22.77 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( 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) ) 22.70/22.77 ( 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))))) ) 22.70/22.77 ( complex, ii ) 22.70/22.77 ( complex, (one_one complex) ) 22.70/22.77 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( 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)) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (uminus_uminus complex))) (= (hAPP complex complex cnj (hAPP complex complex _let_0 X)) (hAPP complex complex _let_0 (hAPP complex complex cnj X)))) ) 22.70/22.77 ( (one_one complex) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less_eq real))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (fun real _let_1))) (let ((_let_6 (fun _let_2 _let_2))) (let ((_let_7 (combs real bool bool))) (let ((_let_8 (hAPP (fun bool _let_1) (fun _let_2 _let_5) (combb bool _let_1 real) fconj))) (let ((_let_9 (combc real real bool))) (= (hAPP _let_2 real (the real) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 _let_8 (hAPP real _let_2 _let_3 (zero_zero real)))) (hAPP _let_2 _let_2 (hAPP _let_5 _let_6 _let_7 (hAPP _let_2 _let_5 _let_8 (hAPP real _let_2 (hAPP _let_4 _let_4 _let_9 _let_3) pi))) (hAPP real _let_2 (hAPP _let_4 _let_4 _let_9 (hAPP _let_0 _let_4 (hAPP _let_4 (fun _let_0 _let_4) (combb real _let_2 real) (fequal real)) cos)) Ya)))) (hAPP real real arccos Ya)))))))))))) ) 22.70/22.77 ( (zero_zero real) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((M $$unsorted)) (= (hAPP int int (abs_abs int) M) (hAPP int int (hAPP int (fun int int) legacy_zgcd M) (zero_zero int))) ) 22.70/22.77 ( v ) 22.70/22.77 ( w ) 22.70/22.77 ( skv_14 ) 22.70/22.77 ( skv_20 ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137911 $$unsorted) (BOUND_VARIABLE_137912 $$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_137911)) BOUND_VARIABLE_137912)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_137911) BOUND_VARIABLE_137912)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_137911)) BOUND_VARIABLE_137912))))))) ) 22.70/22.77 ( int, pls, pls ) 22.70/22.77 ( int, pls, (one_one int) ) 22.70/22.77 ( int, pls, min ) 22.70/22.77 ( int, pls, s ) 22.70/22.77 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, pls, skv_4 ) 22.70/22.77 ( int, pls, skv_5 ) 22.70/22.77 ( int, (one_one int), pls ) 22.70/22.77 ( int, (one_one int), min ) 22.70/22.77 ( int, (one_one int), t ) 22.70/22.77 ( int, min, pls ) 22.70/22.77 ( int, min, min ) 22.70/22.77 ( int, (zero_zero int), pls ) 22.70/22.77 ( int, (zero_zero int), (one_one int) ) 22.70/22.77 ( int, (zero_zero int), min ) 22.70/22.77 ( int, (zero_zero int), s ) 22.70/22.77 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.77 ( int, (zero_zero int), skv_4 ) 22.70/22.77 ( int, (zero_zero int), skv_5 ) 22.70/22.77 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.77 ( real, (hAPP real real (hAPP 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))) ) 22.70/22.77 ( real, (zero_zero real), pi ) 22.70/22.77 ( 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)))) ) 22.70/22.77 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( real, (zero_zero real), skv_10 ) 22.70/22.77 ( real, (zero_zero real), skv_11 ) 22.70/22.77 ( real, (zero_zero real), skv_15 ) 22.70/22.77 ( real, (zero_zero real), skv_18 ) 22.70/22.77 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.77 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_137941 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a bool))) (or (not (ring_char_0 X_a)) (not (hBOOL (hAPP _let_1 bool (hAPP X_a (fun _let_1 bool) (member X_a) BOUND_VARIABLE_137941) (ring_1_Ints X_a)))) (= (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_137941) BOUND_VARIABLE_137941)) (= _let_0 (ti X_a BOUND_VARIABLE_137941)))))) ) 22.70/22.77 ( int, pls ) 22.70/22.77 ( int, (one_one int) ) 22.70/22.77 ( int, min ) 22.70/22.77 ( int, s ) 22.70/22.77 ( 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)))) ) 22.70/22.77 ( int, s1 ) 22.70/22.77 ( int, m ) 22.70/22.77 ( 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) ) 22.70/22.77 ( int, t ) 22.70/22.77 ( int, v ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( int, w ) 22.70/22.77 ( int, y ) 22.70/22.77 ( int, sa ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.77 ( int, x ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.77 ( int, r ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.77 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.70/22.77 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.70/22.77 ( int, m1 ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.77 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( int, skv_14 ) 22.70/22.77 ( int, skv_20 ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.77 ( (fun int int), bit1 ) 22.70/22.77 ( (fun int int), bit0 ) 22.70/22.77 ( (fun int int), succ ) 22.70/22.77 ( (fun int int), pred ) 22.70/22.77 ( (fun int int), (fact_fact int) ) 22.70/22.77 ( (fun int int), zfact ) 22.70/22.77 ( nat, (one_one nat) ) 22.70/22.77 ( nat, n ) 22.70/22.77 ( nat, tn ) 22.70/22.77 ( bool, fTrue ) 22.70/22.77 ( bool, fFalse ) 22.70/22.77 ( real, pi ) 22.70/22.77 ( (fun nat real), (real_1 nat) ) 22.70/22.77 ( (fun nat real), cos_coeff ) 22.70/22.77 ( (fun nat real), sin_coeff ) 22.70/22.77 ( (fun real real), sin ) 22.70/22.77 ( (fun real real), cos ) 22.70/22.77 ( (fun real real), sqrt ) 22.70/22.77 ( (fun real real), tan ) 22.70/22.77 ( (fun real real), ln ) 22.70/22.77 ( (fun real real), arctan ) 22.70/22.77 ( (fun real real), arcsin ) 22.70/22.77 ( (fun real real), arccos ) 22.70/22.77 ( (fun nat nat), suc ) 22.70/22.77 ( (fun nat nat), (fact_fact nat) ) 22.70/22.77 ( (fun nat nat), nat_size ) 22.70/22.77 ( (fun nat nat), (size_size nat) ) 22.70/22.77 ( (fun nat nat), fact ) 22.70/22.77 ( (filter nat), sequentially ) 22.70/22.77 ( (fun int (fun int rat)), fract ) 22.70/22.77 ( complex, ii ) 22.70/22.77 ( (fun int bool), zOdd ) 22.70/22.77 ( (fun int bool), zprime ) 22.70/22.77 ( (fun int bool), zEven ) 22.70/22.77 ( (fun int bool), nat_neg ) 22.70/22.77 ( (fun int bool), nat_is_nat ) 22.70/22.77 ( (fun int bool), (even_odd_even int) ) 22.70/22.77 ( (fun int bool), twoSqu1091635170sum2sq ) 22.70/22.77 ( (fun int (fun int int)), legacy_zgcd ) 22.70/22.77 ( (fun int (fun int int)), (gcd_gcd int) ) 22.70/22.77 ( (fun int (fun int int)), inv ) 22.70/22.77 ( (fun int (fun int int)), multInv ) 22.70/22.77 ( (fun int (fun int int)), legendre ) 22.70/22.77 ( (fun int (fun int int)), standardRes ) 22.70/22.77 ( (fun int (fun int int)), nat_tsub ) 22.70/22.77 ( (fun int (fun int int)), z3div ) 22.70/22.77 ( (fun int (fun int int)), z3mod ) 22.70/22.77 ( (fun int (fun int int)), int_lcm ) 22.70/22.77 ( (fun int (fun int int)), int_gcd ) 22.70/22.77 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.70/22.77 ( (fun bool bool), fNot ) 22.70/22.77 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.70/22.77 ( (fun bool (fun bool bool)), fconj ) 22.70/22.77 ( (fun bool (fun bool bool)), fdisj ) 22.70/22.77 ( (fun bool (fun bool bool)), fimplies ) 22.70/22.77 ( (fun int (fun int bool)), quadRes ) 22.70/22.77 ( (fun int (fun int bool)), d22set ) 22.70/22.77 ( (fun int (fun int bool)), norRRset ) 22.70/22.77 ( (fun int (fun int bool)), sRStar ) 22.70/22.77 ( (fun int (fun int bool)), sr ) 22.70/22.77 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.70/22.77 ( (fun nat bool), (even_odd_even nat) ) 22.70/22.77 ( (fun nat bool), prime ) 22.70/22.77 ( (fun real complex), cis ) 22.70/22.77 ( (fun nat (fun nat bool)), coprime ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.70/22.77 ( (fun (product_prod int int) bool), frac_1 ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.70/22.77 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.70/22.77 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.70/22.77 ( (fun (fun int bool) bool), nat_nat_set ) 22.70/22.77 ( (fun nat (fun real real)), root ) 22.70/22.77 ( (fun real (fun real real)), log ) 22.70/22.77 ( (fun real (fun real real)), powr ) 22.70/22.77 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.70/22.77 ( (fun complex complex), cnj ) 22.70/22.77 ( (fun complex complex), expi ) 22.70/22.77 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.70/22.77 ( (fun nat (fun nat nat)), nat_gcd ) 22.70/22.77 ( (fun nat (fun nat nat)), nat_lcm ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.70/22.77 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.70/22.77 ( (fun int (fun (fun int bool) bool)), resSet ) 22.70/22.77 ( (fun int nat), nat_1 ) 22.70/22.77 ( (fun int nat), phi ) 22.70/22.77 ( (fun complex real), re ) 22.70/22.77 ( (fun complex real), im ) 22.70/22.77 ( (fun complex real), arg ) 22.70/22.77 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.70/22.77 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.70/22.77 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.70/22.77 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.70/22.77 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.70/22.77 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.70/22.77 ( (fun (product_prod nat nat) bool), pred_nat ) 22.70/22.77 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.70/22.77 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.70/22.77 ( (fun (fun int bool) int), (the int) ) 22.70/22.77 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.70/22.77 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.70/22.77 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.70/22.77 ( (fun real (fun real complex)), rcis ) 22.70/22.77 ( (fun real (fun real complex)), complex_1 ) 22.70/22.77 ( (fun int (fun int (fun int bool))), zcong ) 22.70/22.77 ( (fun int (fun int (fun int bool))), wset ) 22.70/22.77 ( (fun int (fun int (fun int bool))), noXRRset ) 22.70/22.77 ( (fun int (fun int (fun int bool))), bnorRset ) 22.70/22.77 ( (fun int (fun int (fun int bool))), zcongm ) 22.70/22.77 ( (fun real nat), natceiling ) 22.70/22.77 ( (fun real nat), natfloor ) 22.70/22.77 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.70/22.77 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.70/22.77 ( (fun int real), (real_1 int) ) 22.70/22.77 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.70/22.77 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.70/22.77 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.70/22.77 ( (fun complex nat), (size_size complex) ) 22.70/22.77 ( (fun complex nat), complex_size ) 22.70/22.77 ( (fun (fun nat rat) bool), vanishes ) 22.70/22.77 ( (fun (product_prod int int) rat), frct ) 22.70/22.77 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.70/22.77 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.70/22.77 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.70/22.77 ( (fun rat real), ratreal ) 22.70/22.77 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.70/22.77 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.70/22.77 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.70/22.77 ( (fun rat (product_prod int int)), quotient_of ) 22.70/22.77 ( (fun int (fun nat nat)), nat_aux ) 22.70/22.77 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.70/22.77 ( (fun int (list int)), quickc666637781d_zero ) 22.70/22.77 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.70/22.77 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.70/22.77 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.70/22.77 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.70/22.77 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.70/22.77 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.70/22.77 ( (fun code_code_numeral int), code_int_of ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138012 $$unsorted) (BOUND_VARIABLE_138013 $$unsorted) (BOUND_VARIABLE_138014 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_138012))) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138013) BOUND_VARIABLE_138014))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138012) (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_138014)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_138013))))))) ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((A_3 $$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_3) 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_3) Ma)) (hAPP int _let_1 rsetR Ma)))))) ) 22.70/22.77 ( (one_one int), t ) 22.70/22.77 ( min, min ) 22.70/22.77 ( min, (zero_zero int) ) 22.70/22.77 ( (zero_zero int), pls ) 22.70/22.77 ( (zero_zero int), (one_one int) ) 22.70/22.77 ( (zero_zero int), min ) 22.70/22.77 ( (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))) ) 22.70/22.77 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.77 ( 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))) ) 22.70/22.77 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (one_one nat) (hAPP nat nat suc (hAPP int nat (number_number_of nat) V)))) ) 22.70/22.77 ( pls ) 22.70/22.77 ( (hAPP int int bit1 pls) ) 22.70/22.77 ( min ) 22.70/22.77 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.77 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V))) (= (hAPP nat nat suc (hAPP int nat _let_0 V)) (hAPP int nat _let_0 (hAPP int int succ V))))) ) 22.70/22.77 ( pls ) 22.70/22.77 ( (hAPP int int bit1 pls) ) 22.70/22.77 ( min ) 22.70/22.77 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.77 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.77 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.77 ) 22.70/22.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138056 $$unsorted) (BOUND_VARIABLE_138057 $$unsorted) (BOUND_VARIABLE_138058 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138057))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138056))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_138058)) (hAPP X_a X_a _let_3 (hAPP X_a X_a _let_2 BOUND_VARIABLE_138058)))))))) ) 22.70/22.77 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (one_one real) (hAPP X_a real (norm_norm X_a) (one_one X_a)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( real ) 22.70/22.78 ( complex ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138155 $$unsorted) (BOUND_VARIABLE_138156 $$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_138156) _let_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_138155) _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_138156) BOUND_VARIABLE_138155))))))) ) 22.70/22.78 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.70/22.78 ( 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))) ) 22.70/22.78 ( int, v, y ) 22.70/22.78 ( int, v, sa ) 22.70/22.78 ( int, v, x ) 22.70/22.78 ( int, v, r ) 22.70/22.78 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.78 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.78 ( int, w, y ) 22.70/22.78 ( int, w, sa ) 22.70/22.78 ( int, w, x ) 22.70/22.78 ( int, w, r ) 22.70/22.78 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.70/22.78 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.70/22.78 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.70/22.78 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.78 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, skv_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))) ) 22.70/22.78 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( 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))))) ) 22.70/22.78 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( 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)))) ) 22.70/22.78 ( complex, ii, ii ) 22.70/22.78 ( 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)) ) 22.70/22.78 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real 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))) (= (hAPP complex real im (hAPP complex complex (inverse_inverse complex) X)) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP real real (uminus_uminus real) _let_4)) (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re X)) _let_3)) (hAPP nat real (hAPP real _let_0 _let_1 _let_4) _let_3))))))))) ) 22.70/22.78 ( (zero_zero complex) ) 22.70/22.78 ( ii ) 22.70/22.78 ( (one_one complex) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int (fun int bool) (dvd_dvd int) I_1))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd I_1) J_2))) (not (hBOOL (hAPP int bool _let_1 (hAPP int int (hAPP int _let_0 (times_times int) K_4) J_2)))) (hBOOL (hAPP int bool _let_1 K_4))))) ) 22.70/22.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_21 ) 22.70/22.78 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((K_4 $$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))))) ) 22.70/22.78 ( (one_one int) ) 22.70/22.78 ( (zero_zero int) ) 22.70/22.78 ( s ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (not (hBOOL (hAPP X_a bool (iszero X_a) (hAPP int X_a (number_number_of X_a) min))))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( real ) 22.70/22.78 ( complex ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((Na $$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)) Na))) (= (hBOOL (hAPP nat bool _let_0 Na)) (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) (one_one nat)))))))) ) 22.70/22.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( n ) 22.70/22.78 ( tn ) 22.70/22.78 ( (hAPP int nat nat_1 t) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (archim2085082626_floor X_a))) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( real ) 22.70/22.78 ( (fun int bool) ) 22.70/22.78 ( (product_prod int int) ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((S $$unsorted)) (= (forall ((M_2 $$unsorted)) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) M_2) N_1))) (not (hBOOL (hAPP _let_0 bool (hAPP nat (fun _let_0 bool) (member nat) N_1) S))))) )) ) (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S)))) ) 22.70/22.78 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (inverse_inverse real))) (= (hAPP real real _let_0 (hAPP real real sqrt X)) (hAPP real real sqrt (hAPP real real _let_0 X)))) ) 22.70/22.78 ( (zero_zero real) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138221 $$unsorted)) (or (not (comm_semiring_1 X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_138221) (zero_zero X_a)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (one_one int) (hAPP X_a int (archim2085082626_floor X_a) (one_one X_a)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( real ) 22.70/22.78 ( complex ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138241 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (ti int BOUND_VARIABLE_138241) (hAPP X_a int (archim2085082626_floor X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_138241)))) ) 22.70/22.78 ( real, (one_one int) ) 22.70/22.78 ( real, (zero_zero int) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (hAPP int nat (number_number_of nat) _let_2))) (let ((_let_4 (times_times int))) (let ((_let_5 (fun nat int))) (let ((_let_6 (power_power int))) (= (hAPP nat int (hAPP int _let_5 _let_6 (hAPP int int (hAPP int _let_0 _let_1 A_1) B)) _let_3) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_5 _let_6 A_1) _let_3)) (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (number_number_of int) _let_2)) A_1)) B))) (hAPP nat int (hAPP int _let_5 _let_6 B) _let_3)))))))))) ) 22.70/22.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.70/22.78 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.70/22.78 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.70/22.78 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.78 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (real_normed_vector X_a)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) _let_0)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( real ) 22.70/22.78 ( complex ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138406 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (field_inverse_zero X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138406) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_138406)) _let_3))))))) ) 22.70/22.78 ( real, (zero_zero real) ) 22.70/22.78 ( complex, ii ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138428 $$unsorted)) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_138428) (one_one nat)) (ti X_a BOUND_VARIABLE_138428))) ) 22.70/22.78 ( int, pls ) 22.70/22.78 ( int, min ) 22.70/22.78 ( int, s ) 22.70/22.78 ( int, s1 ) 22.70/22.78 ( int, m ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, t ) 22.70/22.78 ( int, v ) 22.70/22.78 ( int, w ) 22.70/22.78 ( int, y ) 22.70/22.78 ( int, sa ) 22.70/22.78 ( int, x ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.70/22.78 ( int, r ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.70/22.78 ( int, m1 ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.70/22.78 ( int, skv_6 ) 22.70/22.78 ( int, skv_7 ) 22.70/22.78 ( int, skv_14 ) 22.70/22.78 ( int, skv_16 ) 22.70/22.78 ( int, skv_20 ) 22.70/22.78 ( int, skv_23 ) 22.70/22.78 ( int, skv_24 ) 22.70/22.78 ( (fun int int), bit1 ) 22.70/22.78 ( (fun int int), bit0 ) 22.70/22.78 ( (fun int int), succ ) 22.70/22.78 ( (fun int int), pred ) 22.70/22.78 ( (fun int int), (fact_fact int) ) 22.70/22.78 ( (fun int int), zfact ) 22.70/22.78 ( nat, n ) 22.70/22.78 ( nat, tn ) 22.70/22.78 ( bool, fTrue ) 22.70/22.78 ( bool, fFalse ) 22.70/22.78 ( real, (hAPP int real (number_number_of real) min) ) 22.70/22.78 ( real, pi ) 22.70/22.78 ( 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)))) ) 22.70/22.78 ( (fun nat real), (real_1 nat) ) 22.70/22.78 ( (fun nat real), cos_coeff ) 22.70/22.78 ( (fun nat real), sin_coeff ) 22.70/22.78 ( (fun real real), sin ) 22.70/22.78 ( (fun real real), cos ) 22.70/22.78 ( (fun real real), sqrt ) 22.70/22.78 ( (fun real real), tan ) 22.70/22.78 ( (fun real real), ln ) 22.70/22.78 ( (fun real real), arctan ) 22.70/22.78 ( (fun real real), arcsin ) 22.70/22.78 ( (fun real real), arccos ) 22.70/22.78 ( (fun nat nat), suc ) 22.70/22.78 ( (fun nat nat), (fact_fact nat) ) 22.70/22.78 ( (fun nat nat), nat_size ) 22.70/22.78 ( (fun nat nat), (size_size nat) ) 22.70/22.78 ( (fun nat nat), fact ) 22.70/22.78 ( (filter nat), sequentially ) 22.70/22.78 ( (fun int (fun int rat)), fract ) 22.70/22.78 ( complex, ii ) 22.70/22.78 ( (fun int bool), zOdd ) 22.70/22.78 ( (fun int bool), zprime ) 22.70/22.78 ( (fun int bool), zEven ) 22.70/22.78 ( (fun int bool), nat_neg ) 22.70/22.78 ( (fun int bool), nat_is_nat ) 22.70/22.78 ( (fun int bool), (even_odd_even int) ) 22.70/22.78 ( (fun int bool), twoSqu1091635170sum2sq ) 22.70/22.78 ( (fun int (fun int int)), legacy_zgcd ) 22.70/22.78 ( (fun int (fun int int)), (gcd_gcd int) ) 22.70/22.78 ( (fun int (fun int int)), inv ) 22.70/22.78 ( (fun int (fun int int)), multInv ) 22.70/22.78 ( (fun int (fun int int)), legendre ) 22.70/22.78 ( (fun int (fun int int)), standardRes ) 22.70/22.78 ( (fun int (fun int int)), nat_tsub ) 22.70/22.78 ( (fun int (fun int int)), z3div ) 22.70/22.78 ( (fun int (fun int int)), z3mod ) 22.70/22.78 ( (fun int (fun int int)), int_lcm ) 22.70/22.78 ( (fun int (fun int int)), int_gcd ) 22.70/22.78 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.70/22.78 ( (fun bool bool), fNot ) 22.70/22.78 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.70/22.78 ( (fun bool (fun bool bool)), fconj ) 22.70/22.78 ( (fun bool (fun bool bool)), fdisj ) 22.70/22.78 ( (fun bool (fun bool bool)), fimplies ) 22.70/22.78 ( (fun int (fun int bool)), quadRes ) 22.70/22.78 ( (fun int (fun int bool)), d22set ) 22.70/22.78 ( (fun int (fun int bool)), norRRset ) 22.70/22.78 ( (fun int (fun int bool)), sRStar ) 22.70/22.78 ( (fun int (fun int bool)), sr ) 22.70/22.78 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.70/22.78 ( (fun nat bool), (even_odd_even nat) ) 22.70/22.78 ( (fun nat bool), prime ) 22.70/22.78 ( (fun real complex), cis ) 22.70/22.78 ( (fun nat (fun nat bool)), coprime ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.70/22.78 ( (fun (product_prod int int) bool), frac_1 ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.70/22.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.70/22.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.70/22.78 ( (fun (fun int bool) bool), nat_nat_set ) 22.70/22.78 ( (fun nat (fun real real)), root ) 22.70/22.78 ( (fun real (fun real real)), log ) 22.70/22.78 ( (fun real (fun real real)), powr ) 22.70/22.78 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.70/22.78 ( (fun complex complex), cnj ) 22.70/22.78 ( (fun complex complex), expi ) 22.70/22.78 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.70/22.78 ( (fun nat (fun nat nat)), nat_gcd ) 22.70/22.78 ( (fun nat (fun nat nat)), nat_lcm ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.70/22.78 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.70/22.78 ( (fun int (fun (fun int bool) bool)), resSet ) 22.70/22.78 ( (fun int nat), nat_1 ) 22.70/22.78 ( (fun int nat), phi ) 22.70/22.78 ( (fun complex real), re ) 22.70/22.78 ( (fun complex real), im ) 22.70/22.78 ( (fun complex real), arg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.70/22.78 ( (fun (product_prod nat nat) bool), pred_nat ) 22.70/22.78 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.70/22.78 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.70/22.78 ( (fun (fun int bool) int), (the int) ) 22.70/22.78 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.70/22.78 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.70/22.78 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.70/22.78 ( (fun real (fun real complex)), rcis ) 22.70/22.78 ( (fun real (fun real complex)), complex_1 ) 22.70/22.78 ( (fun int (fun int (fun int bool))), zcong ) 22.70/22.78 ( (fun int (fun int (fun int bool))), wset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), noXRRset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), bnorRset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), zcongm ) 22.70/22.78 ( (fun real nat), natceiling ) 22.70/22.78 ( (fun real nat), natfloor ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.70/22.78 ( (fun int real), (real_1 int) ) 22.70/22.78 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.70/22.78 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.70/22.78 ( (fun complex nat), (size_size complex) ) 22.70/22.78 ( (fun complex nat), complex_size ) 22.70/22.78 ( (fun (fun nat rat) bool), vanishes ) 22.70/22.78 ( (fun (product_prod int int) rat), frct ) 22.70/22.78 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.70/22.78 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.70/22.78 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.70/22.78 ( (fun rat real), ratreal ) 22.70/22.78 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.70/22.78 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.70/22.78 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.70/22.78 ( (fun rat (product_prod int int)), quotient_of ) 22.70/22.78 ( (fun int (fun nat nat)), nat_aux ) 22.70/22.78 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.70/22.78 ( (fun int (list int)), quickc666637781d_zero ) 22.70/22.78 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.70/22.78 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.70/22.78 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.70/22.78 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.70/22.78 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.70/22.78 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.70/22.78 ( (fun code_code_numeral int), code_int_of ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138511 $$unsorted) (BOUND_VARIABLE_138512 $$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_138511) BOUND_VARIABLE_138512)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_138511) BOUND_VARIABLE_138512)) (not (= (ti X_a BOUND_VARIABLE_138512) (ti X_a BOUND_VARIABLE_138511))))))) ) 22.70/22.78 ( int, (one_one int), t ) 22.70/22.78 ( int, min, pls ) 22.70/22.78 ( int, min, min ) 22.70/22.78 ( int, min, (zero_zero int) ) 22.70/22.78 ( int, (zero_zero int), pls ) 22.70/22.78 ( int, (zero_zero int), (one_one int) ) 22.70/22.78 ( int, (zero_zero int), min ) 22.70/22.78 ( int, (zero_zero int), s ) 22.70/22.78 ( 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))) ) 22.70/22.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (zero_zero int), skv_4 ) 22.70/22.78 ( int, (zero_zero int), skv_5 ) 22.70/22.78 ( 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))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.78 ( 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))) ) 22.70/22.78 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( 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))) ) 22.70/22.78 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.78 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.78 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( nat, (zero_zero nat), n ) 22.70/22.78 ( nat, (zero_zero nat), tn ) 22.70/22.78 ( real, pi, (zero_zero real) ) 22.70/22.78 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.78 ( real, (hAPP real real (hAPP 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))) ) 22.70/22.78 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( real, (zero_zero real), pi ) 22.70/22.78 ( 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)))) ) 22.70/22.78 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( real, (zero_zero real), skv_2 ) 22.70/22.78 ( real, (zero_zero real), skv_9 ) 22.70/22.78 ( real, (zero_zero real), skv_10 ) 22.70/22.78 ( real, (zero_zero real), skv_11 ) 22.70/22.78 ( real, (zero_zero real), skv_12 ) 22.70/22.78 ( real, (zero_zero real), skv_15 ) 22.70/22.78 ( real, (zero_zero real), skv_18 ) 22.70/22.78 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.78 ( 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) ) 22.70/22.78 ( 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 ) 22.70/22.78 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (plus_plus X_a))) (or (not (plus X_a)) (not (dvd X_a)) (not (linorder X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( (fun int int) ) 22.70/22.78 ( nat ) 22.70/22.78 ( bool ) 22.70/22.78 ( real ) 22.70/22.78 ( (fun nat real) ) 22.70/22.78 ( (fun real real) ) 22.70/22.78 ( complex ) 22.70/22.78 ( (fun int bool) ) 22.70/22.78 ( (product_prod int int) ) 22.70/22.78 ( (fun (product_prod int int) int) ) 22.70/22.78 ( (fun int (fun int bool)) ) 22.70/22.78 ( (fun nat bool) ) 22.70/22.78 ( (fun (product_prod int int) bool) ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.70/22.78 ( (fun real bool) ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ( (fun int (fun int (fun int bool))) ) 22.70/22.78 ( (fun int real) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X $$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 (zero_zero real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP nat real (real_1 nat) (hAPP real nat natfloor X))) X))))) ) 22.70/22.78 ( pi ) 22.70/22.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( (one_one real) ) 22.70/22.78 ( (zero_zero real) ) 22.70/22.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( skv_10 ) 22.70/22.78 ( skv_11 ) 22.70/22.78 ( skv_15 ) 22.70/22.78 ( skv_18 ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (semiring_1 X_a)) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) _let_0) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( (fun int int) ) 22.70/22.78 ( nat ) 22.70/22.78 ( bool ) 22.70/22.78 ( real ) 22.70/22.78 ( (fun real real) ) 22.70/22.78 ( (fun nat nat) ) 22.70/22.78 ( complex ) 22.70/22.78 ( (product_prod int int) ) 22.70/22.78 ( (fun bool bool) ) 22.70/22.78 ( (fun nat bool) ) 22.70/22.78 ( (fun nat (fun nat bool)) ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ( (fun nat (product_prod int int)) ) 22.70/22.78 ( (product_prod real real) ) 22.70/22.78 ( (product_prod nat nat) ) 22.70/22.78 ( (fun (product_prod nat nat) bool) ) 22.70/22.78 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.70/22.78 ( (fun nat (product_prod nat nat)) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138625 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_1 X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP _let_3 bool (summable X_a) BOUND_VARIABLE_138625))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (tendsto nat X_a) (hAPP _let_2 _let_3 (hAPP _let_4 (fun _let_2 _let_3) (combb _let_1 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_138625)) (hAPP nat _let_2 (ord_atLeastLessThan nat) (zero_zero nat)))) (hAPP _let_3 X_a (suminf X_a) BOUND_VARIABLE_138625)) sequentially)))))))) ) 22.70/22.78 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 (fun (fun nat nat) _let_0) (combb nat real nat) (real_1 nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138650 $$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_138650)) (ti X_a BOUND_VARIABLE_138650)))) ) 22.70/22.78 ( int, pls ) 22.70/22.78 ( int, min ) 22.70/22.78 ( int, s ) 22.70/22.78 ( int, s1 ) 22.70/22.78 ( int, m ) 22.70/22.78 ( int, t ) 22.70/22.78 ( int, v ) 22.70/22.78 ( int, w ) 22.70/22.78 ( int, y ) 22.70/22.78 ( int, sa ) 22.70/22.78 ( int, x ) 22.70/22.78 ( int, r ) 22.70/22.78 ( int, m1 ) 22.70/22.78 ( int, skv_14 ) 22.70/22.78 ( int, skv_20 ) 22.70/22.78 ( (fun int int), bit1 ) 22.70/22.78 ( (fun int int), bit0 ) 22.70/22.78 ( (fun int int), succ ) 22.70/22.78 ( (fun int int), pred ) 22.70/22.78 ( (fun int int), (fact_fact int) ) 22.70/22.78 ( (fun int int), zfact ) 22.70/22.78 ( nat, n ) 22.70/22.78 ( nat, tn ) 22.70/22.78 ( bool, fTrue ) 22.70/22.78 ( bool, fFalse ) 22.70/22.78 ( real, pi ) 22.70/22.78 ( real, (zero_zero real) ) 22.70/22.78 ( (fun nat real), (real_1 nat) ) 22.70/22.78 ( (fun nat real), cos_coeff ) 22.70/22.78 ( (fun nat real), sin_coeff ) 22.70/22.78 ( (fun real real), sin ) 22.70/22.78 ( (fun real real), cos ) 22.70/22.78 ( (fun real real), sqrt ) 22.70/22.78 ( (fun real real), tan ) 22.70/22.78 ( (fun real real), ln ) 22.70/22.78 ( (fun real real), arctan ) 22.70/22.78 ( (fun real real), arcsin ) 22.70/22.78 ( (fun real real), arccos ) 22.70/22.78 ( (fun nat nat), suc ) 22.70/22.78 ( (fun nat nat), (fact_fact nat) ) 22.70/22.78 ( (fun nat nat), nat_size ) 22.70/22.78 ( (fun nat nat), (size_size nat) ) 22.70/22.78 ( (fun nat nat), fact ) 22.70/22.78 ( (filter nat), sequentially ) 22.70/22.78 ( (fun int (fun int rat)), fract ) 22.70/22.78 ( complex, ii ) 22.70/22.78 ( (fun int bool), zOdd ) 22.70/22.78 ( (fun int bool), zprime ) 22.70/22.78 ( (fun int bool), zEven ) 22.70/22.78 ( (fun int bool), nat_neg ) 22.70/22.78 ( (fun int bool), nat_is_nat ) 22.70/22.78 ( (fun int bool), (even_odd_even int) ) 22.70/22.78 ( (fun int bool), twoSqu1091635170sum2sq ) 22.70/22.78 ( (fun int (fun int int)), legacy_zgcd ) 22.70/22.78 ( (fun int (fun int int)), (gcd_gcd int) ) 22.70/22.78 ( (fun int (fun int int)), inv ) 22.70/22.78 ( (fun int (fun int int)), multInv ) 22.70/22.78 ( (fun int (fun int int)), legendre ) 22.70/22.78 ( (fun int (fun int int)), standardRes ) 22.70/22.78 ( (fun int (fun int int)), nat_tsub ) 22.70/22.78 ( (fun int (fun int int)), z3div ) 22.70/22.78 ( (fun int (fun int int)), z3mod ) 22.70/22.78 ( (fun int (fun int int)), int_lcm ) 22.70/22.78 ( (fun int (fun int int)), int_gcd ) 22.70/22.78 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.70/22.78 ( (fun bool bool), fNot ) 22.70/22.78 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.70/22.78 ( (fun bool (fun bool bool)), fconj ) 22.70/22.78 ( (fun bool (fun bool bool)), fdisj ) 22.70/22.78 ( (fun bool (fun bool bool)), fimplies ) 22.70/22.78 ( (fun int (fun int bool)), quadRes ) 22.70/22.78 ( (fun int (fun int bool)), d22set ) 22.70/22.78 ( (fun int (fun int bool)), norRRset ) 22.70/22.78 ( (fun int (fun int bool)), sRStar ) 22.70/22.78 ( (fun int (fun int bool)), sr ) 22.70/22.78 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.70/22.78 ( (fun nat bool), (even_odd_even nat) ) 22.70/22.78 ( (fun nat bool), prime ) 22.70/22.78 ( (fun real complex), cis ) 22.70/22.78 ( (fun nat (fun nat bool)), coprime ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.70/22.78 ( (fun (product_prod int int) bool), frac_1 ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.70/22.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.70/22.78 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.70/22.78 ( (fun (fun int bool) bool), nat_nat_set ) 22.70/22.78 ( (fun nat (fun real real)), root ) 22.70/22.78 ( (fun real (fun real real)), log ) 22.70/22.78 ( (fun real (fun real real)), powr ) 22.70/22.78 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.70/22.78 ( (fun complex complex), cnj ) 22.70/22.78 ( (fun complex complex), expi ) 22.70/22.78 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.70/22.78 ( (fun nat (fun nat nat)), nat_gcd ) 22.70/22.78 ( (fun nat (fun nat nat)), nat_lcm ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.70/22.78 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.70/22.78 ( (fun int (fun (fun int bool) bool)), resSet ) 22.70/22.78 ( (fun int nat), nat_1 ) 22.70/22.78 ( (fun int nat), phi ) 22.70/22.78 ( (fun complex real), re ) 22.70/22.78 ( (fun complex real), im ) 22.70/22.78 ( (fun complex real), arg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.70/22.78 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.70/22.78 ( (fun (product_prod nat nat) bool), pred_nat ) 22.70/22.78 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.70/22.78 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.70/22.78 ( (fun (fun int bool) int), (the int) ) 22.70/22.78 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.70/22.78 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.70/22.78 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.70/22.78 ( (fun real (fun real complex)), rcis ) 22.70/22.78 ( (fun real (fun real complex)), complex_1 ) 22.70/22.78 ( (fun int (fun int (fun int bool))), zcong ) 22.70/22.78 ( (fun int (fun int (fun int bool))), wset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), noXRRset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), bnorRset ) 22.70/22.78 ( (fun int (fun int (fun int bool))), zcongm ) 22.70/22.78 ( (fun real nat), natceiling ) 22.70/22.78 ( (fun real nat), natfloor ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.70/22.78 ( (fun int real), (real_1 int) ) 22.70/22.78 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.70/22.78 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.70/22.78 ( (fun complex nat), (size_size complex) ) 22.70/22.78 ( (fun complex nat), complex_size ) 22.70/22.78 ( (fun (fun nat rat) bool), vanishes ) 22.70/22.78 ( (fun (product_prod int int) rat), frct ) 22.70/22.78 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.70/22.78 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.70/22.78 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.70/22.78 ( (fun rat real), ratreal ) 22.70/22.78 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.70/22.78 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.70/22.78 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.70/22.78 ( (fun rat (product_prod int int)), quotient_of ) 22.70/22.78 ( (fun int (fun nat nat)), nat_aux ) 22.70/22.78 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.70/22.78 ( (fun int (list int)), quickc666637781d_zero ) 22.70/22.78 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.70/22.78 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.70/22.78 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.70/22.78 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.70/22.78 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.70/22.78 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.70/22.78 ( (fun code_code_numeral int), code_int_of ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (number_number_of rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract (hAPP int int (number_number_of int) K_4)) (one_one int))) ) 22.70/22.78 ( pls ) 22.70/22.78 ( (hAPP int int bit1 pls) ) 22.70/22.78 ( min ) 22.70/22.78 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.78 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (one_one X_a)))) ) 22.70/22.78 ( rat ) 22.70/22.78 ( int ) 22.70/22.78 ( nat ) 22.70/22.78 ( bool ) 22.70/22.78 ( real ) 22.70/22.78 ( (filter nat) ) 22.70/22.78 ( complex ) 22.70/22.78 ( (fun int bool) ) 22.70/22.78 ( (product_prod int int) ) 22.70/22.78 ( (fun nat bool) ) 22.70/22.78 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.70/22.78 ( quickcheck_code_int ) 22.70/22.78 ( code_code_numeral ) 22.70/22.78 ( (product_prod real real) ) 22.70/22.78 ( (filter real) ) 22.70/22.78 ( (product_prod nat nat) ) 22.70/22.78 ( (fun nat rat) ) 22.70/22.78 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138672 $$unsorted)) (let ((_let_0 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_138672))) (or (not (linordered_idom X_a)) (= _let_0 (hAPP X_a X_a (abs_abs X_a) _let_0)))) ) 22.70/22.78 ( int, (zero_zero nat) ) 22.70/22.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, (one_one nat) ) 22.70/22.78 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.78 ( int, n ) 22.70/22.78 ( real, (zero_zero nat) ) 22.70/22.78 ( real, (one_one nat) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (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))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real tan X)) _let_0)))))) ) 22.70/22.78 ( pi ) 22.70/22.78 ( (zero_zero real) ) 22.70/22.78 ( (hAPP real 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))))) ) 22.70/22.78 ( (hAPP real real (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))))) ) 22.70/22.78 ( (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)))) ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((A_1 $$unsorted) (X $$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))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) A_1) (hAPP real int (archim2085082626_floor real) X)))) ) 22.70/22.78 ( (zero_zero int), pi ) 22.70/22.78 ( (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)))) ) 22.70/22.78 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( (zero_zero int), skv_10 ) 22.70/22.78 ( (zero_zero int), skv_11 ) 22.70/22.78 ( (zero_zero int), skv_15 ) 22.70/22.78 ( (zero_zero int), skv_18 ) 22.70/22.78 ) 22.70/22.78 (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 $$unsorted)) (let ((_let_1 (hAPP real (fun real bool) (ord_less real) E))) (or (not (hBOOL (hAPP real bool _let_1 D1))) (not (hBOOL (hAPP real bool _let_1 D2))) (not (hBOOL (hAPP real bool _let_0 E))))) )))) ) 22.70/22.78 ( pi, pi ) 22.70/22.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( skv_2, skv_2 ) 22.70/22.78 ( skv_9, skv_9 ) 22.70/22.78 ( skv_12, skv_12 ) 22.70/22.78 ) 22.70/22.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138746 $$unsorted) (BOUND_VARIABLE_138747 $$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_138746) BOUND_VARIABLE_138747)) (= (ti X_a BOUND_VARIABLE_138747) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_138746)))) ) 22.70/22.78 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.70/22.78 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.70/22.78 ( 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) ) 22.70/22.78 ( 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) ) 22.70/22.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.70/22.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.70/22.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.70/22.79 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.70/22.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( nat, (one_one nat), (one_one nat) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138780 $$unsorted) (BOUND_VARIABLE_138781 $$unsorted) (BOUND_VARIABLE_138782 $$unsorted) (BOUND_VARIABLE_138783 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (let ((_let_3 (minus_minus X_a))) (let ((_let_4 (times_times X_a))) (or (not (field X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_138783)) (= _let_0 (ti X_a BOUND_VARIABLE_138782)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_3 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138780) BOUND_VARIABLE_138783)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_138781) BOUND_VARIABLE_138782)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_138780) BOUND_VARIABLE_138782)) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_138781) BOUND_VARIABLE_138783))) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_138783) BOUND_VARIABLE_138782))))))))) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.70/22.79 ( int, x, y, w, v ) 22.70/22.79 ( int, r, sa, w, v ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w, v ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138814 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_138814) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_138814)) (one_one int))))) ) 22.70/22.79 ( int, (one_one int) ) 22.70/22.79 ( int, min ) 22.70/22.79 ( int, (zero_zero int) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.70/22.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( real, (zero_zero real) ) 22.70/22.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( real, skv_10 ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_a $$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)))) ) 22.70/22.79 ( rat ) 22.70/22.79 ( int ) 22.70/22.79 ( (fun int int) ) 22.70/22.79 ( nat ) 22.70/22.79 ( bool ) 22.70/22.79 ( real ) 22.70/22.79 ( (fun nat real) ) 22.70/22.79 ( (fun real real) ) 22.70/22.79 ( complex ) 22.70/22.79 ( (fun int bool) ) 22.70/22.79 ( (product_prod int int) ) 22.70/22.79 ( (fun (product_prod int int) int) ) 22.70/22.79 ( (fun int (fun int bool)) ) 22.70/22.79 ( (fun nat bool) ) 22.70/22.79 ( (fun (product_prod int int) bool) ) 22.70/22.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.70/22.79 ( (fun real bool) ) 22.70/22.79 ( code_code_numeral ) 22.70/22.79 ( (fun int (fun int (fun int bool))) ) 22.70/22.79 ( (fun int real) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_138841 $$unsorted) (BOUND_VARIABLE_138842 $$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_138841) BOUND_VARIABLE_138842))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_138841) BOUND_VARIABLE_138842)) (= (ti X_a BOUND_VARIABLE_138841) (ti X_a BOUND_VARIABLE_138842)))) ) 22.70/22.79 ( int, (one_one int), t ) 22.70/22.79 ( int, min, pls ) 22.70/22.79 ( int, min, min ) 22.70/22.79 ( int, min, (zero_zero int) ) 22.70/22.79 ( int, (zero_zero int), pls ) 22.70/22.79 ( int, (zero_zero int), (one_one int) ) 22.70/22.79 ( int, (zero_zero int), min ) 22.70/22.79 ( int, (zero_zero int), s ) 22.70/22.79 ( 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))) ) 22.70/22.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.79 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.70/22.79 ( int, (zero_zero int), skv_4 ) 22.70/22.79 ( int, (zero_zero int), skv_5 ) 22.70/22.79 ( 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))) ) 22.70/22.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.79 ( 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))) ) 22.70/22.79 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( 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))) ) 22.70/22.79 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.79 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.70/22.79 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.79 ( nat, (zero_zero nat), n ) 22.70/22.79 ( nat, (zero_zero nat), tn ) 22.70/22.79 ( real, pi, (zero_zero real) ) 22.70/22.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.70/22.79 ( 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))) ) 22.70/22.79 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( real, (zero_zero real), pi ) 22.70/22.79 ( 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)))) ) 22.70/22.79 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ( real, (zero_zero real), skv_2 ) 22.70/22.79 ( real, (zero_zero real), skv_9 ) 22.70/22.79 ( real, (zero_zero real), skv_10 ) 22.70/22.79 ( real, (zero_zero real), skv_11 ) 22.70/22.79 ( real, (zero_zero real), skv_12 ) 22.70/22.79 ( real, (zero_zero real), skv_15 ) 22.70/22.79 ( real, (zero_zero real), skv_18 ) 22.70/22.79 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.70/22.79 ( 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) ) 22.70/22.79 ( 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 ) 22.70/22.79 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((C_1 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int _let_0))) (let ((_let_2 (hAPP int _let_1 zcong A_1))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 B) M))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (hAPP int _let_1 zcong B) C_1) M))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 C_1) M)))))) ) 22.70/22.79 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) s1) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (not (order T_1)) (order (fun T_2 T_1))) ) 22.70/22.79 ( rat, real ) 22.70/22.79 ( rat, (product_prod int int) ) 22.70/22.79 ( int, rat ) 22.70/22.79 ( int, int ) 22.70/22.79 ( int, (fun int int) ) 22.70/22.79 ( int, nat ) 22.70/22.79 ( int, bool ) 22.70/22.79 ( int, real ) 22.70/22.79 ( int, (fun nat real) ) 22.70/22.79 ( int, (fun real real) ) 22.70/22.79 ( int, (fun nat nat) ) 22.70/22.79 ( int, (fun int rat) ) 22.70/22.79 ( int, (fun int bool) ) 22.70/22.79 ( int, (product_prod int int) ) 22.70/22.79 ( int, (fun (product_prod int int) int) ) 22.70/22.79 ( int, (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.70/22.79 ( int, (fun nat int) ) 22.70/22.79 ( int, (fun bool bool) ) 22.70/22.79 ( int, (fun int (fun bool bool)) ) 22.70/22.79 ( int, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( int, (fun int (fun int bool)) ) 22.70/22.79 ( int, (fun nat bool) ) 22.70/22.79 ( int, (fun (product_prod int int) bool) ) 22.70/22.79 ( int, (fun int (fun (product_prod int int) bool)) ) 22.70/22.79 ( int, quickcheck_code_int ) 22.70/22.79 ( int, (fun (fun int bool) bool) ) 22.70/22.79 ( int, (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.70/22.79 ( int, (product_prod int (product_prod int int)) ) 22.70/22.79 ( int, (fun int (product_prod int (product_prod int int))) ) 22.70/22.79 ( int, (fun int (fun int (product_prod int (product_prod int int)))) ) 22.70/22.79 ( int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 22.70/22.79 ( int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 22.70/22.79 ( int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 22.70/22.79 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 22.70/22.79 ( int, (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 22.70/22.79 ( int, (fun nat (fun bool bool)) ) 22.70/22.79 ( int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( int, (fun int (product_prod int int)) ) 22.70/22.79 ( int, (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 22.70/22.79 ( int, (fun int (fun (fun int bool) bool)) ) 22.70/22.79 ( int, (fun (fun int int) (fun int bool)) ) 22.70/22.79 ( int, (list int) ) 22.70/22.79 ( int, (fun int (fun int (fun int bool))) ) 22.70/22.79 ( int, (fun int real) ) 22.70/22.79 ( int, (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun int int), (fun int int) ) 22.70/22.79 ( (fun int int), (fun int bool) ) 22.70/22.79 ( (fun int int), (fun int (fun int int)) ) 22.70/22.79 ( (fun int int), (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun int int), (fun int (fun int bool)) ) 22.70/22.79 ( (fun int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.70/22.79 ( nat, rat ) 22.70/22.79 ( nat, int ) 22.70/22.79 ( nat, (fun int int) ) 22.70/22.79 ( nat, nat ) 22.70/22.79 ( nat, bool ) 22.70/22.79 ( nat, real ) 22.70/22.79 ( nat, (fun real real) ) 22.70/22.79 ( nat, (fun nat nat) ) 22.70/22.79 ( nat, complex ) 22.70/22.79 ( nat, (product_prod int int) ) 22.70/22.79 ( nat, (fun bool bool) ) 22.70/22.79 ( nat, (fun nat bool) ) 22.70/22.79 ( nat, (fun nat (fun nat bool)) ) 22.70/22.79 ( nat, (fun nat (product_prod int int)) ) 22.70/22.79 ( nat, (product_prod real real) ) 22.70/22.79 ( nat, (product_prod nat nat) ) 22.70/22.79 ( nat, (fun (product_prod nat nat) bool) ) 22.70/22.79 ( nat, (fun nat (fun (product_prod nat nat) bool)) ) 22.70/22.79 ( nat, (fun nat (product_prod nat nat)) ) 22.70/22.79 ( bool, bool ) 22.70/22.79 ( bool, (fun bool bool) ) 22.70/22.79 ( real, nat ) 22.70/22.79 ( real, bool ) 22.70/22.79 ( real, real ) 22.70/22.79 ( real, (fun nat real) ) 22.70/22.79 ( real, (fun real real) ) 22.70/22.79 ( real, (fun (filter nat) bool) ) 22.70/22.79 ( real, complex ) 22.70/22.79 ( real, (fun int bool) ) 22.70/22.79 ( real, (fun bool bool) ) 22.70/22.79 ( real, (fun int (fun int bool)) ) 22.70/22.79 ( real, (fun real complex) ) 22.70/22.79 ( real, (fun real bool) ) 22.70/22.79 ( real, (fun nat (product_prod real real)) ) 22.70/22.79 ( real, (fun real (fun nat (product_prod real real))) ) 22.70/22.79 ( real, (fun (filter real) bool) ) 22.70/22.79 ( real, (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( real, (let ((_let_0 (fun int bool))) (fun _let_0 (fun int _let_0))) ) 22.70/22.79 ( real, (fun int (fun int (fun bool bool))) ) 22.70/22.79 ( real, (fun int (fun nat bool)) ) 22.70/22.79 ( real, (let ((_let_0 (fun nat bool))) (fun _let_0 (fun int _let_0))) ) 22.70/22.79 ( real, (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( real, (fun int (fun nat (fun bool bool))) ) 22.70/22.79 ( real, (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.70/22.79 ( real, (fun (fun nat real) (fun nat bool)) ) 22.70/22.79 ( real, (fun (fun int real) (fun int bool)) ) 22.70/22.79 ( real, (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.70/22.79 ( (fun nat real), (fun nat real) ) 22.70/22.79 ( (fun nat real), (fun nat bool) ) 22.70/22.79 ( (fun nat real), (fun nat (fun real real)) ) 22.70/22.79 ( (fun nat real), (fun int (fun nat real)) ) 22.70/22.79 ( (fun real real), (fun real real) ) 22.70/22.79 ( (fun real real), (fun real (fun real bool)) ) 22.70/22.79 ( (fun real real), (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun real real), (fun real (fun real real)) ) 22.70/22.79 ( (fun real real), (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun nat nat), (fun nat real) ) 22.70/22.79 ( (fun nat nat), (fun nat (fun nat bool)) ) 22.70/22.79 ( (fun nat nat), (fun nat (fun nat nat)) ) 22.70/22.79 ( (filter nat), bool ) 22.70/22.79 ( complex, nat ) 22.70/22.79 ( complex, real ) 22.70/22.79 ( complex, complex ) 22.70/22.79 ( (fun int bool), int ) 22.70/22.79 ( (fun int bool), bool ) 22.70/22.79 ( (fun int bool), (fun int bool) ) 22.70/22.79 ( (fun int bool), (fun int (fun int int)) ) 22.70/22.79 ( (fun int bool), (fun int (fun bool bool)) ) 22.70/22.79 ( (fun int bool), (fun int (fun int bool)) ) 22.70/22.79 ( (fun int bool), (fun (fun int int) (fun int bool)) ) 22.70/22.79 ( (fun int bool), (fun real (fun int (fun int bool))) ) 22.70/22.79 ( (fun int (fun int int)), (let ((_let_0 (fun int int))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( (fun int (fun int int)), (fun int (fun int (fun int bool))) ) 22.70/22.79 ( (product_prod int int), rat ) 22.70/22.79 ( (product_prod int int), int ) 22.70/22.79 ( (product_prod int int), (fun int int) ) 22.70/22.79 ( (product_prod int int), bool ) 22.70/22.79 ( (product_prod int int), (fun int bool) ) 22.70/22.79 ( (product_prod int int), (product_prod int int) ) 22.70/22.79 ( (product_prod int int), (fun (product_prod int int) int) ) 22.70/22.79 ( (product_prod int int), (fun bool bool) ) 22.70/22.79 ( (product_prod int int), (fun (product_prod int int) bool) ) 22.70/22.79 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (product_prod int int), (fun (product_prod int int) (fun int bool)) ) 22.70/22.79 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.70/22.79 ( (product_prod int int), (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun (product_prod int int) int), (fun (product_prod int int) int) ) 22.70/22.79 ( (fun (product_prod int int) int), (fun (product_prod int int) bool) ) 22.70/22.79 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)) ) 22.70/22.79 ( (fun (product_prod int int) int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))) ) 22.70/22.79 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int int)) ) 22.70/22.79 ( (fun bool bool), (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun int (fun bool bool)), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (fun int (fun int bool)), (fun int bool) ) 22.70/22.79 ( (fun int (fun int bool)), (fun int (fun int bool)) ) 22.70/22.79 ( (fun int (fun int bool)), (fun int (fun (fun int int) (fun int bool))) ) 22.70/22.79 ( (fun int (fun int bool)), (fun int (fun int (fun bool bool))) ) 22.70/22.79 ( (fun nat bool), bool ) 22.70/22.79 ( (fun nat bool), (fun nat bool) ) 22.70/22.79 ( (fun nat bool), (fun nat (fun bool bool)) ) 22.70/22.79 ( (fun nat bool), (fun int (fun nat bool)) ) 22.70/22.79 ( (fun nat bool), (fun real (fun int (fun nat bool))) ) 22.70/22.79 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)), bool ) 22.70/22.79 ( (fun (product_prod int int) bool), (fun (product_prod int int) bool) ) 22.70/22.79 ( (fun (product_prod int int) bool), (fun (product_prod int int) (fun bool bool)) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (fun (product_prod int int) (fun int bool)), (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (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)))) ) 22.70/22.79 ( (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)))) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (fun real bool), real ) 22.70/22.79 ( (fun real bool), (fun real bool) ) 22.70/22.79 ( (fun real bool), (fun real (fun bool bool)) ) 22.70/22.79 ( (fun real bool), (fun (fun nat real) (fun nat bool)) ) 22.70/22.79 ( (fun real bool), (fun (fun int real) (fun int bool)) ) 22.70/22.79 ( quickcheck_code_int, int ) 22.70/22.79 ( quickcheck_code_int, nat ) 22.70/22.79 ( quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 22.70/22.79 ( quickcheck_code_int, (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int)) ) 22.70/22.79 ( (fun real (fun real bool)), (fun real (fun (fun nat real) (fun nat bool))) ) 22.70/22.79 ( (fun real (fun real bool)), (fun real (fun (fun int real) (fun int bool))) ) 22.70/22.79 ( code_code_numeral, int ) 22.70/22.79 ( code_code_numeral, nat ) 22.70/22.79 ( code_code_numeral, (fun nat nat) ) 22.70/22.79 ( code_code_numeral, code_code_numeral ) 22.70/22.79 ( code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 22.70/22.79 ( code_code_numeral, (fun code_code_numeral (product_prod code_code_numeral code_code_numeral)) ) 22.70/22.79 ( (fun nat (fun bool bool)), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 22.70/22.79 ( (product_prod real real), bool ) 22.70/22.79 ( (fun (product_prod real real) bool), (fun real (fun real (fun nat (product_prod real real)))) ) 22.70/22.79 ( (filter real), bool ) 22.70/22.79 ( (product_prod nat nat), bool ) 22.70/22.79 ( (product_prod nat nat), (fun (product_prod nat nat) bool) ) 22.70/22.79 ( (fun nat rat), bool ) 22.70/22.79 ( (fun int (fun int (fun int bool))), (fun int (fun int (fun int bool))) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (fun int (fun int (fun bool bool))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)), bool ) 22.70/22.79 ( (fun int real), (fun int bool) ) 22.70/22.79 ( (fun int real), (fun int real) ) 22.70/22.79 ( (fun int real), (fun int (fun real real)) ) 22.70/22.79 ( (fun int real), (fun int (fun int real)) ) 22.70/22.79 ( (fun real (fun int bool)), (fun real bool) ) 22.70/22.79 ( (fun int (fun nat bool)), (fun int bool) ) 22.70/22.79 ( (fun int (fun nat bool)), (fun int (fun nat (fun bool bool))) ) 22.70/22.79 ( (fun real (fun int (fun nat bool))), (fun real (fun int bool)) ) 22.70/22.79 ( (fun real (fun int (fun nat bool))), (fun real (fun int (fun nat (fun bool bool)))) ) 22.70/22.79 ( (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))) ) 22.70/22.79 ( (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)))) ) 22.70/22.79 ( (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.70/22.79 ( (fun int (fun nat real)), (fun int (fun nat bool)) ) 22.70/22.79 ( (fun int (fun nat real)), (fun real (fun int (fun nat bool))) ) 22.70/22.79 ( (fun (fun nat real) (fun nat bool)), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 22.70/22.79 ( (fun real (fun (fun nat real) (fun nat bool))), (fun real (fun (fun int (fun nat real)) (fun int (fun nat bool)))) ) 22.70/22.79 ( (fun int (fun real real)), (let ((_let_0 (fun nat real))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( (fun int (fun real real)), (let ((_let_0 (fun int real))) (fun int (fun _let_0 _let_0))) ) 22.70/22.79 ( (fun (fun int real) (fun int bool)), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 22.70/22.79 ( (fun real (fun int (fun int bool))), (fun real (fun int bool)) ) 22.70/22.79 ( (fun real (fun int (fun int bool))), (fun real (fun int (fun int (fun bool bool)))) ) 22.70/22.79 ( (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)))) ) 22.70/22.79 ( (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun real (fun int (fun _let_0 _let_0)))) ) 22.70/22.79 ( (fun int (fun int real)), (fun int (fun int bool)) ) 22.70/22.79 ( (fun int (fun int real)), (fun real (fun int (fun int bool))) ) 22.70/22.79 ( (fun real (fun (fun int real) (fun int bool))), (fun real (fun (fun int (fun int real)) (fun int (fun int bool)))) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_138981 $$unsorted) (BOUND_VARIABLE_138982 $$unsorted) (BOUND_VARIABLE_138983 $$unsorted) (BOUND_VARIABLE_138984 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (real_normed_vector X_a)) (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_138982) BOUND_VARIABLE_138983) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_138984)))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) BOUND_VARIABLE_138981))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_138984)) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_1) BOUND_VARIABLE_138984))) S_1))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP X_b real (norm_norm X_b) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (minus_minus X_b) (hAPP X_a X_b BOUND_VARIABLE_138982 X_1)) BOUND_VARIABLE_138983))) BOUND_VARIABLE_138981))))) ))) ))))) ) 22.70/22.79 ( real, real, pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (gcd_gcd nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) M) N))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) M)) N))))) ) 22.70/22.79 ( (one_one nat), (hAPP int nat nat_1 t) ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Wa $$unsorted)) (= (and (= A_3 (hAPP int real (number_number_of real) Wa)) (= (zero_zero real) B_2)) (= (hAPP real complex (hAPP real (fun real complex) complex_1 A_3) B_2) (hAPP int complex (number_number_of complex) Wa))) ) 22.70/22.79 ( (one_one real), (zero_zero real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.70/22.79 ( (zero_zero real), (one_one real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.70/22.79 ( (zero_zero real), (zero_zero real), min ) 22.70/22.79 ) 22.70/22.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139122 $$unsorted) (BOUND_VARIABLE_139123 $$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_139123))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_1) BOUND_VARIABLE_139122))) (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_139123) BOUND_VARIABLE_139122))))))) ) 22.70/22.79 ( 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)))) ) 22.70/22.79 ( 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) ) 22.70/22.79 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.70/22.79 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.70/22.79 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.79 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.70/22.79 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.83 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.80/22.83 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.83 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.80/22.83 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.80/22.83 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.80/22.83 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.83 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.80/22.83 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.83 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.83 ( nat, (one_one nat), (one_one nat) ) 22.80/22.83 ) 22.80/22.83 (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 (zero_zero int))) (let ((_let_4 (ord_less_eq 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_4 _let_3) (hAPP int int (hAPP int _let_2 (plus_plus int) A_4) B_4)))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) _let_4 B_4) _let_3))) (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))))) ) 22.80/22.83 ( (ord_less int), (one_one int), t ) 22.80/22.83 ( (ord_less int), min, min ) 22.80/22.83 ( (ord_less int), min, (zero_zero int) ) 22.80/22.83 ( (ord_less int), (zero_zero int), pls ) 22.80/22.83 ( (ord_less int), (zero_zero int), (one_one int) ) 22.80/22.83 ( (ord_less int), (zero_zero int), min ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ( (ord_less_eq int), (one_one int), t ) 22.80/22.83 ( (ord_less_eq int), min, pls ) 22.80/22.83 ( (ord_less_eq int), min, min ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), pls ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), min ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), s ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), skv_4 ) 22.80/22.83 ( (ord_less_eq int), (zero_zero int), skv_5 ) 22.80/22.83 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ( 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) ) 22.80/22.83 ( (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) (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)) ) 22.80/22.83 ( (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (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))) ) 22.80/22.83 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((Xa $$unsorted) (Ya $$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) Ya))) (= (= Xa (hAPP real real _let_2 (hAPP real real _let_1 Z))) (= (hAPP real real _let_1 Xa) (hAPP real real _let_2 Z)))))) ) 22.80/22.83 ( pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.83 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt X)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.80/22.83 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.83 ( (one_one real) ) 22.80/22.83 ( (zero_zero real) ) 22.80/22.83 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_139339 $$unsorted) (BOUND_VARIABLE_139340 $$unsorted) (BOUND_VARIABLE_139341 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (or (not (metric_space X_b)) (not (metric_space X_a)) (= (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((S_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) S_1))) (not (forall ((X_1 $$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 (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) X_1) BOUND_VARIABLE_139341)) S_1))) (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_139341)) (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_139339 X_1)) BOUND_VARIABLE_139340)) R_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_139339) BOUND_VARIABLE_139340) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_139341))))))) ) 22.80/22.83 ( 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)))) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139397 $$unsorted) (BOUND_VARIABLE_139398 $$unsorted) (BOUND_VARIABLE_139399 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_139397))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_139398)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_139399)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_139397))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139398) BOUND_VARIABLE_139399)))))) ) 22.80/22.83 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (real_1 nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= (hAPP real real (hAPP real (fun real real) (minus_minus real) (hAPP nat real _let_0 M)) (hAPP nat real _let_0 N)) (hAPP nat real _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) M) N))))) ) 22.80/22.83 ( (one_one nat), (hAPP int nat nat_1 t) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((P_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 int (hAPP (fun int (fun int int)) (fun _let_0 int) (product_prod_case int int int) (div_div int)) (hAPP rat _let_0 quotient_of P_4)) (hAPP rat int (archim2085082626_floor rat) P_4))) ) 22.80/22.83 ( (one_one rat) ) 22.80/22.83 ( (zero_zero rat) ) 22.80/22.83 ) 22.80/22.83 (instantiation (forall ((Y $$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)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) (one_one real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real arccos Y)))))) ) 22.80/22.83 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.83 ( (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)))) ) 22.80/22.83 ( (zero_zero real) ) 22.80/22.83 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.83 ( skv_10 ) 22.80/22.83 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139476 $$unsorted) (BOUND_VARIABLE_139477 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat real))) (let ((_let_2 (fun real real))) (let ((_let_3 (inverse_divide real))) (let ((_let_4 (times_times real))) (let ((_let_5 (real_1 nat))) (let ((_let_6 (fun nat nat))) (let ((_let_7 (fact_fact nat))) (let ((_let_8 (fun nat bool))) (let ((_let_9 (fun nat _let_2))) (let ((_let_10 (fun _let_1 _let_1))) (let ((_let_11 (combs nat real real))) (let ((_let_12 (fun real _let_2))) (let ((_let_13 (fun _let_1 _let_9))) (let ((_let_14 (combb real _let_2 nat))) (let ((_let_15 (hAPP real _let_1 (power_power real) (zero_zero real)))) (let ((_let_16 (fun X_a real))) (let ((_let_17 (zero_zero X_a))) (or (not (zero X_a)) (not (hBOOL (hAPP nat bool (hAPP nat _let_8 (ord_less nat) _let_0) BOUND_VARIABLE_139477))) (= (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_139476 _let_0) _let_17) (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP _let_8 real (hAPP _let_1 (fun _let_8 real) (big_co1399186613setsum nat real) (hAPP _let_1 _let_1 (hAPP _let_9 _let_10 _let_11 (hAPP _let_1 _let_9 (hAPP _let_12 _let_13 _let_14 _let_3) (hAPP _let_1 _let_1 (hAPP _let_9 _let_10 _let_11 (hAPP _let_1 _let_9 (hAPP _let_12 _let_13 _let_14 _let_4) (hAPP X_a _let_1 (hAPP (fun nat _let_16) (fun X_a _let_1) (combc nat X_a real) BOUND_VARIABLE_139476) _let_17))) _let_15))) (hAPP _let_6 _let_1 (hAPP _let_1 (fun _let_6 _let_1) (combb nat real nat) _let_5) _let_7))) (hAPP nat _let_8 (hAPP nat (fun nat _let_8) (ord_atLeastLessThan nat) _let_0) BOUND_VARIABLE_139477))) (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_2 _let_4 (hAPP X_a real (hAPP nat _let_16 BOUND_VARIABLE_139476 BOUND_VARIABLE_139477) _let_17)) (hAPP nat real _let_15 BOUND_VARIABLE_139477))) (hAPP nat real _let_5 (hAPP nat nat _let_7 BOUND_VARIABLE_139477)))))))))))))))))))))))) ) 22.80/22.84 ( real, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((A_1 $$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 B) (hAPP int int _let_1 A_1)))))) ) 22.80/22.84 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.84 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139557 $$unsorted) (BOUND_VARIABLE_139558 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (ring_11004092258visors X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_139558)) (not (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_139558) BOUND_VARIABLE_139557))))) ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.80/22.84 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.80/22.84 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.80/22.84 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.80/22.84 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.80/22.84 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.80/22.84 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.80/22.84 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.80/22.84 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.80/22.84 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.80/22.84 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y))))) ) 22.80/22.84 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.80/22.84 ( 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))) ) 22.80/22.84 ( v, y ) 22.80/22.84 ( v, sa ) 22.80/22.84 ( v, x ) 22.80/22.84 ( v, r ) 22.80/22.84 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.80/22.84 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.80/22.84 ( w, y ) 22.80/22.84 ( w, sa ) 22.80/22.84 ( w, x ) 22.80/22.84 ( w, r ) 22.80/22.84 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.80/22.84 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.80/22.84 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.80/22.84 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.84 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.80/22.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( skv_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))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((M $$unsorted)) (= M (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) M) (zero_zero nat))) ) 22.80/22.84 ( (one_one nat) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X $$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)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real cos X)) _let_2)))))) ) 22.80/22.84 ( pi ) 22.80/22.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (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)))) ) 22.80/22.84 ( (zero_zero real) ) 22.80/22.84 ( (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))))) ) 22.80/22.84 ( (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) ) 22.80/22.84 ( (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))))) ) 22.80/22.84 ( (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)))) ) 22.80/22.84 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 22.80/22.84 ( skv_10 ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139729 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP real X_a _let_0 BOUND_VARIABLE_139729)) (hAPP real X_a _let_0 (hAPP real real (uminus_uminus real) BOUND_VARIABLE_139729))))) ) 22.80/22.84 ( complex, (one_one real) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139748 $$unsorted) (BOUND_VARIABLE_139749 $$unsorted) (BOUND_VARIABLE_139750 $$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_139749))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_139750))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139750) BOUND_VARIABLE_139748))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_139748)))))) ) 22.80/22.84 ( int, pls, min, pls ) 22.80/22.84 ( int, pls, (zero_zero int), min ) 22.80/22.84 ( int, (one_one int), (zero_zero int), pls ) 22.80/22.84 ( int, min, min, min ) 22.80/22.84 ( int, t, (zero_zero int), (one_one int) ) 22.80/22.84 ( 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))) ) 22.80/22.84 ( 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)))) ) 22.80/22.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real), skv_10 ) 22.80/22.84 ( 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) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139787 $$unsorted)) (or (not (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_139787) (ti X_a BOUND_VARIABLE_139787))) ) 22.80/22.84 ( int, pls ) 22.80/22.84 ( int, min ) 22.80/22.84 ( int, s ) 22.80/22.84 ( int, s1 ) 22.80/22.84 ( int, m ) 22.80/22.84 ( int, t ) 22.80/22.84 ( int, v ) 22.80/22.84 ( int, w ) 22.80/22.84 ( int, y ) 22.80/22.84 ( int, sa ) 22.80/22.84 ( int, x ) 22.80/22.84 ( int, r ) 22.80/22.84 ( int, m1 ) 22.80/22.84 ( int, skv_14 ) 22.80/22.84 ( int, skv_20 ) 22.80/22.84 ( (fun int int), bit1 ) 22.80/22.84 ( (fun int int), bit0 ) 22.80/22.84 ( (fun int int), succ ) 22.80/22.84 ( (fun int int), pred ) 22.80/22.84 ( (fun int int), (fact_fact int) ) 22.80/22.84 ( (fun int int), zfact ) 22.80/22.84 ( nat, n ) 22.80/22.84 ( nat, tn ) 22.80/22.84 ( bool, fTrue ) 22.80/22.84 ( bool, fFalse ) 22.80/22.84 ( real, pi ) 22.80/22.84 ( (fun nat real), (real_1 nat) ) 22.80/22.84 ( (fun nat real), cos_coeff ) 22.80/22.84 ( (fun nat real), sin_coeff ) 22.80/22.84 ( (fun real real), sin ) 22.80/22.84 ( (fun real real), cos ) 22.80/22.84 ( (fun real real), sqrt ) 22.80/22.84 ( (fun real real), tan ) 22.80/22.84 ( (fun real real), ln ) 22.80/22.84 ( (fun real real), arctan ) 22.80/22.84 ( (fun real real), arcsin ) 22.80/22.84 ( (fun real real), arccos ) 22.80/22.84 ( (fun nat nat), suc ) 22.80/22.84 ( (fun nat nat), (fact_fact nat) ) 22.80/22.84 ( (fun nat nat), nat_size ) 22.80/22.84 ( (fun nat nat), (size_size nat) ) 22.80/22.84 ( (fun nat nat), fact ) 22.80/22.84 ( (filter nat), sequentially ) 22.80/22.84 ( (fun int (fun int rat)), fract ) 22.80/22.84 ( complex, ii ) 22.80/22.84 ( (fun int bool), zOdd ) 22.80/22.84 ( (fun int bool), zprime ) 22.80/22.84 ( (fun int bool), zEven ) 22.80/22.84 ( (fun int bool), nat_neg ) 22.80/22.84 ( (fun int bool), nat_is_nat ) 22.80/22.84 ( (fun int bool), (even_odd_even int) ) 22.80/22.84 ( (fun int bool), twoSqu1091635170sum2sq ) 22.80/22.84 ( (fun int (fun int int)), legacy_zgcd ) 22.80/22.84 ( (fun int (fun int int)), (gcd_gcd int) ) 22.80/22.84 ( (fun int (fun int int)), inv ) 22.80/22.84 ( (fun int (fun int int)), multInv ) 22.80/22.84 ( (fun int (fun int int)), legendre ) 22.80/22.84 ( (fun int (fun int int)), standardRes ) 22.80/22.84 ( (fun int (fun int int)), nat_tsub ) 22.80/22.84 ( (fun int (fun int int)), z3div ) 22.80/22.84 ( (fun int (fun int int)), z3mod ) 22.80/22.84 ( (fun int (fun int int)), int_lcm ) 22.80/22.84 ( (fun int (fun int int)), int_gcd ) 22.80/22.84 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.80/22.84 ( (fun bool bool), fNot ) 22.80/22.84 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.80/22.84 ( (fun bool (fun bool bool)), fconj ) 22.80/22.84 ( (fun bool (fun bool bool)), fdisj ) 22.80/22.84 ( (fun bool (fun bool bool)), fimplies ) 22.80/22.84 ( (fun int (fun int bool)), quadRes ) 22.80/22.84 ( (fun int (fun int bool)), d22set ) 22.80/22.84 ( (fun int (fun int bool)), norRRset ) 22.80/22.84 ( (fun int (fun int bool)), sRStar ) 22.80/22.84 ( (fun int (fun int bool)), sr ) 22.80/22.84 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.80/22.84 ( (fun nat bool), (even_odd_even nat) ) 22.80/22.84 ( (fun nat bool), prime ) 22.80/22.84 ( (fun real complex), cis ) 22.80/22.84 ( (fun nat (fun nat bool)), coprime ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.80/22.84 ( (fun (product_prod int int) bool), frac_1 ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.80/22.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.80/22.84 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.80/22.84 ( (fun (fun int bool) bool), nat_nat_set ) 22.80/22.84 ( (fun nat (fun real real)), root ) 22.80/22.84 ( (fun real (fun real real)), log ) 22.80/22.84 ( (fun real (fun real real)), powr ) 22.80/22.84 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.80/22.84 ( (fun complex complex), cnj ) 22.80/22.84 ( (fun complex complex), expi ) 22.80/22.84 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.80/22.84 ( (fun nat (fun nat nat)), nat_gcd ) 22.80/22.84 ( (fun nat (fun nat nat)), nat_lcm ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.80/22.84 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.80/22.84 ( (fun int (fun (fun int bool) bool)), resSet ) 22.80/22.84 ( (fun int nat), nat_1 ) 22.80/22.84 ( (fun int nat), phi ) 22.80/22.84 ( (fun complex real), re ) 22.80/22.84 ( (fun complex real), im ) 22.80/22.84 ( (fun complex real), arg ) 22.80/22.84 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.80/22.84 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.80/22.84 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.80/22.84 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.80/22.84 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.80/22.84 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.80/22.84 ( (fun (product_prod nat nat) bool), pred_nat ) 22.80/22.84 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.80/22.84 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.80/22.84 ( (fun (fun int bool) int), (the int) ) 22.80/22.84 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.80/22.84 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.80/22.84 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.80/22.84 ( (fun real (fun real complex)), rcis ) 22.80/22.84 ( (fun real (fun real complex)), complex_1 ) 22.80/22.84 ( (fun int (fun int (fun int bool))), zcong ) 22.80/22.84 ( (fun int (fun int (fun int bool))), wset ) 22.80/22.84 ( (fun int (fun int (fun int bool))), noXRRset ) 22.80/22.84 ( (fun int (fun int (fun int bool))), bnorRset ) 22.80/22.84 ( (fun int (fun int (fun int bool))), zcongm ) 22.80/22.84 ( (fun real nat), natceiling ) 22.80/22.84 ( (fun real nat), natfloor ) 22.80/22.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.80/22.84 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.80/22.84 ( (fun int real), (real_1 int) ) 22.80/22.84 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.80/22.84 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.80/22.84 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.80/22.84 ( (fun complex nat), (size_size complex) ) 22.80/22.84 ( (fun complex nat), complex_size ) 22.80/22.84 ( (fun (fun nat rat) bool), vanishes ) 22.80/22.84 ( (fun (product_prod int int) rat), frct ) 22.80/22.84 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.80/22.84 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.80/22.84 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.80/22.84 ( (fun rat real), ratreal ) 22.80/22.84 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.80/22.84 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.80/22.84 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.80/22.84 ( (fun rat (product_prod int int)), quotient_of ) 22.80/22.84 ( (fun int (fun nat nat)), nat_aux ) 22.80/22.84 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.80/22.84 ( (fun int (list int)), quickc666637781d_zero ) 22.80/22.84 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.80/22.84 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.80/22.84 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.80/22.84 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.80/22.84 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.80/22.84 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.80/22.84 ( (fun code_code_numeral int), code_int_of ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139808 $$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 X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_139808)) _let_2)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139808) _let_2))))))) ) 22.80/22.84 ( rat, (zero_zero rat) ) 22.80/22.84 ( real, (zero_zero real) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139831 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (number_ring X_a)) (not (linord1117847801e_zero X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_139831))) (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_139831) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.80/22.84 ( real, pi ) 22.80/22.84 ( real, (one_one real) ) 22.80/22.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.80/22.84 ) 22.80/22.84 (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)))) ) 22.80/22.84 ( (one_one real), (zero_zero real) ) 22.80/22.84 ( (zero_zero real), (one_one real) ) 22.80/22.84 ( (zero_zero real), (zero_zero real) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139865 $$unsorted) (BOUND_VARIABLE_139866 $$unsorted) (BOUND_VARIABLE_139867 $$unsorted) (BOUND_VARIABLE_139868 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_139867) BOUND_VARIABLE_139868))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_139865) BOUND_VARIABLE_139866))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_139867) BOUND_VARIABLE_139865)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_139868) BOUND_VARIABLE_139866)))))))) ) 22.80/22.84 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int), (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int (fun int int) (times_times int) K_4))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_1) J_2))) (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 I_1)) (hAPP int int _let_2 J_2))))))) ) 22.80/22.84 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_139903 $$unsorted) (BOUND_VARIABLE_139904 $$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_139903) BOUND_VARIABLE_139904))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_139904) BOUND_VARIABLE_139903))))) ) 22.80/22.84 ( int, pls, (zero_zero int) ) 22.80/22.84 ( int, (one_one int), (zero_zero int) ) 22.80/22.84 ( int, (one_one int), t ) 22.80/22.84 ( int, min, pls ) 22.80/22.84 ( int, min, min ) 22.80/22.84 ( int, min, (zero_zero int) ) 22.80/22.84 ( int, (zero_zero int), pls ) 22.80/22.84 ( int, (zero_zero int), (one_one int) ) 22.80/22.84 ( int, (zero_zero int), min ) 22.80/22.84 ( int, (zero_zero int), s ) 22.80/22.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.84 ( int, (zero_zero int), skv_4 ) 22.80/22.84 ( int, (zero_zero int), skv_5 ) 22.80/22.84 ( 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))), (zero_zero int) ) 22.80/22.84 ( 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))), s ) 22.80/22.84 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 ) 22.80/22.84 ( 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_4 ) 22.80/22.84 ( 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_5 ) 22.80/22.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.80/22.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.84 ( int, t, (one_one int) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.80/22.84 ( nat, n, (zero_zero nat) ) 22.80/22.84 ( nat, tn, (zero_zero nat) ) 22.80/22.84 ( real, pi, (zero_zero real) ) 22.80/22.84 ( 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)) ) 22.80/22.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.84 ( 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)))) ) 22.80/22.84 ( 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))) ) 22.80/22.84 ( 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) ) 22.80/22.84 ( real, (zero_zero real), pi ) 22.80/22.84 ( 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)))) ) 22.80/22.84 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( 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))))) ) 22.80/22.84 ( real, (zero_zero real), skv_10 ) 22.80/22.84 ( real, (zero_zero real), skv_11 ) 22.80/22.84 ( real, (zero_zero real), skv_15 ) 22.80/22.84 ( real, (zero_zero real), skv_18 ) 22.80/22.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.80/22.84 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.84 ( real, skv_2, (zero_zero real) ) 22.80/22.84 ( real, skv_9, (zero_zero real) ) 22.80/22.84 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( real, skv_12, (zero_zero real) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140136 $$unsorted) (BOUND_VARIABLE_140137 $$unsorted) (BOUND_VARIABLE_140138 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_140138))) (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_140138))) (= (= BOUND_VARIABLE_140136 BOUND_VARIABLE_140137) (= (hAPP nat X_a _let_0 BOUND_VARIABLE_140137) (hAPP nat X_a _let_0 BOUND_VARIABLE_140136))))) ) 22.80/22.84 ( 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 ) 22.80/22.84 ( 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 ) 22.80/22.84 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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))), v ) 22.80/22.84 ( 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))), w ) 22.80/22.84 ( 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))), y ) 22.80/22.84 ( 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))), x ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.80/22.84 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.80/22.84 ( 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_6 ) 22.80/22.84 ( 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_7 ) 22.80/22.84 ( 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_16 ) 22.80/22.84 ( 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_23 ) 22.80/22.84 ( 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_24 ) 22.80/22.84 ( 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 ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP real nat natfloor X)) A_1) (hAPP real nat natfloor (hAPP real real (hAPP real (fun real real) (minus_minus real) X) _let_0))))) ) 22.80/22.84 ( (zero_zero nat), pi ) 22.80/22.84 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( (zero_zero nat), skv_10 ) 22.80/22.84 ( (zero_zero nat), skv_11 ) 22.80/22.84 ( (zero_zero nat), skv_15 ) 22.80/22.84 ( (zero_zero nat), skv_18 ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Ya))) (hBOOL (hAPP real bool _let_0 Ya))))) ) 22.80/22.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140294 $$unsorted) (BOUND_VARIABLE_140295 $$unsorted) (BOUND_VARIABLE_140296 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_140294))) (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_140296))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_140295))) (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_140296) BOUND_VARIABLE_140295))))) ) 22.80/22.84 ( int, (zero_zero 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) ) 22.80/22.84 ( int, (zero_zero int), (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.80/22.84 ( 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) ) 22.80/22.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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) ) 22.80/22.84 ( 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) ) 22.80/22.84 ( int, m1, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.80/22.84 ( 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) ) 22.80/22.84 ( int, skv_5, (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) ) 22.80/22.84 ( nat, (zero_zero nat), (one_one nat), (one_one nat) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140333 $$unsorted) (BOUND_VARIABLE_140334 $$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_140333) BOUND_VARIABLE_140334))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_140334) (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_140334)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_140333))))))) ) 22.80/22.84 ( int, (one_one int), t ) 22.80/22.84 ( int, min, pls ) 22.80/22.84 ( int, min, min ) 22.80/22.84 ( int, (zero_zero int), pls ) 22.80/22.84 ( int, (zero_zero int), (one_one int) ) 22.80/22.84 ( int, (zero_zero int), min ) 22.80/22.84 ( int, (zero_zero int), s ) 22.80/22.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.84 ( int, (zero_zero int), skv_4 ) 22.80/22.84 ( int, (zero_zero int), skv_5 ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.84 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.84 ( 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))) ) 22.80/22.84 ( real, (zero_zero real), pi ) 22.80/22.84 ( 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)))) ) 22.80/22.84 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.84 ( real, (zero_zero real), skv_10 ) 22.80/22.84 ( real, (zero_zero real), skv_11 ) 22.80/22.84 ( real, (zero_zero real), skv_15 ) 22.80/22.84 ( real, (zero_zero real), skv_18 ) 22.80/22.84 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.84 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP real bool _let_1 Y))) (= (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real ln X)) (hAPP real real ln Y)) (hAPP real real ln (hAPP real real (hAPP real _let_0 (times_times real) X) Y)))))) ) 22.80/22.84 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( 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))))) ) 22.80/22.84 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( (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)))) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((R_3 $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) ii) (hAPP real complex (of_real complex) R_3)) (hAPP real complex (hAPP real (fun real complex) complex_1 (zero_zero real)) R_3)) ) 22.80/22.84 ( (hAPP int real (number_number_of real) min) ) 22.80/22.84 ( pi ) 22.80/22.84 ( (one_one real) ) 22.80/22.84 ( (zero_zero real) ) 22.80/22.84 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((Xa $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Xa))) (= (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP int nat nat_1 Xa))) (hBOOL (hAPP int bool (even_odd_even int) Xa)))) ) 22.80/22.84 ( pls ) 22.80/22.84 ( (one_one int) ) 22.80/22.84 ( min ) 22.80/22.84 ( (zero_zero int) ) 22.80/22.84 ( s ) 22.80/22.84 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.84 ( t ) 22.80/22.84 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.80/22.84 ( skv_4 ) 22.80/22.84 ( skv_5 ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140429 $$unsorted) (BOUND_VARIABLE_140430 $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a _let_0 BOUND_VARIABLE_140429)) (hAPP nat X_a _let_0 BOUND_VARIABLE_140430)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_140429) BOUND_VARIABLE_140430)))) ) 22.80/22.84 ( int, (zero_zero nat), (zero_zero nat) ) 22.80/22.84 ( int, (zero_zero nat), (one_one nat) ) 22.80/22.84 ) 22.80/22.84 (instantiation (forall ((Xa $$unsorted)) (= (= Xa (hAPP real real (exp real) (hAPP real real ln Xa))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Xa))) ) 22.80/22.84 ( pi ) 22.80/22.84 ( (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)))) ) 22.80/22.84 ( (one_one real) ) 22.80/22.85 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.85 ( skv_2 ) 22.80/22.85 ( skv_9 ) 22.80/22.85 ( skv_12 ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (S $$unsorted) (R_2 $$unsorted)) (let ((_let_0 (fun (product_prod X_a X_b) bool))) (= (forall ((X_1 $$unsorted) (Xa_1 $$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_1) Xa_1)))) (= (hBOOL (hAPP _let_0 bool _let_2 R_2)) (hBOOL (hAPP _let_0 bool _let_2 S))))) ) (= (ti _let_0 S) (ti _let_0 R_2)))) ) 22.80/22.85 ( int, int, frac_1, frac_1 ) 22.80/22.85 ( nat, nat, pred_nat, pred_nat ) 22.80/22.85 ( (product_prod int int), (product_prod int int), ratrel, ratrel ) 22.80/22.85 ( (product_prod nat nat), (product_prod nat nat), pair_less, pair_leq ) 22.80/22.85 ( (product_prod nat nat), (product_prod nat nat), pair_leq, pair_less ) 22.80/22.85 ( (product_prod nat nat), (product_prod nat nat), pair_leq, pair_leq ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140504 $$unsorted) (BOUND_VARIABLE_140505 $$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_140505) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_140504) _let_3))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_140504)) (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_140505) BOUND_VARIABLE_140504)) _let_3))))))) ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.80/22.85 ( 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)))) ) 22.80/22.85 ( 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))) ) 22.80/22.85 ( 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)))) ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.80/22.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.80/22.85 ( 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) ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X $$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)) (= (ti int X) (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) _let_1))) (one_one int)))))) ) 22.80/22.85 ( pls ) 22.80/22.85 ( (one_one int) ) 22.80/22.85 ( min ) 22.80/22.85 ( (zero_zero int) ) 22.80/22.85 ( s ) 22.80/22.85 ( s1 ) 22.80/22.85 ( m ) 22.80/22.85 ( t ) 22.80/22.85 ( v ) 22.80/22.85 ( w ) 22.80/22.85 ( y ) 22.80/22.85 ( sa ) 22.80/22.85 ( x ) 22.80/22.85 ( r ) 22.80/22.85 ( m1 ) 22.80/22.85 ( skv_14 ) 22.80/22.85 ( skv_20 ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140606 $$unsorted) (BOUND_VARIABLE_140607 $$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)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_140607))) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_140606) BOUND_VARIABLE_140607)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_140606)) BOUND_VARIABLE_140607)))))) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.80/22.85 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( 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 ) 22.80/22.85 ( 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))), m1 ) 22.80/22.85 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.80/22.85 ( 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_21 ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.80/22.85 ( int, y, v ) 22.80/22.85 ( int, y, w ) 22.80/22.85 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, sa, v ) 22.80/22.85 ( int, sa, w ) 22.80/22.85 ( int, x, v ) 22.80/22.85 ( int, x, w ) 22.80/22.85 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.85 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, r, v ) 22.80/22.85 ( int, r, w ) 22.80/22.85 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.80/22.85 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.80/22.85 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.80/22.85 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.80/22.85 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.85 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.80/22.85 ( 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)))))) ) 22.80/22.85 ( 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 ) 22.80/22.85 ( complex, ii, ii ) 22.80/22.85 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.80/22.85 ( 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 ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140651 $$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_140651) (zero_zero X_a)) (ti X_a BOUND_VARIABLE_140651))) ) 22.80/22.85 ( int, pls ) 22.80/22.85 ( int, min ) 22.80/22.85 ( int, s ) 22.80/22.85 ( 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)))) ) 22.80/22.85 ( int, s1 ) 22.80/22.85 ( int, m ) 22.80/22.85 ( int, t ) 22.80/22.85 ( int, v ) 22.80/22.85 ( int, w ) 22.80/22.85 ( int, y ) 22.80/22.85 ( int, sa ) 22.80/22.85 ( int, x ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.80/22.85 ( int, r ) 22.80/22.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.80/22.85 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.80/22.85 ( int, m1 ) 22.80/22.85 ( 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))) m1))) ) 22.80/22.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.80/22.85 ( int, skv_14 ) 22.80/22.85 ( int, skv_20 ) 22.80/22.85 ( (fun int int), bit1 ) 22.80/22.85 ( (fun int int), bit0 ) 22.80/22.85 ( (fun int int), succ ) 22.80/22.85 ( (fun int int), pred ) 22.80/22.85 ( (fun int int), (fact_fact int) ) 22.80/22.85 ( (fun int int), zfact ) 22.80/22.85 ( nat, n ) 22.80/22.85 ( nat, tn ) 22.80/22.85 ( nat, (hAPP int nat nat_1 t) ) 22.80/22.85 ( bool, fTrue ) 22.80/22.85 ( bool, fFalse ) 22.80/22.85 ( real, pi ) 22.80/22.85 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.80/22.85 ( (fun nat real), (real_1 nat) ) 22.80/22.85 ( (fun nat real), cos_coeff ) 22.80/22.85 ( (fun nat real), sin_coeff ) 22.80/22.85 ( (fun real real), sin ) 22.80/22.85 ( (fun real real), cos ) 22.80/22.85 ( (fun real real), sqrt ) 22.80/22.85 ( (fun real real), tan ) 22.80/22.85 ( (fun real real), ln ) 22.80/22.85 ( (fun real real), arctan ) 22.80/22.85 ( (fun real real), arcsin ) 22.80/22.85 ( (fun real real), arccos ) 22.80/22.85 ( (fun nat nat), suc ) 22.80/22.85 ( (fun nat nat), (fact_fact nat) ) 22.80/22.85 ( (fun nat nat), nat_size ) 22.80/22.85 ( (fun nat nat), (size_size nat) ) 22.80/22.85 ( (fun nat nat), fact ) 22.80/22.85 ( (filter nat), sequentially ) 22.80/22.85 ( (fun int (fun int rat)), fract ) 22.80/22.85 ( complex, ii ) 22.80/22.85 ( (fun int bool), zOdd ) 22.80/22.85 ( (fun int bool), zprime ) 22.80/22.85 ( (fun int bool), zEven ) 22.80/22.85 ( (fun int bool), nat_neg ) 22.80/22.85 ( (fun int bool), nat_is_nat ) 22.80/22.85 ( (fun int bool), (even_odd_even int) ) 22.80/22.85 ( (fun int bool), twoSqu1091635170sum2sq ) 22.80/22.85 ( (fun int (fun int int)), legacy_zgcd ) 22.80/22.85 ( (fun int (fun int int)), (gcd_gcd int) ) 22.80/22.85 ( (fun int (fun int int)), inv ) 22.80/22.85 ( (fun int (fun int int)), multInv ) 22.80/22.85 ( (fun int (fun int int)), legendre ) 22.80/22.85 ( (fun int (fun int int)), standardRes ) 22.80/22.85 ( (fun int (fun int int)), nat_tsub ) 22.80/22.85 ( (fun int (fun int int)), z3div ) 22.80/22.85 ( (fun int (fun int int)), z3mod ) 22.80/22.85 ( (fun int (fun int int)), int_lcm ) 22.80/22.85 ( (fun int (fun int int)), int_gcd ) 22.80/22.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.80/22.85 ( (fun bool bool), fNot ) 22.80/22.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.80/22.85 ( (fun bool (fun bool bool)), fconj ) 22.80/22.85 ( (fun bool (fun bool bool)), fdisj ) 22.80/22.85 ( (fun bool (fun bool bool)), fimplies ) 22.80/22.85 ( (fun int (fun int bool)), quadRes ) 22.80/22.85 ( (fun int (fun int bool)), d22set ) 22.80/22.85 ( (fun int (fun int bool)), norRRset ) 22.80/22.85 ( (fun int (fun int bool)), sRStar ) 22.80/22.85 ( (fun int (fun int bool)), sr ) 22.80/22.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.80/22.85 ( (fun nat bool), (even_odd_even nat) ) 22.80/22.85 ( (fun nat bool), prime ) 22.80/22.85 ( (fun real complex), cis ) 22.80/22.85 ( (fun nat (fun nat bool)), coprime ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.80/22.85 ( (fun (product_prod int int) bool), frac_1 ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.80/22.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.80/22.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.80/22.85 ( (fun (fun int bool) bool), nat_nat_set ) 22.80/22.85 ( (fun nat (fun real real)), root ) 22.80/22.85 ( (fun real (fun real real)), log ) 22.80/22.85 ( (fun real (fun real real)), powr ) 22.80/22.85 ( code_code_numeral, (zero_zero code_code_numeral) ) 22.80/22.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.80/22.85 ( (fun complex complex), cnj ) 22.80/22.85 ( (fun complex complex), expi ) 22.80/22.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.80/22.85 ( (fun nat (fun nat nat)), nat_gcd ) 22.80/22.85 ( (fun nat (fun nat nat)), nat_lcm ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.80/22.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.80/22.85 ( (fun int (fun (fun int bool) bool)), resSet ) 22.80/22.85 ( (fun int nat), nat_1 ) 22.80/22.85 ( (fun int nat), phi ) 22.80/22.85 ( (fun complex real), re ) 22.80/22.85 ( (fun complex real), im ) 22.80/22.85 ( (fun complex real), arg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.80/22.85 ( (fun (product_prod nat nat) bool), pred_nat ) 22.80/22.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.80/22.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.80/22.85 ( (fun (fun int bool) int), (the int) ) 22.80/22.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.80/22.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.80/22.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.80/22.85 ( (fun real (fun real complex)), rcis ) 22.80/22.85 ( (fun real (fun real complex)), complex_1 ) 22.80/22.85 ( (fun int (fun int (fun int bool))), zcong ) 22.80/22.85 ( (fun int (fun int (fun int bool))), wset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), noXRRset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), bnorRset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), zcongm ) 22.80/22.85 ( (fun real nat), natceiling ) 22.80/22.85 ( (fun real nat), natfloor ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.80/22.85 ( (fun int real), (real_1 int) ) 22.80/22.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.80/22.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.80/22.85 ( (fun complex nat), (size_size complex) ) 22.80/22.85 ( (fun complex nat), complex_size ) 22.80/22.85 ( (fun (fun nat rat) bool), vanishes ) 22.80/22.85 ( (fun (product_prod int int) rat), frct ) 22.80/22.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.80/22.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.80/22.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.80/22.85 ( (fun rat real), ratreal ) 22.80/22.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.80/22.85 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.80/22.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.80/22.85 ( (fun rat (product_prod int int)), quotient_of ) 22.80/22.85 ( (fun int (fun nat nat)), nat_aux ) 22.80/22.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.80/22.85 ( (fun int (list int)), quickc666637781d_zero ) 22.80/22.85 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.80/22.85 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.80/22.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.80/22.85 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.80/22.85 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.80/22.85 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.80/22.85 ( (fun code_code_numeral int), code_int_of ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140670 $$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_140670))) (= (ti X_a BOUND_VARIABLE_140670) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_140670))) ) 22.80/22.85 ( int, pls ) 22.80/22.85 ( int, (one_one int) ) 22.80/22.85 ( int, min ) 22.80/22.85 ( int, s ) 22.80/22.85 ( int, s1 ) 22.80/22.85 ( int, m ) 22.80/22.85 ( 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))) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, t ) 22.80/22.85 ( int, v ) 22.80/22.85 ( int, w ) 22.80/22.85 ( int, y ) 22.80/22.85 ( int, sa ) 22.80/22.85 ( int, x ) 22.80/22.85 ( int, r ) 22.80/22.85 ( int, m1 ) 22.80/22.85 ( int, skv_14 ) 22.80/22.85 ( int, skv_20 ) 22.80/22.85 ( (fun int int), bit1 ) 22.80/22.85 ( (fun int int), bit0 ) 22.80/22.85 ( (fun int int), succ ) 22.80/22.85 ( (fun int int), pred ) 22.80/22.85 ( (fun int int), (fact_fact int) ) 22.80/22.85 ( (fun int int), zfact ) 22.80/22.85 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.85 ( nat, n ) 22.80/22.85 ( nat, tn ) 22.80/22.85 ( bool, fTrue ) 22.80/22.85 ( bool, fFalse ) 22.80/22.85 ( real, pi ) 22.80/22.85 ( 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)))) ) 22.80/22.85 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.85 ( real, skv_2 ) 22.80/22.85 ( real, skv_9 ) 22.80/22.85 ( real, skv_12 ) 22.80/22.85 ( (fun nat real), (real_1 nat) ) 22.80/22.85 ( (fun nat real), cos_coeff ) 22.80/22.85 ( (fun nat real), sin_coeff ) 22.80/22.85 ( (fun real real), sin ) 22.80/22.85 ( (fun real real), cos ) 22.80/22.85 ( (fun real real), sqrt ) 22.80/22.85 ( (fun real real), tan ) 22.80/22.85 ( (fun real real), ln ) 22.80/22.85 ( (fun real real), arctan ) 22.80/22.85 ( (fun real real), arcsin ) 22.80/22.85 ( (fun real real), arccos ) 22.80/22.85 ( (fun nat nat), suc ) 22.80/22.85 ( (fun nat nat), (fact_fact nat) ) 22.80/22.85 ( (fun nat nat), nat_size ) 22.80/22.85 ( (fun nat nat), (size_size nat) ) 22.80/22.85 ( (fun nat nat), fact ) 22.80/22.85 ( (filter nat), sequentially ) 22.80/22.85 ( (fun int (fun int rat)), fract ) 22.80/22.85 ( complex, ii ) 22.80/22.85 ( (fun int bool), zOdd ) 22.80/22.85 ( (fun int bool), zprime ) 22.80/22.85 ( (fun int bool), zEven ) 22.80/22.85 ( (fun int bool), nat_neg ) 22.80/22.85 ( (fun int bool), nat_is_nat ) 22.80/22.85 ( (fun int bool), (even_odd_even int) ) 22.80/22.85 ( (fun int bool), twoSqu1091635170sum2sq ) 22.80/22.85 ( (fun int (fun int int)), legacy_zgcd ) 22.80/22.85 ( (fun int (fun int int)), (gcd_gcd int) ) 22.80/22.85 ( (fun int (fun int int)), inv ) 22.80/22.85 ( (fun int (fun int int)), multInv ) 22.80/22.85 ( (fun int (fun int int)), legendre ) 22.80/22.85 ( (fun int (fun int int)), standardRes ) 22.80/22.85 ( (fun int (fun int int)), nat_tsub ) 22.80/22.85 ( (fun int (fun int int)), z3div ) 22.80/22.85 ( (fun int (fun int int)), z3mod ) 22.80/22.85 ( (fun int (fun int int)), int_lcm ) 22.80/22.85 ( (fun int (fun int int)), int_gcd ) 22.80/22.85 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.80/22.85 ( (fun bool bool), fNot ) 22.80/22.85 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.80/22.85 ( (fun bool (fun bool bool)), fconj ) 22.80/22.85 ( (fun bool (fun bool bool)), fdisj ) 22.80/22.85 ( (fun bool (fun bool bool)), fimplies ) 22.80/22.85 ( (fun int (fun int bool)), quadRes ) 22.80/22.85 ( (fun int (fun int bool)), d22set ) 22.80/22.85 ( (fun int (fun int bool)), norRRset ) 22.80/22.85 ( (fun int (fun int bool)), sRStar ) 22.80/22.85 ( (fun int (fun int bool)), sr ) 22.80/22.85 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.80/22.85 ( (fun nat bool), (even_odd_even nat) ) 22.80/22.85 ( (fun nat bool), prime ) 22.80/22.85 ( (fun real complex), cis ) 22.80/22.85 ( (fun nat (fun nat bool)), coprime ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.80/22.85 ( (fun (product_prod int int) bool), frac_1 ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.80/22.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.80/22.85 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.80/22.85 ( (fun (fun int bool) bool), nat_nat_set ) 22.80/22.85 ( (fun nat (fun real real)), root ) 22.80/22.85 ( (fun real (fun real real)), log ) 22.80/22.85 ( (fun real (fun real real)), powr ) 22.80/22.85 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.80/22.85 ( (fun complex complex), cnj ) 22.80/22.85 ( (fun complex complex), expi ) 22.80/22.85 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.80/22.85 ( (fun nat (fun nat nat)), nat_gcd ) 22.80/22.85 ( (fun nat (fun nat nat)), nat_lcm ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.80/22.85 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.80/22.85 ( (fun int (fun (fun int bool) bool)), resSet ) 22.80/22.85 ( (fun int nat), nat_1 ) 22.80/22.85 ( (fun int nat), phi ) 22.80/22.85 ( (fun complex real), re ) 22.80/22.85 ( (fun complex real), im ) 22.80/22.85 ( (fun complex real), arg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.80/22.85 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.80/22.85 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.80/22.85 ( (fun (product_prod nat nat) bool), pred_nat ) 22.80/22.85 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.80/22.85 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.80/22.85 ( (fun (fun int bool) int), (the int) ) 22.80/22.85 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.80/22.85 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.80/22.85 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.80/22.85 ( (fun real (fun real complex)), rcis ) 22.80/22.85 ( (fun real (fun real complex)), complex_1 ) 22.80/22.85 ( (fun int (fun int (fun int bool))), zcong ) 22.80/22.85 ( (fun int (fun int (fun int bool))), wset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), noXRRset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), bnorRset ) 22.80/22.85 ( (fun int (fun int (fun int bool))), zcongm ) 22.80/22.85 ( (fun real nat), natceiling ) 22.80/22.85 ( (fun real nat), natfloor ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.80/22.85 ( (fun int real), (real_1 int) ) 22.80/22.85 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.80/22.85 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.80/22.85 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.80/22.85 ( (fun complex nat), (size_size complex) ) 22.80/22.85 ( (fun complex nat), complex_size ) 22.80/22.85 ( (fun (fun nat rat) bool), vanishes ) 22.80/22.85 ( (fun (product_prod int int) rat), frct ) 22.80/22.85 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.80/22.85 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.80/22.85 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.80/22.85 ( (fun rat real), ratreal ) 22.80/22.85 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.80/22.85 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.80/22.85 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.80/22.85 ( (fun rat (product_prod int int)), quotient_of ) 22.80/22.85 ( (fun int (fun nat nat)), nat_aux ) 22.80/22.85 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.80/22.85 ( (fun int (list int)), quickc666637781d_zero ) 22.80/22.85 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.80/22.85 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.80/22.85 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.80/22.85 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.80/22.85 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.80/22.85 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.80/22.85 ( (fun code_code_numeral int), code_int_of ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (hAPP X_a X_c B_1_1 (ti X_a B_2_1)) (hAPP X_a X_c B_1_1 B_2_1)) ) 22.80/22.85 ( int, int, bit1, pls ) 22.80/22.85 ( int, int, bit1, min ) 22.80/22.85 ( int, int, (uminus_uminus int), pls ) 22.80/22.85 ( int, int, (uminus_uminus int), min ) 22.80/22.85 ( int, int, bit0, pls ) 22.80/22.85 ( int, int, bit0, min ) 22.80/22.85 ( int, int, succ, pls ) 22.80/22.85 ( int, int, succ, min ) 22.80/22.85 ( int, int, (number_number_of int), pls ) 22.80/22.85 ( int, int, (number_number_of int), min ) 22.80/22.85 ( 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 ) 22.80/22.85 ( int, int, (abs_abs int), v ) 22.80/22.85 ( int, int, (abs_abs int), w ) 22.80/22.85 ( int, int, pred, pls ) 22.80/22.85 ( int, int, pred, min ) 22.80/22.85 ( int, int, (fact_fact int), pls ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), pls ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1 ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) sa), v ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) sa), w ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) x), v ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) x), w ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) y), v ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) y), w ) 22.80/22.85 ( 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 ) 22.80/22.85 ( 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))))), m1 ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) r), v ) 22.80/22.85 ( int, int, (hAPP int (fun int int) (times_times int) r), w ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), v ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), v ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), w ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), w ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), v ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), w ) 22.80/22.85 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w)))))), m1 ) 22.80/22.85 ( int, (fun int int), (times_times int), pls ) 22.80/22.85 ( int, (fun int int), (times_times int), y ) 22.80/22.85 ( int, (fun int int), (times_times int), sa ) 22.80/22.85 ( int, (fun int int), (times_times int), x ) 22.80/22.85 ( int, (fun int int), (times_times int), r ) 22.80/22.85 ( int, (fun int int), (minus_minus int), y ) 22.80/22.85 ( int, (fun int int), (minus_minus int), x ) 22.80/22.85 ( int, nat, (number_number_of nat), pls ) 22.80/22.85 ( int, nat, nat_1, pls ) 22.80/22.85 ( int, nat, nat_1, t ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less int) min), pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less int) min), min ) 22.80/22.85 ( int, bool, nat_neg, pls ) 22.80/22.85 ( int, bool, nat_is_nat, pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 22.80/22.85 ( int, bool, (even_odd_even int), pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less int) pls), min ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 22.80/22.85 ( int, bool, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 22.80/22.85 ( int, real, (number_number_of real), min ) 22.80/22.85 ( int, real, (real_1 int), pls ) 22.80/22.85 ( int, (fun int rat), fract, pls ) 22.80/22.85 ( int, complex, (number_number_of complex), min ) 22.80/22.85 ( int, (fun int bool), (ord_less int), pls ) 22.80/22.85 ( int, (fun int bool), (ord_less int), min ) 22.80/22.85 ( int, (fun int bool), (ord_less int), s ) 22.80/22.85 ( int, (fun int bool), (ord_less int), t ) 22.80/22.85 ( int, (fun int bool), (ord_less int), m1 ) 22.80/22.85 ( int, (fun int bool), (ord_less_eq int), pls ) 22.80/22.85 ( int, (fun int bool), (ord_less_eq int), min ) 22.80/22.85 ( int, (fun int bool), (let ((_let_0 (fun int (fun int bool)))) (hAPP _let_0 _let_0 (combc int int bool) (fequal int))), pls ) 22.80/22.85 ( int, (fun int bool), (hAPP int (fun int (fun int bool)) zcong s1), s ) 22.80/22.85 ( int, (fun nat int), (power_power int), s ) 22.80/22.85 ( int, (fun nat int), (power_power int), s1 ) 22.80/22.85 ( int, (fun nat int), (power_power int), v ) 22.80/22.85 ( int, (fun nat int), (power_power int), w ) 22.80/22.85 ( int, (fun nat int), (power_power int), y ) 22.80/22.85 ( int, (fun nat int), (power_power int), x ) 22.80/22.85 ( int, (fun int (fun int bool)), zcong, s1 ) 22.80/22.85 ( 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 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), pls ) 22.80/22.85 ( int, quickcheck_code_int, (number_number_of quickcheck_code_int), pls ) 22.80/22.85 ( int, code_code_numeral, (number_number_of code_code_numeral), pls ) 22.80/22.85 ( int, (fun int (product_prod int int)), (product_Pair int int), pls ) 22.80/22.85 ( int, (fun int (product_prod int int)), (product_Pair int int), s ) 22.80/22.85 ( nat, int, (semiring_1_of_nat int), n ) 22.80/22.85 ( nat, bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 22.80/22.85 ( nat, bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 22.80/22.85 ( bool, (fun nat bool), (combk bool nat), fTrue ) 22.80/22.85 ( real, bool, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 22.80/22.85 ( real, bool, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 22.80/22.85 ( 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 ) 22.80/22.85 ( 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 ) 22.80/22.85 ( real, real, sin, pi ) 22.80/22.85 ( real, real, cos, pi ) 22.80/22.85 ( real, real, tan, pi ) 22.80/22.85 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.85 ( real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 22.80/22.85 ( real, (fun real real), (inverse_divide real), pi ) 22.80/22.85 ( real, complex, (of_real complex), pi ) 22.80/22.85 ( real, (fun real bool), (ord_less real), pi ) 22.80/22.85 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 22.80/22.85 ( (fun nat real), (fun (fun nat nat) (fun nat real)), (combb nat real nat), (real_1 nat) ) 22.80/22.85 ( (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_1))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun (fun nat real) (fun int (fun nat real))) (combc int (fun nat real) (fun nat real)) (hAPP _let_4 _let_3 (hAPP (fun _let_0 _let_1) (fun _let_4 _let_3) (combb _let_0 _let_1 int) (combb real real nat)) (hAPP _let_2 _let_4 (hAPP (fun real _let_0) (fun _let_2 _let_4) (combb real _let_0 int) (inverse_divide real)) (real_1 int))))))))), (real_1 nat) ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (filter nat), bool, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 22.80/22.85 ( (filter nat), bool, (trivial_limit nat), sequentially ) 22.80/22.85 ( complex, real, re, ii ) 22.80/22.85 ( complex, real, im, ii ) 22.80/22.85 ( complex, complex, cnj, ii ) 22.80/22.85 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 22.80/22.85 ( complex, complex, (uminus_uminus complex), ii ) 22.80/22.85 ( complex, complex, (inverse_inverse complex), ii ) 22.80/22.85 ( 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 ) 22.80/22.85 ( complex, (fun complex complex), (times_times complex), ii ) 22.80/22.85 ( complex, (fun nat complex), (power_power complex), ii ) 22.80/22.85 ( (fun int bool), bool, (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 22.80/22.85 ( (fun int (fun int int)), (fun int (fun int (fun int bool))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int 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 _let_2 _let_3 (combb int _let_1 int) (fequal int))))))), int_gcd ) 22.80/22.85 ( (fun bool bool), (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), (combb bool bool int), fNot ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (fun bool bool), (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (combb bool bool nat), fNot ) 22.80/22.85 ( (fun bool (fun bool bool)), (fun (fun int bool) (fun int (fun bool bool))), (combb bool (fun bool bool) int), fconj ) 22.80/22.85 ( (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 ) 22.80/22.85 ( (fun bool (fun bool bool)), (fun (fun nat bool) (fun nat (fun bool bool))), (combb bool (fun bool bool) nat), fconj ) 22.80/22.85 ( (fun bool (fun bool bool)), (fun (fun real bool) (fun real (fun bool bool))), (combb bool (fun bool bool) real), fconj ) 22.80/22.85 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 22.80/22.85 ( (fun int nat), (fun (fun int bool) bool), (nat_tr1645093318rphism int nat), nat_1 ) 22.80/22.85 ( (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) ) 22.80/22.85 ( (fun int real), (fun int (fun int real)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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))))))))), (real_1 int) ) 22.80/22.85 ) 22.80/22.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140812 $$unsorted) (BOUND_VARIABLE_140813 $$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_140812) BOUND_VARIABLE_140813)) (or (= _let_0 (ti X_a BOUND_VARIABLE_140812)) (= _let_0 (ti X_a BOUND_VARIABLE_140813)))))) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.80/22.85 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( 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 ) 22.80/22.85 ( 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))), m1 ) 22.80/22.85 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.80/22.85 ( 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_21 ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.80/22.85 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.80/22.85 ( int, y, v ) 22.80/22.85 ( int, y, w ) 22.80/22.85 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, sa, v ) 22.80/22.85 ( int, sa, w ) 22.80/22.85 ( int, x, v ) 22.80/22.85 ( int, x, w ) 22.80/22.85 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.85 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, r, v ) 22.80/22.85 ( int, r, w ) 22.80/22.85 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.80/22.85 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.80/22.85 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.80/22.85 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.80/22.85 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.85 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.86 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.80/22.86 ( 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)))))) ) 22.80/22.86 ( 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 ) 22.80/22.86 ( complex, ii, ii ) 22.80/22.86 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.80/22.86 ( 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 ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140856 $$unsorted) (BOUND_VARIABLE_140857 $$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_140856) (ti X_a BOUND_VARIABLE_140857)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_140856) BOUND_VARIABLE_140857)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_140857) BOUND_VARIABLE_140856))))) ) 22.80/22.86 ( int, pls, (zero_zero int) ) 22.80/22.86 ( int, (one_one int), (zero_zero int) ) 22.80/22.86 ( int, (one_one int), t ) 22.80/22.86 ( int, min, min ) 22.80/22.86 ( int, min, (zero_zero int) ) 22.80/22.86 ( int, (zero_zero int), pls ) 22.80/22.86 ( int, (zero_zero int), (one_one int) ) 22.80/22.86 ( int, (zero_zero int), min ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.86 ( int, t, (one_one int) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.86 ( nat, (zero_zero nat), n ) 22.80/22.86 ( nat, (zero_zero nat), tn ) 22.80/22.86 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.80/22.86 ( nat, n, (zero_zero nat) ) 22.80/22.86 ( nat, tn, (zero_zero nat) ) 22.80/22.86 ( real, pi, (zero_zero real) ) 22.80/22.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( 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)) ) 22.80/22.86 ( 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)))) ) 22.80/22.86 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.86 ( 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)))), (zero_zero real) ) 22.80/22.86 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( real, (zero_zero real), pi ) 22.80/22.86 ( 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)))) ) 22.80/22.86 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( 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))))) ) 22.80/22.86 ( real, (zero_zero real), skv_2 ) 22.80/22.86 ( real, (zero_zero real), skv_9 ) 22.80/22.86 ( real, (zero_zero real), skv_12 ) 22.80/22.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.80/22.86 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.86 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.86 ( 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) ) 22.80/22.86 ( 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 ) 22.80/22.86 ( real, skv_2, (zero_zero real) ) 22.80/22.86 ( real, skv_9, (zero_zero real) ) 22.80/22.86 ( real, skv_12, (zero_zero real) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$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 A_3) B_2))) (not (forall ((X_1 $$unsorted)) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 A_3) X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X_1) B_2))) (not (forall ((Y_1 $$unsorted)) (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 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) Y_1)))) )))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F A_3)) (hAPP real real F B_2)))))) ) 22.80/22.86 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.80/22.86 ( sqrt, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.86 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140935 $$unsorted) (BOUND_VARIABLE_140936 $$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 (times_times X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_140935) BOUND_VARIABLE_140936)) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) BOUND_VARIABLE_140935) BOUND_VARIABLE_140936)) (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_140935) _let_0)) (hAPP nat X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_140936) _let_0))))))))) ) 22.80/22.86 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.80/22.86 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.80/22.86 ( 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)))), (one_one int) ) 22.80/22.86 ( 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)))), (hAPP int int (number_number_of int) min) ) 22.80/22.86 ( 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), (one_one int) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.80/22.86 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.86 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.86 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.80/22.86 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.86 ( nat, (one_one nat), (one_one nat) ) 22.80/22.86 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.80/22.86 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.80/22.86 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_140956 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat (fact_fact nat) BOUND_VARIABLE_140956))))) ) 22.80/22.86 ( int, (one_one nat) ) 22.80/22.86 ( real, (one_one nat) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141026 $$unsorted) (BOUND_VARIABLE_141027 $$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 (minus_minus X_a) BOUND_VARIABLE_141026) BOUND_VARIABLE_141027) (hAPP X_a X_a (hAPP X_a _let_0 (plus_plus X_a) BOUND_VARIABLE_141026) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_141027))))) ) 22.80/22.86 ( int, (one_one int), pls ) 22.80/22.86 ( 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)))), (hAPP int int (number_number_of int) min) ) 22.80/22.86 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.86 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.80/22.86 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.86 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 22.80/22.86 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 22.80/22.86 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141099 $$unsorted) (BOUND_VARIABLE_141100 $$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_141099) BOUND_VARIABLE_141100)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141099))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_141100)))) ) 22.80/22.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.80/22.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.80/22.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.80/22.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.80/22.86 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.80/22.86 ( int, y, v ) 22.80/22.86 ( int, y, w ) 22.80/22.86 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, sa, v ) 22.80/22.86 ( int, sa, w ) 22.80/22.86 ( int, x, v ) 22.80/22.86 ( int, x, w ) 22.80/22.86 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.86 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, r, v ) 22.80/22.86 ( int, r, w ) 22.80/22.86 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.80/22.86 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.80/22.86 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.80/22.86 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.86 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.80/22.86 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.80/22.86 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.80/22.86 ( 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)))))) ) 22.80/22.86 ( 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 ) 22.80/22.86 ( complex, ii, ii ) 22.80/22.86 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.80/22.86 ( 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 ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141152 $$unsorted)) (or (not (ring_char_0 X_a)) (= (= (zero_zero int) (ti int BOUND_VARIABLE_141152)) (= (zero_zero X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_141152)))) ) 22.80/22.86 ( real, (one_one int) ) 22.80/22.86 ( real, (zero_zero int) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (norm_norm real) A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) ))) ) 22.80/22.86 ( real ) 22.80/22.86 ( complex ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (R_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (C $$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_2) (hAPP X_b _let_2 (hAPP X_a (fun X_b _let_2) (product_Pair X_a X_b) A_3) B_2)) C))) (hBOOL (hAPP X_c bool (hAPP X_b _let_0 (hAPP X_a _let_1 R_2 A_3) B_2) C)))))) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, int, int, zcong, s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( int, int, int, zcong, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.86 ( (filter nat), (fun nat real), real, (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 22.80/22.86 ( (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))))) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real re X)) (hAPP complex real re (hAPP complex complex (uminus_uminus complex) X))) ) 22.80/22.86 ( ii ) 22.80/22.86 ( (one_one complex) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (finite_finite_1 X_a) A_2))) (= (hAPP _let_1 nat (finite_card _let_0) (hAPP _let_0 _let_1 (pow X_a) A_2)) (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) (hAPP _let_0 nat (finite_card X_a) A_2)))))) ) 22.80/22.86 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_4 (plus_plus real))) (let ((_let_5 (hAPP real real (uminus_uminus real) X))) (= (zero_zero real) (hAPP real real (hAPP real _let_2 _let_4 (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_2 _let_4 (hAPP real real sin _let_5)) (hAPP real real sin X))) _let_3)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_2 (minus_minus real) (hAPP real real cos _let_5)) (hAPP real real cos X))) _let_3))))))))) ) 22.80/22.86 ( (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)))) ) 22.80/22.86 ( (one_one real) ) 22.80/22.86 ( (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) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141345 $$unsorted) (BOUND_VARIABLE_141355 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (semiring_1_of_nat X_a))) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP int bool _let_1 (hAPP int int _let_2 BOUND_VARIABLE_141345)))) (= (hAPP nat X_a _let_3 (hAPP int nat _let_0 BOUND_VARIABLE_141345)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_141345))) (or (hBOOL (hAPP int bool _let_1 (hAPP int int _let_2 BOUND_VARIABLE_141355))) (= (zero_zero X_a) (hAPP nat X_a _let_3 (hAPP int nat _let_0 BOUND_VARIABLE_141355)))))))))) ) 22.80/22.86 ( rat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.80/22.86 ( int, min, min ) 22.80/22.86 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.86 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.80/22.86 ) 22.80/22.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141380 $$unsorted) (BOUND_VARIABLE_141381 $$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_141380) BOUND_VARIABLE_141381))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141381) BOUND_VARIABLE_141380)))))) ) 22.80/22.86 ( int, pls, (zero_zero int) ) 22.80/22.86 ( int, (one_one int), (zero_zero int) ) 22.80/22.86 ( int, (one_one int), t ) 22.80/22.86 ( int, min, min ) 22.80/22.86 ( int, min, (zero_zero int) ) 22.80/22.86 ( int, (zero_zero int), pls ) 22.80/22.86 ( int, (zero_zero int), (one_one int) ) 22.80/22.86 ( int, (zero_zero int), min ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( 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))) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.86 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.80/22.87 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.80/22.87 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.87 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.87 ( int, t, (one_one int) ) 22.80/22.87 ( 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))) ) 22.80/22.87 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( 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))) ) 22.80/22.87 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.87 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( nat, (zero_zero nat), n ) 22.80/22.87 ( nat, (zero_zero nat), tn ) 22.80/22.87 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.80/22.87 ( nat, n, (zero_zero nat) ) 22.80/22.87 ( nat, tn, (zero_zero nat) ) 22.80/22.87 ( real, pi, (zero_zero real) ) 22.80/22.87 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( 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)) ) 22.80/22.87 ( 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)))) ) 22.80/22.87 ( real, (hAPP real real (hAPP 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))) ) 22.80/22.87 ( real, (hAPP real real (hAPP 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) ) 22.80/22.87 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( real, (zero_zero real), pi ) 22.80/22.87 ( 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)))) ) 22.80/22.87 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( 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))))) ) 22.80/22.87 ( real, (zero_zero real), skv_2 ) 22.80/22.87 ( real, (zero_zero real), skv_9 ) 22.80/22.87 ( real, (zero_zero real), skv_12 ) 22.80/22.87 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.80/22.87 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.87 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.80/22.87 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.80/22.87 ( 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) ) 22.80/22.87 ( 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 ) 22.80/22.87 ( real, skv_2, (zero_zero real) ) 22.80/22.87 ( real, skv_9, (zero_zero real) ) 22.80/22.87 ( real, skv_12, (zero_zero real) ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int int (number_number_of int) W))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_2))) (= (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) _let_2) (hAPP _let_1 int (product_fst int int) (hAPP int _let_1 (hAPP int (fun int _let_1) posDivAlg _let_0) _let_2))))))) ) 22.80/22.87 ( pls ) 22.80/22.87 ( (hAPP int int bit1 pls) ) 22.80/22.87 ( min ) 22.80/22.87 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.80/22.87 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141466 $$unsorted) (BOUND_VARIABLE_141467 $$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_141467)) (= (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_141466) BOUND_VARIABLE_141467)) (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_141466) BOUND_VARIABLE_141467)) BOUND_VARIABLE_141467)))))) ) 22.80/22.87 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.80/22.87 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.80/22.87 ( 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) ) 22.80/22.87 ( 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) ) 22.80/22.87 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.80/22.87 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.80/22.87 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.87 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.87 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.80/22.87 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( nat, (one_one nat), (one_one nat) ) 22.80/22.87 ) 22.80/22.87 (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)))) ) 22.80/22.87 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.80/22.87 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.80/22.87 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.80/22.87 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.80/22.87 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.80/22.87 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 22.80/22.87 ( 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))) ) 22.80/22.87 ( v, y ) 22.80/22.87 ( v, sa ) 22.80/22.87 ( v, x ) 22.80/22.87 ( v, r ) 22.80/22.87 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.80/22.87 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.80/22.87 ( w, y ) 22.80/22.87 ( w, sa ) 22.80/22.87 ( w, x ) 22.80/22.87 ( w, r ) 22.80/22.87 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 22.80/22.87 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.80/22.87 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 22.80/22.87 ( y, v ) 22.80/22.87 ( y, w ) 22.80/22.87 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( sa, v ) 22.80/22.87 ( sa, w ) 22.80/22.87 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( x, v ) 22.80/22.87 ( x, w ) 22.80/22.87 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.80/22.87 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( r, v ) 22.80/22.87 ( r, w ) 22.80/22.87 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.80/22.87 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.80/22.87 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.80/22.87 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.80/22.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.80/22.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.80/22.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.80/22.87 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.80/22.87 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.80/22.87 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.80/22.87 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.80/22.87 ( skv_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))) ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= X (hAPP real real (exp real) (hAPP real real ln X)))) ) 22.80/22.87 ( pi ) 22.80/22.87 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( (one_one real) ) 22.80/22.87 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ( skv_2 ) 22.80/22.87 ( skv_9 ) 22.80/22.87 ( skv_12 ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (zero_zero int) (hAPP X_a int (archim2085082626_floor X_a) (zero_zero X_a)))) ) 22.80/22.87 ( rat ) 22.80/22.87 ( int ) 22.80/22.87 ( nat ) 22.80/22.87 ( real ) 22.80/22.87 ( complex ) 22.80/22.87 ( quickcheck_code_int ) 22.80/22.87 ( code_code_numeral ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141582 $$unsorted) (BOUND_VARIABLE_141583 $$unsorted) (BOUND_VARIABLE_141584 $$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 (times_times X_a))) (let ((_let_4 (zero_zero X_a))) (or (not (linord581940658strict X_a)) (= (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_141582) BOUND_VARIABLE_141583)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_141584) BOUND_VARIABLE_141583))) (or (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) BOUND_VARIABLE_141583)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141582) BOUND_VARIABLE_141584))) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141583) _let_4)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141584) BOUND_VARIABLE_141582))))))))))) ) 22.80/22.87 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.80/22.87 ) 22.80/22.87 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP int nat nat_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)) (hAPP nat nat (hAPP nat (fun nat nat) (power_power nat) (hAPP int nat nat_1 X)) N))) ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.80/22.87 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.80/22.87 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.80/22.87 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.80/22.87 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.80/22.87 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.80/22.87 ( (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.87/22.91 ( (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.87/22.91 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.87/22.91 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.87/22.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.87/22.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.87/22.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.87/22.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.87/22.91 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141624 $$unsorted) (BOUND_VARIABLE_141625 $$unsorted) (BOUND_VARIABLE_141626 $$unsorted)) (or (not (order X_a)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_141626 N_1)) (hAPP nat X_a BOUND_VARIABLE_141626 (hAPP nat nat suc N_1)))) )) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_141624) BOUND_VARIABLE_141625)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_141626 BOUND_VARIABLE_141624)) (hAPP nat X_a BOUND_VARIABLE_141626 BOUND_VARIABLE_141625))))) ) 22.87/22.91 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 22.87/22.91 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP int int (uminus_uminus int) A_1) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) (hAPP int int (number_number_of int) min))) ) 22.87/22.91 ( pls ) 22.87/22.91 ( (one_one int) ) 22.87/22.91 ( min ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted) (F $$unsorted)) (or (not (forall ((X_1 $$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_1) (zero_zero real)))) )) (= (hAPP real real F Ya) (hAPP real real F Xa))) ) 22.87/22.91 ( pi, pi, tan ) 22.87/22.91 ( 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)))) ) 22.87/22.91 ( pi, pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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))))))) ) 22.87/22.91 ( pi, (zero_zero real), cos ) 22.87/22.91 ( pi, (zero_zero real), tan ) 22.87/22.91 ( pi, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.91 ( 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 ) 22.87/22.91 ( pi, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), sin ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (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))), sqrt ) 22.87/22.91 ( (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))))) ) 22.87/22.91 ( (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))))) ) 22.87/22.91 ( (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)))) ) 22.87/22.91 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real), sqrt ) 22.87/22.91 ( (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) ) 22.87/22.91 ( (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), cos ) 22.87/22.91 ( (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 ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (hAPP real real (hAPP 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))), cos ) 22.87/22.91 ( (hAPP real real (hAPP 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) ) 22.87/22.91 ( (hAPP real real (hAPP 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) ) 22.87/22.91 ( (hAPP real real (hAPP 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) ) 22.87/22.91 ( (hAPP real real (hAPP 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 bit1 (hAPP int int bit1 pls)))), sin ) 22.87/22.91 ( (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)))), (uminus_uminus real) ) 22.87/22.91 ( (one_one real), (one_one real), ln ) 22.87/22.91 ( (one_one real), (one_one real), arctan ) 22.87/22.91 ( (one_one real), (zero_zero real), arctan ) 22.87/22.91 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), sqrt ) 22.87/22.91 ( (one_one 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 ) 22.87/22.91 ( (zero_zero real), pi, cos ) 22.87/22.91 ( (zero_zero real), pi, tan ) 22.87/22.91 ( (zero_zero real), (one_one real), arctan ) 22.87/22.91 ( (zero_zero real), (zero_zero real), cos ) 22.87/22.91 ( (zero_zero real), (zero_zero real), (sgn_sgn real) ) 22.87/22.91 ( (zero_zero real), (zero_zero real), sqrt ) 22.87/22.91 ( (zero_zero real), (zero_zero real), (inverse_inverse real) ) 22.87/22.91 ( (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 bit0 (hAPP int int bit1 pls))))), sin ) 22.87/22.91 ( (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 bit1 (hAPP int int bit1 pls)))), cos ) 22.87/22.91 ( (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))), (hAPP real (fun real real) (inverse_divide real) pi) ) 22.87/22.91 ( (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 bit0 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) pi) ) 22.87/22.91 ( (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 (hAPP int int bit1 pls)))), (hAPP real (fun real real) (inverse_divide real) pi) ) 22.87/22.91 ( (hAPP real 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), sin ) 22.87/22.91 ( (hAPP real 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))))), sin ) 22.87/22.91 ( (hAPP real 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) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), sin ) 22.87/22.91 ( (hAPP real 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))))), cos ) 22.87/22.91 ( (hAPP real 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))))), tan ) 22.87/22.91 ( (hAPP real real (hAPP 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))), cos ) 22.87/22.91 ( (hAPP real real (hAPP 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)))), cos ) 22.87/22.91 ( (hAPP real real (hAPP 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), (uminus_uminus real) ) 22.87/22.91 ( (hAPP real real (hAPP 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), sin ) 22.87/22.91 ( (hAPP real real (hAPP 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) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi), cos ) 22.87/22.91 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), 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)))) ) 22.87/22.91 ( (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 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 22.87/22.91 ( (hAPP real real (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 ) 22.87/22.91 ( (hAPP real real (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))))), tan ) 22.87/22.91 ( (hAPP real real (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 ) 22.87/22.91 ( (hAPP real real (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 ) 22.87/22.91 ( (hAPP real real (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 bit1 (hAPP int int bit1 pls)))), sin ) 22.87/22.91 ( (hAPP real real (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 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), cos ) 22.87/22.91 ( (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))), sqrt ) 22.87/22.91 ( (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 bit1 (hAPP int int bit1 pls))), (hAPP real (fun real real) (inverse_divide real) pi) ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (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, cos ) 22.87/22.91 ( (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)))), (zero_zero real), tan ) 22.87/22.91 ( (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 (hAPP int int bit1 pls))))), sin ) 22.87/22.91 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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, sin ) 22.87/22.91 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), (hAPP real 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 ) 22.87/22.91 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), (hAPP real real (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 ) 22.87/22.91 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), sin ) 22.87/22.91 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))), cos ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (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 bit0 (hAPP int int bit1 pls))))), arctan ) 22.87/22.91 ( (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))))) ) 22.87/22.91 ( (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)) ) 22.87/22.91 ( (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 ) 22.87/22.91 ( (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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))) ) 22.87/22.91 ( skv_10, skv_10, cos ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141750 $$unsorted) (BOUND_VARIABLE_141751 $$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 (hAPP X_a X_a _let_2 BOUND_VARIABLE_141750)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_141751))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_141751) BOUND_VARIABLE_141750))))))) ) 22.87/22.91 ( int, pls, pls ) 22.87/22.91 ( int, pls, (one_one int) ) 22.87/22.91 ( int, pls, (zero_zero int) ) 22.87/22.91 ( int, (one_one int), pls ) 22.87/22.91 ( int, (one_one int), (one_one int) ) 22.87/22.91 ( int, (one_one int), (zero_zero int) ) 22.87/22.91 ( int, min, min ) 22.87/22.91 ( int, min, (zero_zero int) ) 22.87/22.91 ( int, (zero_zero int), min ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.87/22.91 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.87/22.91 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.87/22.91 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.87/22.91 ( int, t, (one_one int) ) 22.87/22.91 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.87/22.91 ( nat, n, (zero_zero nat) ) 22.87/22.91 ( nat, tn, (zero_zero nat) ) 22.87/22.91 ( real, pi, (zero_zero real) ) 22.87/22.91 ( 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)) ) 22.87/22.91 ( 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)))) ) 22.87/22.91 ( real, (hAPP real real (hAPP 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) ) 22.87/22.91 ( real, (zero_zero real), pi ) 22.87/22.91 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.91 ( 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))))) ) 22.87/22.91 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.87/22.91 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.87/22.91 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.87/22.91 ( real, skv_2, (zero_zero real) ) 22.87/22.91 ( real, skv_9, (zero_zero real) ) 22.87/22.91 ( real, skv_12, (zero_zero real) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya)) zOdd)))))) ) 22.87/22.91 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.87/22.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.87/22.91 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.87/22.91 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 22.87/22.91 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) Na))) (or (hBOOL (hAPP nat bool _let_0 Ma)) (= (= Na Ma) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc Ma)))))) ) 22.87/22.91 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zOdd))) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun int int))) (not (= (ti int Xa) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) K_1)) (one_one int))))) )))) ) 22.87/22.91 ( (one_one int) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= (zero_zero real) (hAPP nat real sin_coeff X_1))) ) 22.87/22.91 ( (zero_zero nat) ) 22.87/22.91 ( (one_one nat) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (= (hAPP nat real sin_coeff X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) X_1) (hAPP nat nat suc (zero_zero nat)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP nat real (real_1 nat) (hAPP nat nat (fact_fact nat) X_1)))))) ) 22.87/22.91 ( (zero_zero nat) ) 22.87/22.91 ( (one_one nat) ) 22.87/22.91 ( (hAPP int nat nat_1 t) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((R_3 $$unsorted)) (= (hAPP real complex (of_real complex) R_3) (hAPP real complex (hAPP real (fun real complex) complex_1 R_3) (zero_zero real))) ) 22.87/22.91 ( (hAPP int real (number_number_of real) min) ) 22.87/22.91 ( pi ) 22.87/22.91 ( (one_one real) ) 22.87/22.91 ( (zero_zero real) ) 22.87/22.91 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 22.87/22.91 ) 22.87/22.91 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (fun (product_prod X_a X_b) X_c))) (or (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (= (hAPP X_b X_c (hAPP X_a (fun X_b X_c) F X_1) Y_1) (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_1) Y_1)))) )) (= (hAPP (fun X_a (fun X_b X_c)) _let_0 (product_prod_case X_a X_b X_c) F) (ti _let_0 G)))) ) 22.87/22.92 ( int, int, int, (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))) (let ((_let_4 (fun _let_0 _let_1))) (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_3 _let_4 (combc int _let_0 _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 int int)) (hAPP _let_0 _let_1 (hAPP _let_1 _let_4 (combb int _let_0 int) (plus_plus int)) _let_5))) _let_5))))))), twoSqu1094008024sum2sq ) 22.87/22.92 ( int, bool, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun int _let_1))) (let ((_let_7 (fun _let_0 _let_6))) (let ((_let_8 (fun int _let_6))) (let ((_let_9 (fun _let_6 _let_6))) (hAPP _let_6 _let_6 (hAPP _let_5 _let_9 (combb _let_1 _let_1 int) (hAPP _let_4 _let_5 (combs int bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_3) (fun _let_1 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_1 (ord_less int) (zero_zero int))))) (hAPP int _let_6 (hAPP _let_8 _let_8 (combc int int _let_1) (hAPP _let_8 _let_8 (hAPP _let_9 (fun _let_8 _let_8) (combb _let_6 _let_6 int) (combc int int bool)) (hAPP _let_2 _let_8 (hAPP _let_7 (fun _let_2 _let_8) (combb _let_0 _let_6 int) (hAPP _let_6 _let_7 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int))))))))))))), frac_1 ) 22.87/22.92 ( 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 ) 22.87/22.92 ( (product_prod int int), bool, (product_prod int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (fun _let_2 _let_4))) (let ((_let_11 (fun _let_2 _let_1))) (let ((_let_12 (fun _let_3 _let_11))) (let ((_let_13 (hAPP (fun int _let_1) _let_12 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_10 (hAPP (fun bool _let_4) (fun (fun _let_2 bool) _let_10) (combb bool _let_4 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_4 _let_7 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_11 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_3 _let_11 _let_13 _let_5)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_3))) (let ((_let_16 (fun _let_3 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_11))) (let ((_let_19 (fun _let_3 _let_3))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_3 _let_15))) (let ((_let_22 (fun _let_2 _let_0))) (let ((_let_23 (hAPP _let_3 _let_22 (hAPP (fun int _let_0) (fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb _let_3 _let_11 _let_2) _let_13) (hAPP _let_3 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_3 _let_3) (hAPP _let_22 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_22 _let_20) (combb _let_0 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_5)))) (hAPP _let_3 _let_15 (hAPP _let_24 _let_21 (combb int _let_3 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_5))))))))))))))))))))))))))))), ratrel ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141919 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (linordered_idom X_a)) (= (not (= _let_0 (ti X_a BOUND_VARIABLE_141919))) (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_141919) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 22.87/22.92 ( int, pls ) 22.87/22.92 ( int, min ) 22.87/22.92 ( int, s ) 22.87/22.92 ( int, s1 ) 22.87/22.92 ( int, m ) 22.87/22.92 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( int, t ) 22.87/22.92 ( int, v ) 22.87/22.92 ( int, w ) 22.87/22.92 ( int, y ) 22.87/22.92 ( int, sa ) 22.87/22.92 ( int, x ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.87/22.92 ( int, r ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.87/22.92 ( int, m1 ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.87/22.92 ( int, skv_6 ) 22.87/22.92 ( int, skv_7 ) 22.87/22.92 ( int, skv_14 ) 22.87/22.92 ( int, skv_16 ) 22.87/22.92 ( int, skv_20 ) 22.87/22.92 ( int, skv_23 ) 22.87/22.92 ( int, skv_24 ) 22.87/22.92 ( (fun int int), bit1 ) 22.87/22.92 ( (fun int int), bit0 ) 22.87/22.92 ( (fun int int), succ ) 22.87/22.92 ( (fun int int), pred ) 22.87/22.92 ( (fun int int), (fact_fact int) ) 22.87/22.92 ( (fun int int), zfact ) 22.87/22.92 ( nat, n ) 22.87/22.92 ( nat, tn ) 22.87/22.92 ( bool, fTrue ) 22.87/22.92 ( bool, fFalse ) 22.87/22.92 ( real, (hAPP int real (number_number_of real) min) ) 22.87/22.92 ( real, pi ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( (fun nat real), (real_1 nat) ) 22.87/22.92 ( (fun nat real), cos_coeff ) 22.87/22.92 ( (fun nat real), sin_coeff ) 22.87/22.92 ( (fun real real), sin ) 22.87/22.92 ( (fun real real), cos ) 22.87/22.92 ( (fun real real), sqrt ) 22.87/22.92 ( (fun real real), tan ) 22.87/22.92 ( (fun real real), ln ) 22.87/22.92 ( (fun real real), arctan ) 22.87/22.92 ( (fun real real), arcsin ) 22.87/22.92 ( (fun real real), arccos ) 22.87/22.92 ( (fun nat nat), suc ) 22.87/22.92 ( (fun nat nat), (fact_fact nat) ) 22.87/22.92 ( (fun nat nat), nat_size ) 22.87/22.92 ( (fun nat nat), (size_size nat) ) 22.87/22.92 ( (fun nat nat), fact ) 22.87/22.92 ( (filter nat), sequentially ) 22.87/22.92 ( (fun int (fun int rat)), fract ) 22.87/22.92 ( complex, ii ) 22.87/22.92 ( (fun int bool), zOdd ) 22.87/22.92 ( (fun int bool), zprime ) 22.87/22.92 ( (fun int bool), zEven ) 22.87/22.92 ( (fun int bool), nat_neg ) 22.87/22.92 ( (fun int bool), nat_is_nat ) 22.87/22.92 ( (fun int bool), (even_odd_even int) ) 22.87/22.92 ( (fun int bool), twoSqu1091635170sum2sq ) 22.87/22.92 ( (fun int (fun int int)), legacy_zgcd ) 22.87/22.92 ( (fun int (fun int int)), (gcd_gcd int) ) 22.87/22.92 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bool)), sr ) 22.87/22.92 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.87/22.92 ( (fun nat bool), (even_odd_even nat) ) 22.87/22.92 ( (fun nat bool), prime ) 22.87/22.92 ( (fun real complex), cis ) 22.87/22.92 ( (fun nat (fun nat bool)), coprime ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.87/22.92 ( (fun (product_prod int int) bool), frac_1 ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.87/22.92 ( (fun int (fun (product_prod int int) bool)), 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code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.87/22.92 ( (fun real (fun real complex)), rcis ) 22.87/22.92 ( (fun real (fun real complex)), complex_1 ) 22.87/22.92 ( (fun int (fun int (fun int bool))), zcong ) 22.87/22.92 ( (fun int (fun int (fun int bool))), wset ) 22.87/22.92 ( (fun int (fun int (fun int bool))), noXRRset ) 22.87/22.92 ( (fun int (fun int (fun int bool))), bnorRset ) 22.87/22.92 ( (fun int (fun int (fun int bool))), zcongm ) 22.87/22.92 ( (fun real nat), natceiling ) 22.87/22.92 ( (fun real nat), natfloor ) 22.87/22.92 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.87/22.92 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.87/22.92 ( (fun int real), (real_1 int) ) 22.87/22.92 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.87/22.92 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.87/22.92 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.87/22.92 ( (fun complex nat), (size_size complex) ) 22.87/22.92 ( (fun complex nat), complex_size ) 22.87/22.92 ( (fun (fun nat rat) bool), vanishes ) 22.87/22.92 ( (fun (product_prod int int) rat), frct ) 22.87/22.92 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.87/22.92 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.87/22.92 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.87/22.92 ( (fun rat real), ratreal ) 22.87/22.92 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.87/22.92 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.87/22.92 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.87/22.92 ( (fun rat (product_prod int int)), quotient_of ) 22.87/22.92 ( (fun int (fun nat nat)), nat_aux ) 22.87/22.92 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.87/22.92 ( (fun int (list int)), quickc666637781d_zero ) 22.87/22.92 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.87/22.92 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.87/22.92 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.87/22.92 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.87/22.92 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.87/22.92 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.87/22.92 ( (fun code_code_numeral int), code_int_of ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun nat _let_1))) (let ((_let_5 (fun _let_0 _let_0))) (let ((_let_6 (fun (fun nat nat) _let_0))) (let ((_let_7 (combb nat real nat))) (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) Xa)) _let_3))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto nat real) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 (combs nat real real) (hAPP _let_0 _let_4 (hAPP (fun real _let_1) (fun _let_0 _let_4) (combb real _let_1 nat) (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_5 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_3)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_6 _let_7 (real_1 nat)) _let_9)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_6 _let_7 (hAPP real _let_0 (power_power real) Xa)) _let_9))) (zero_zero real)) sequentially))))))))))))) ) 22.87/22.92 ( (hAPP int real (number_number_of real) min) ) 22.87/22.92 ( (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)))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_141980 $$unsorted) (BOUND_VARIABLE_141981 $$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_141980) BOUND_VARIABLE_141981))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int _let_0 BOUND_VARIABLE_141980)) (hAPP X_a int _let_0 BOUND_VARIABLE_141981))))) ) 22.87/22.92 ( int, (one_one int), t ) 22.87/22.92 ( int, min, pls ) 22.87/22.92 ( int, min, min ) 22.87/22.92 ( int, (zero_zero int), pls ) 22.87/22.92 ( int, (zero_zero int), (one_one int) ) 22.87/22.92 ( int, (zero_zero int), min ) 22.87/22.92 ( int, (zero_zero int), s ) 22.87/22.92 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), skv_4 ) 22.87/22.92 ( int, (zero_zero int), skv_5 ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.87/22.92 ( real, (hAPP real real (hAPP 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))) ) 22.87/22.92 ( real, (zero_zero real), pi ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.92 ( real, (zero_zero real), skv_10 ) 22.87/22.92 ( real, (zero_zero real), skv_11 ) 22.87/22.92 ( real, (zero_zero real), skv_15 ) 22.87/22.92 ( real, (zero_zero real), skv_18 ) 22.87/22.92 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.87/22.92 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (times_times int))) (or (not (= (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_2 A_1) B)) C_1) (hAPP nat int (hAPP int (fun nat int) (power_power int) D_3) N))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) N))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd A_1) B))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd B) C_1))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd C_1) A_1))) (and (not (forall ((K_1 $$unsorted)) (not (= (hAPP int int (abs_abs int) A_1) (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) N))) )) (not (forall ((L_3 $$unsorted)) (not (= (hAPP int int (abs_abs int) B) (hAPP nat int (hAPP int (fun nat int) (power_power int) L_3) N))) )) (not (forall ((M_2 $$unsorted)) (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) M_2) N) (hAPP int int (abs_abs int) C_1))) ))))))) ) 22.87/22.92 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))), v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((A_2 $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun nat bool))) (or (not (hBOOL (hAPP int bool nat_is_nat Xa))) (not (hBOOL (hAPP _let_0 bool nat_nat_set A_2))) (= (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) A_2)) (hBOOL (hAPP _let_1 bool (hAPP nat (fun _let_1 bool) (member nat) (hAPP int nat nat_1 Xa)) (hAPP _let_0 _let_1 (hAPP (fun int nat) (fun _let_0 _let_1) (image int nat) nat_1) A_2))))))) ) 22.87/22.92 ( zEven, (one_one int) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (minus_minus X_a))) (or (not (minus X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 22.87/22.92 ( rat ) 22.87/22.92 ( int ) 22.87/22.92 ( (fun int int) ) 22.87/22.92 ( nat ) 22.87/22.92 ( bool ) 22.87/22.92 ( real ) 22.87/22.92 ( (fun nat real) ) 22.87/22.92 ( (fun real real) ) 22.87/22.92 ( complex ) 22.87/22.92 ( (fun int bool) ) 22.87/22.92 ( (product_prod int int) ) 22.87/22.92 ( (fun (product_prod int int) int) ) 22.87/22.92 ( (fun int (fun int bool)) ) 22.87/22.92 ( (fun nat bool) ) 22.87/22.92 ( (fun (product_prod int int) bool) ) 22.87/22.92 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.87/22.92 ( (fun real bool) ) 22.87/22.92 ( quickcheck_code_int ) 22.87/22.92 ( code_code_numeral ) 22.87/22.92 ( (fun int (fun int (fun int bool))) ) 22.87/22.92 ( (fun int real) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((P_2 $$unsorted) (P_1 $$unsorted) (Xa $$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)) Xa)))) (or (and _let_2 (= (not _let_0) _let_1)) (= (and _let_2 _let_0) (and _let_1 _let_2)))))) ) 22.87/22.92 ( (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (one_one int) ) 22.87/22.92 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int nat (number_number_of nat) _let_1))) (let ((_let_3 (fun int bool))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int bool (hAPP int _let_3 (hAPP int (fun int _let_3) zcong (hAPP nat int (hAPP int _let_4 _let_5 s) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 s1) _let_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 _let_1))) m)) (one_one int))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int nat (number_number_of nat) _let_1))) (let ((_let_3 (fun int bool))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int bool (hAPP int _let_3 (hAPP int (fun int _let_3) zcong (hAPP nat int (hAPP int _let_4 _let_5 s) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 s1) _let_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 _let_1))) m)) (one_one int))))))))), pls ) 22.87/22.92 ( (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.92 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (one_one int)), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (one_one int)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( fTrue, fTrue, min ) 22.87/22.92 ( (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.87/22.92 ( (hAPP real bool (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))))), (hAPP real bool (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))))), skv_4 ) 22.87/22.92 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), skv_5 ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142118 $$unsorted) (BOUND_VARIABLE_142119 $$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_142118) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_142119) E))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_142118) BOUND_VARIABLE_142119))) ) 22.87/22.92 ( int, (one_one int), t ) 22.87/22.92 ( int, min, pls ) 22.87/22.92 ( int, min, min ) 22.87/22.92 ( int, (zero_zero int), pls ) 22.87/22.92 ( int, (zero_zero int), (one_one int) ) 22.87/22.92 ( int, (zero_zero int), min ) 22.87/22.92 ( int, (zero_zero int), s ) 22.87/22.92 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), skv_4 ) 22.87/22.92 ( int, (zero_zero int), skv_5 ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.87/22.92 ( real, (hAPP real real (hAPP 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))) ) 22.87/22.92 ( real, (zero_zero real), pi ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.92 ( real, (zero_zero real), skv_10 ) 22.87/22.92 ( real, (zero_zero real), skv_11 ) 22.87/22.92 ( real, (zero_zero real), skv_15 ) 22.87/22.92 ( real, (zero_zero real), skv_18 ) 22.87/22.92 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.87/22.92 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142168 $$unsorted) (BOUND_VARIABLE_142169 $$unsorted) (BOUND_VARIABLE_142170 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_142169))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_142170))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_142170) BOUND_VARIABLE_142168))))) ) 22.87/22.92 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( int, skv_21, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_0 (inverse_divide real))) (let ((_let_1 (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_1 (hAPP real real (hAPP real (fun real real) _let_0 X) Y)) (hAPP real real (hAPP real (fun real real) _let_0 (hAPP real real _let_1 X)) (hAPP real real _let_1 Y)))))) ) 22.87/22.92 ( (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))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((Nat_1 $$unsorted)) (= (hAPP nat nat nat_size (hAPP nat nat suc Nat_1)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP nat nat nat_size Nat_1)) (hAPP nat nat suc (zero_zero nat)))) ) 22.87/22.92 ( (zero_zero nat) ) 22.87/22.92 ( (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.92 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.87/22.92 ) 22.87/22.92 (instantiation (forall ((X_a $$unsorted) (A_3 $$unsorted) (Ra $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP (fun X_a _let_0) _let_0 (accp X_a) Ra))) (or (not (hBOOL (hAPP X_a bool _let_1 B_2))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 Ra A_3) B_2))) (hBOOL (hAPP X_a bool _let_1 A_3))))) ) 22.87/22.92 ( int, (one_one int), (ord_less int), t ) 22.87/22.92 ( int, (one_one int), (ord_less_eq int), t ) 22.87/22.92 ( int, min, (ord_less int), min ) 22.87/22.92 ( int, min, (ord_less int), (zero_zero int) ) 22.87/22.92 ( int, min, (ord_less_eq int), pls ) 22.87/22.92 ( int, min, (ord_less_eq int), min ) 22.87/22.92 ( int, (zero_zero int), (ord_less int), pls ) 22.87/22.92 ( int, (zero_zero int), (ord_less int), (one_one int) ) 22.87/22.92 ( int, (zero_zero int), (ord_less int), min ) 22.87/22.92 ( int, (zero_zero 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))) ) 22.87/22.92 ( int, (zero_zero int), (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), pls ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), (one_one int) ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), min ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), s ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), skv_4 ) 22.87/22.92 ( int, (zero_zero int), (ord_less_eq int), skv_5 ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.87/22.92 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.87/22.92 ( int, (hAPP int int (number_number_of int) min), (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))) ) 22.87/22.92 ( int, (hAPP int int (number_number_of int) min), (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))) ) 22.87/22.92 ( int, (hAPP int int (number_number_of int) min), (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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))) ) 22.87/22.92 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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))) ) 22.87/22.92 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (dvd_dvd int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( int, m1, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( 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))) ) 22.87/22.92 ( int, skv_5, (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))) ) 22.87/22.92 ( int, skv_5, (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))) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (ord_less_eq int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.92 ( nat, (zero_zero nat), (ord_less nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ( nat, (zero_zero nat), (ord_less nat), n ) 22.87/22.92 ( nat, (zero_zero nat), (ord_less nat), tn ) 22.87/22.92 ( real, pi, (ord_less real), (zero_zero real) ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (ord_less_eq real), pi ) 22.87/22.92 ( real, (hAPP real real (hAPP 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))) ) 22.87/22.92 ( real, (hAPP real real (hAPP 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))) ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (zero_zero real), (ord_less real), pi ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (zero_zero real), (ord_less real), skv_2 ) 22.87/22.92 ( real, (zero_zero real), (ord_less real), skv_9 ) 22.87/22.92 ( real, (zero_zero real), (ord_less real), skv_12 ) 22.87/22.92 ( real, (zero_zero real), (ord_less_eq real), pi ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( 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)))) ) 22.87/22.92 ( real, (zero_zero real), (ord_less_eq real), skv_10 ) 22.87/22.92 ( real, (zero_zero real), (ord_less_eq real), skv_11 ) 22.87/22.92 ( real, (zero_zero real), (ord_less_eq real), skv_15 ) 22.87/22.92 ( real, (zero_zero real), (ord_less_eq real), skv_18 ) 22.87/22.92 ( 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) ) 22.87/22.92 ( 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) ) 22.87/22.92 ( 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) ) 22.87/22.92 ( 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 ) 22.87/22.92 ( real, skv_10, (ord_less_eq real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.92 ) 22.87/22.93 (instantiation (forall ((N $$unsorted)) (= (hAPP nat real (semiring_1_of_nat real) N) (hAPP complex real re (hAPP nat complex (semiring_1_of_nat complex) N))) ) 22.87/22.93 ( (zero_zero nat) ) 22.87/22.93 ( (one_one nat) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) Na)) (not (forall ((K_1 $$unsorted)) (not (= Na (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) K_1)))) ))) ) 22.87/22.93 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( (zero_zero nat), n ) 22.87/22.93 ( (zero_zero nat), tn ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) M) N))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) M) N))) ) 22.87/22.93 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( (zero_zero nat), n ) 22.87/22.93 ( (zero_zero nat), tn ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod int int))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (hAPP int int (hAPP int (fun int int) (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 _let_2 negDivAlg A_1))) (let ((_let_6 (hAPP int _let_0 _let_5 B))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (and (or _let_4 (= _let_6 (hAPP _let_0 _let_0 (hAPP int (fun _let_0 _let_0) adjust B) (hAPP int _let_0 _let_5 (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)))) B))))) (or (not _let_4) (= _let_6 (hAPP int _let_0 (hAPP int _let_2 (product_Pair int int) (hAPP int int _let_1 min)) _let_3)))))))))))) ) 22.87/22.93 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.87/22.93 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.87/22.93 ( (hAPP nat int (hAPP 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) ) 22.87/22.93 ( (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) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.87/22.93 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (number_number_of real))) (let ((_let_3 (fun real real))) (let ((_let_4 (times_times real))) (let ((_let_5 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_6 (hAPP int nat (number_number_of nat) _let_5))) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_3 _let_4 (hAPP int real _let_2 _let_5)) X)) _let_6) (hAPP real real (hAPP real _let_3 _let_4 (hAPP int real _let_2 (hAPP int int bit0 _let_5))) (hAPP nat real (hAPP real _let_0 _let_1 X) _let_6)))))))))) ) 22.87/22.93 ( pi ) 22.87/22.93 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (inverse_divide real))) (let ((_let_4 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_5 (hAPP complex real im X))) (let ((_let_6 (hAPP real real (hAPP real _let_2 (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re X)) _let_4)) (hAPP nat real (hAPP real _let_0 _let_1 _let_5) _let_4)))) (= (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real (hAPP real _let_2 _let_3 (hAPP complex real re X)) _let_6)) (hAPP real real (hAPP real _let_2 _let_3 (hAPP real real (uminus_uminus real) _let_5)) _let_6)) (hAPP complex complex (inverse_inverse complex) X))))))))) ) 22.87/22.93 ( (zero_zero complex) ) 22.87/22.93 ( ii ) 22.87/22.93 ( (one_one complex) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((N $$unsorted)) (= (hAPP real int (archim2085082626_floor real) (hAPP nat real (real_1 nat) N)) (hAPP nat int (semiring_1_of_nat int) N)) ) 22.87/22.93 ( (zero_zero nat) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( (one_one nat) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.93 ( n ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B) (hAPP rat int (archim2085082626_floor rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B))) ) 22.87/22.93 ( (one_one int), (one_one int) ) 22.87/22.93 ( (zero_zero int), (one_one int) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142526 $$unsorted) (BOUND_VARIABLE_142527 $$unsorted) (BOUND_VARIABLE_142528 $$unsorted)) (or (not (order X_a)) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_142528 N_1)) (hAPP nat X_a BOUND_VARIABLE_142528 (hAPP nat nat suc N_1)))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_142526) BOUND_VARIABLE_142527))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_142528 BOUND_VARIABLE_142526)) (hAPP nat X_a BOUND_VARIABLE_142528 BOUND_VARIABLE_142527)))) ) 22.87/22.93 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (hAPP int int (number_number_of int) min))) (let ((_let_2 (ti int Na))) (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) Na))))))) ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.87/22.93 ( y, v ) 22.87/22.93 ( y, w ) 22.87/22.93 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( sa, v ) 22.87/22.93 ( sa, w ) 22.87/22.93 ( x, v ) 22.87/22.93 ( x, w ) 22.87/22.93 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.93 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( r, v ) 22.87/22.93 ( r, w ) 22.87/22.93 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.87/22.93 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.87/22.93 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.87/22.93 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.87/22.93 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (even_odd_even nat))) (= (not (hBOOL (hAPP nat bool _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Ma) Na)))) (= (hBOOL (hAPP nat bool _let_0 Ma)) (not (hBOOL (hAPP nat bool _let_0 Na)))))) ) 22.87/22.93 ( (one_one nat), (one_one nat) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142620 $$unsorted) (BOUND_VARIABLE_142621 $$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_142621)) (= (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_142621)) BOUND_VARIABLE_142620) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_142621) BOUND_VARIABLE_142620))))))) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.87/22.93 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.87/22.93 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.87/22.93 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.87/22.93 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.87/22.93 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.87/22.93 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.87/22.93 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.87/22.93 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.87/22.93 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Na $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real bool))) (let ((_let_3 (hAPP real _let_2 (ord_less real) (zero_zero real)))) (let ((_let_4 (fun real _let_2))) (let ((_let_5 (fun real _let_1))) (or (not (hBOOL (hAPP real bool _let_3 Xa))) (= (hAPP _let_2 real (the real) (hAPP _let_2 _let_2 (hAPP _let_5 (fun _let_2 _let_2) (combs real bool bool) (hAPP _let_2 _let_5 (hAPP (fun bool _let_1) (fun _let_2 _let_5) (combb bool _let_1 real) fconj) _let_3)) (hAPP real _let_2 (hAPP _let_4 _let_4 (combc real real bool) (hAPP _let_0 _let_4 (hAPP _let_4 (fun _let_0 _let_4) (combb real _let_2 real) (fequal real)) (hAPP nat _let_0 (hAPP (fun real (fun nat real)) (fun nat _let_0) (combc real nat real) (power_power real)) Na))) Xa))) (hAPP real real (hAPP nat _let_0 root Na) Xa))))))))) ) 22.87/22.93 ( (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))) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 22.87/22.93 ( (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))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Na $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less real))) (let ((_let_5 (hAPP real _let_3 _let_4 _let_2))) (let ((_let_6 (fun real _let_3))) (let ((_let_7 (uminus_uminus real))) (let ((_let_8 (fun real _let_1))) (let ((_let_9 (hAPP real real (hAPP nat _let_0 root Na) Xa))) (let ((_let_10 (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 Xa) _let_2)))) (or (hBOOL (hAPP real bool _let_5 Xa)) (and (or (not _let_10) (= _let_9 (hAPP real real _let_7 (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_8 (fun _let_3 _let_3) (combs real bool bool) (hAPP _let_3 _let_8 (hAPP (fun bool _let_1) (fun _let_3 _let_8) (combb bool _let_1 real) fconj) _let_5)) (hAPP real _let_3 (hAPP _let_6 _let_6 (combc real real bool) (hAPP _let_0 _let_6 (hAPP _let_6 (fun _let_0 _let_6) (combb real _let_3 real) (fequal real)) (hAPP nat _let_0 (hAPP (fun real (fun nat real)) (fun nat _let_0) (combc real nat real) (power_power real)) Na))) (hAPP real real _let_7 Xa))))))) (or _let_10 (= _let_2 _let_9))))))))))))))) ) 22.87/22.93 ( (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))) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero real) ) 22.87/22.93 ( (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))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y))))) ) 22.87/22.93 ( (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)))) ) 22.87/22.93 ( (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) ) 22.87/22.93 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 22.87/22.93 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 22.87/22.93 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.87/22.93 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.87/22.93 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.87/22.93 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.87/22.93 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.87/22.93 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142711 $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (hAPP nat real (semiring_1_of_nat real) BOUND_VARIABLE_142711)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_142711))) ) 22.87/22.93 ( int, (zero_zero nat) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( int, (one_one nat) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.93 ( int, n ) 22.87/22.93 ( real, (zero_zero nat) ) 22.87/22.93 ( real, (one_one nat) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) P_5))) ) 22.87/22.93 ( (zero_zero nat) ) 22.87/22.93 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_142912 $$unsorted)) (or (not (linordered_semidom X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_142912)))) ) 22.87/22.93 ( int, (zero_zero nat) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( int, (one_one nat) ) 22.87/22.93 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.93 ( int, n ) 22.87/22.93 ( real, (zero_zero nat) ) 22.87/22.93 ( real, (one_one nat) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fact_fact nat))) (let ((_let_2 (minus_minus nat))) (let ((_let_3 (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc M)) N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) N) (hAPP nat nat suc M)))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) _let_3) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 _let_2 M) N))) (hAPP nat nat _let_1 _let_3))))))) ) 22.87/22.93 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X_a $$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)))) ) 22.87/22.93 ( rat ) 22.87/22.93 ( int ) 22.87/22.93 ( (fun int int) ) 22.87/22.93 ( nat ) 22.87/22.93 ( bool ) 22.87/22.93 ( real ) 22.87/22.93 ( (fun nat real) ) 22.87/22.93 ( (fun real real) ) 22.87/22.93 ( complex ) 22.87/22.93 ( (fun int bool) ) 22.87/22.93 ( (product_prod int int) ) 22.87/22.93 ( (fun (product_prod int int) int) ) 22.87/22.93 ( (fun int (fun int bool)) ) 22.87/22.93 ( (fun nat bool) ) 22.87/22.93 ( (fun (product_prod int int) bool) ) 22.87/22.93 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.87/22.93 ( (fun real bool) ) 22.87/22.93 ( quickcheck_code_int ) 22.87/22.93 ( code_code_numeral ) 22.87/22.93 ( (fun int (fun int (fun int bool))) ) 22.87/22.93 ( (fun int real) ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (ti int X))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) X))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) X) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (= _let_1 _let_2) (= (one_one int) _let_2))))) ) 22.87/22.93 ( pls ) 22.87/22.93 ( (one_one int) ) 22.87/22.93 ( min ) 22.87/22.93 ( (zero_zero int) ) 22.87/22.93 ( s ) 22.87/22.93 ( s1 ) 22.87/22.93 ( m ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.93 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.93 ( t ) 22.87/22.93 ( v ) 22.87/22.93 ( w ) 22.87/22.93 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.93 ( y ) 22.87/22.93 ( sa ) 22.87/22.93 ( x ) 22.87/22.93 ( r ) 22.87/22.93 ( m1 ) 22.87/22.93 ( skv_4 ) 22.87/22.93 ( skv_5 ) 22.87/22.93 ( skv_14 ) 22.87/22.93 ( skv_20 ) 22.87/22.93 ) 22.87/22.93 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (let ((_let_4 (minus_minus int))) (= (hAPP int int (hAPP int _let_0 _let_4 (hAPP nat int (hAPP int _let_2 _let_3 A_1) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 B) _let_1)) (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_4 A_1) B)))))))) ) 22.87/22.93 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 22.87/22.93 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 22.87/22.93 ( (hAPP nat int (hAPP 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) ) 22.87/22.93 ( (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) ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.87/22.94 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (= (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int bit0 (hAPP int int (hAPP int _let_0 _let_1 K_4) L_4))) L_4) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int bit1 K_4)) L_4)))) ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP int real (number_number_of real) min)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 Xa) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (deriv real) arcsin) Xa) (hAPP real real (inverse_inverse real) (hAPP real real sqrt (hAPP real real (hAPP real _let_0 (minus_minus real) _let_1) (hAPP nat real (hAPP real (fun nat real) (power_power real) Xa) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))))))))) ) 22.87/22.94 ( (hAPP int real (number_number_of real) min) ) 22.87/22.94 ( pi ) 22.87/22.94 ( (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)))) ) 22.87/22.94 ( (one_one real) ) 22.87/22.94 ( (zero_zero real) ) 22.87/22.94 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( (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))))) ) 22.87/22.94 ( (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)))) ) 22.87/22.94 ( (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)) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143031 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (t2_space X_a)) (not (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_143031))) (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_143031) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_143031))))) ) 22.87/22.94 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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))) ) 22.87/22.94 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((R_3 $$unsorted) (Q_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) _let_2) A_1))) (not (= (ti int A_1) (hAPP int int (hAPP int _let_0 (plus_plus int) R_3) (hAPP int int (hAPP int _let_0 (times_times int) A_1) Q_3)))) (not (hBOOL (hAPP int bool (hAPP int _let_1 _let_3 _let_2) R_3))) (hBOOL (hAPP int bool (hAPP int _let_1 _let_3 Q_3) (one_one int)))))))) ) 22.87/22.94 ( (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w, y ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w, sa ) 22.87/22.94 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_143064 $$unsorted) (BOUND_VARIABLE_143065 $$unsorted) (BOUND_VARIABLE_143066 $$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_143064) BOUND_VARIABLE_143065) BOUND_VARIABLE_143066))) (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_143064)) (hAPP X_b real _let_3 BOUND_VARIABLE_143065)) BOUND_VARIABLE_143066))))))) ) 22.87/22.94 ( nat, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real), sequentially ) 22.87/22.94 ( 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))))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Z $$unsorted)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (abs_abs int) Z)) (one_one int))) (= (zero_zero int) (ti int Z))) ) 22.87/22.94 ( pls ) 22.87/22.94 ( min ) 22.87/22.94 ( s ) 22.87/22.94 ( s1 ) 22.87/22.94 ( m ) 22.87/22.94 ( t ) 22.87/22.94 ( v ) 22.87/22.94 ( w ) 22.87/22.94 ( y ) 22.87/22.94 ( sa ) 22.87/22.94 ( x ) 22.87/22.94 ( r ) 22.87/22.94 ( m1 ) 22.87/22.94 ( skv_14 ) 22.87/22.94 ( skv_20 ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143105 $$unsorted)) (or (not (semiring_div X_a)) (= (ti X_a BOUND_VARIABLE_143105) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_div X_a) BOUND_VARIABLE_143105) (one_one X_a)))) ) 22.87/22.94 ( int, pls ) 22.87/22.94 ( int, min ) 22.87/22.94 ( int, s ) 22.87/22.94 ( int, s1 ) 22.87/22.94 ( int, m ) 22.87/22.94 ( int, t ) 22.87/22.94 ( int, v ) 22.87/22.94 ( int, w ) 22.87/22.94 ( int, y ) 22.87/22.94 ( int, sa ) 22.87/22.94 ( int, x ) 22.87/22.94 ( int, r ) 22.87/22.94 ( int, m1 ) 22.87/22.94 ( int, skv_14 ) 22.87/22.94 ( int, skv_20 ) 22.87/22.94 ( (fun int int), bit1 ) 22.87/22.94 ( (fun int int), bit0 ) 22.87/22.94 ( (fun int int), succ ) 22.87/22.94 ( (fun int int), pred ) 22.87/22.94 ( (fun int int), (fact_fact int) ) 22.87/22.94 ( (fun int int), zfact ) 22.87/22.94 ( nat, n ) 22.87/22.94 ( nat, tn ) 22.87/22.94 ( bool, fTrue ) 22.87/22.94 ( bool, fFalse ) 22.87/22.94 ( real, pi ) 22.87/22.94 ( (fun nat real), (real_1 nat) ) 22.87/22.94 ( (fun nat real), cos_coeff ) 22.87/22.94 ( (fun nat real), sin_coeff ) 22.87/22.94 ( (fun real real), sin ) 22.87/22.94 ( (fun real real), cos ) 22.87/22.94 ( (fun real real), sqrt ) 22.87/22.94 ( (fun real real), tan ) 22.87/22.94 ( (fun real real), ln ) 22.87/22.94 ( (fun real real), arctan ) 22.87/22.94 ( (fun real real), arcsin ) 22.87/22.94 ( (fun real real), arccos ) 22.87/22.94 ( (fun nat nat), suc ) 22.87/22.94 ( (fun nat nat), (fact_fact nat) ) 22.87/22.94 ( (fun nat nat), nat_size ) 22.87/22.94 ( (fun nat nat), (size_size nat) ) 22.87/22.94 ( (fun nat nat), fact ) 22.87/22.94 ( (filter nat), sequentially ) 22.87/22.94 ( (fun int (fun int rat)), fract ) 22.87/22.94 ( complex, ii ) 22.87/22.94 ( (fun int bool), zOdd ) 22.87/22.94 ( (fun int bool), zprime ) 22.87/22.94 ( (fun int bool), zEven ) 22.87/22.94 ( (fun int bool), nat_neg ) 22.87/22.94 ( (fun int bool), nat_is_nat ) 22.87/22.94 ( (fun int bool), (even_odd_even int) ) 22.87/22.94 ( (fun int bool), twoSqu1091635170sum2sq ) 22.87/22.94 ( (fun int (fun int int)), legacy_zgcd ) 22.87/22.94 ( (fun int (fun int int)), (gcd_gcd int) ) 22.87/22.94 ( (fun int (fun int int)), inv ) 22.87/22.94 ( (fun int (fun int int)), multInv ) 22.87/22.94 ( (fun int (fun int int)), legendre ) 22.87/22.94 ( (fun int (fun int int)), standardRes ) 22.87/22.94 ( (fun int (fun int int)), nat_tsub ) 22.87/22.94 ( (fun int (fun int int)), z3div ) 22.87/22.94 ( (fun int (fun int int)), z3mod ) 22.87/22.94 ( (fun int (fun int int)), int_lcm ) 22.87/22.94 ( (fun int (fun int int)), int_gcd ) 22.87/22.94 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.87/22.94 ( (fun bool bool), fNot ) 22.87/22.94 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.87/22.94 ( (fun bool (fun bool bool)), fconj ) 22.87/22.94 ( (fun bool (fun bool bool)), fdisj ) 22.87/22.94 ( (fun bool (fun bool bool)), fimplies ) 22.87/22.94 ( (fun int (fun int bool)), quadRes ) 22.87/22.94 ( (fun int (fun int bool)), d22set ) 22.87/22.94 ( (fun int (fun int bool)), norRRset ) 22.87/22.94 ( (fun int (fun int bool)), sRStar ) 22.87/22.94 ( (fun int (fun int bool)), sr ) 22.87/22.94 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.87/22.94 ( (fun nat bool), (even_odd_even nat) ) 22.87/22.94 ( (fun nat bool), prime ) 22.87/22.94 ( (fun real complex), cis ) 22.87/22.94 ( (fun nat (fun nat bool)), coprime ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.87/22.94 ( (fun (product_prod int int) bool), frac_1 ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.87/22.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.87/22.94 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.87/22.94 ( (fun (fun int bool) bool), nat_nat_set ) 22.87/22.94 ( (fun nat (fun real real)), root ) 22.87/22.94 ( (fun real (fun real real)), log ) 22.87/22.94 ( (fun real (fun real real)), powr ) 22.87/22.94 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.87/22.94 ( (fun complex complex), cnj ) 22.87/22.94 ( (fun complex complex), expi ) 22.87/22.94 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.87/22.94 ( (fun nat (fun nat nat)), nat_gcd ) 22.87/22.94 ( (fun nat (fun nat nat)), nat_lcm ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.87/22.94 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.87/22.94 ( (fun int (fun (fun int bool) bool)), resSet ) 22.87/22.94 ( (fun int nat), nat_1 ) 22.87/22.94 ( (fun int nat), phi ) 22.87/22.94 ( (fun complex real), re ) 22.87/22.94 ( (fun complex real), im ) 22.87/22.94 ( (fun complex real), arg ) 22.87/22.94 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.87/22.94 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.87/22.94 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.87/22.94 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.87/22.94 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.87/22.94 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.87/22.94 ( (fun (product_prod nat nat) bool), pred_nat ) 22.87/22.94 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.87/22.94 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.87/22.94 ( (fun (fun int bool) int), (the int) ) 22.87/22.94 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.87/22.94 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.87/22.94 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.87/22.94 ( (fun real (fun real complex)), rcis ) 22.87/22.94 ( (fun real (fun real complex)), complex_1 ) 22.87/22.94 ( (fun int (fun int (fun int bool))), zcong ) 22.87/22.94 ( (fun int (fun int (fun int bool))), wset ) 22.87/22.94 ( (fun int (fun int (fun int bool))), noXRRset ) 22.87/22.94 ( (fun int (fun int (fun int bool))), bnorRset ) 22.87/22.94 ( (fun int (fun int (fun int bool))), zcongm ) 22.87/22.94 ( (fun real nat), natceiling ) 22.87/22.94 ( (fun real nat), natfloor ) 22.87/22.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.87/22.94 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.87/22.94 ( (fun int real), (real_1 int) ) 22.87/22.94 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.87/22.94 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.87/22.94 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.87/22.94 ( (fun complex nat), (size_size complex) ) 22.87/22.94 ( (fun complex nat), complex_size ) 22.87/22.94 ( (fun (fun nat rat) bool), vanishes ) 22.87/22.94 ( (fun (product_prod int int) rat), frct ) 22.87/22.94 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.87/22.94 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.87/22.94 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.87/22.94 ( (fun rat real), ratreal ) 22.87/22.94 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.87/22.94 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.87/22.94 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.87/22.94 ( (fun rat (product_prod int int)), quotient_of ) 22.87/22.94 ( (fun int (fun nat nat)), nat_aux ) 22.87/22.94 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.87/22.94 ( (fun int (list int)), quickc666637781d_zero ) 22.87/22.94 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.87/22.94 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.87/22.94 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.87/22.94 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.87/22.94 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.87/22.94 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.87/22.94 ( (fun code_code_numeral int), code_int_of ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143120 $$unsorted) (BOUND_VARIABLE_143121 $$unsorted) (BOUND_VARIABLE_143122 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143120))) (or (not (ab_semigroup_add X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_143121)) BOUND_VARIABLE_143122) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143121) BOUND_VARIABLE_143122))))))) ) 22.87/22.94 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), m1 ) 22.87/22.94 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.94 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) _let_2) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP int int (hAPP int _let_0 legendre A_1) P_5)) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_1) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) (one_one int))) _let_2)))) P_5)))))) ) 22.87/22.94 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (one_one real) (hAPP real real (sgn_sgn real) X))) ) 22.87/22.94 ( pi ) 22.87/22.94 ( (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)))) ) 22.87/22.94 ( (zero_zero real) ) 22.87/22.94 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( skv_2 ) 22.87/22.94 ( skv_9 ) 22.87/22.94 ( skv_12 ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143207 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP X_a real (norm_norm X_a) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_143207)) (hAPP real real (abs_abs real) (hAPP int real (ring_1_of_int real) BOUND_VARIABLE_143207)))) ) 22.87/22.94 ( real, (one_one int) ) 22.87/22.94 ( real, (zero_zero int) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Na $$unsorted)) (= (= (zero_zero nat) Na) (= (zero_zero int) (hAPP nat int (semiring_1_of_nat int) Na))) ) 22.87/22.94 ( (zero_zero nat) ) 22.87/22.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.94 ( (one_one nat) ) 22.87/22.94 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.94 ( n ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((P_1 $$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))))) ) 22.87/22.94 ( (ord_less int), (one_one int), t ) 22.87/22.94 ( (ord_less int), min, min ) 22.87/22.94 ( (ord_less int), min, (zero_zero int) ) 22.87/22.94 ( (ord_less int), (zero_zero int), pls ) 22.87/22.94 ( (ord_less int), (zero_zero int), (one_one int) ) 22.87/22.94 ( (ord_less int), (zero_zero int), min ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ( (ord_less_eq int), (one_one int), t ) 22.87/22.94 ( (ord_less_eq int), min, pls ) 22.87/22.94 ( (ord_less_eq int), min, min ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), pls ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), min ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), s ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), skv_4 ) 22.87/22.94 ( (ord_less_eq int), (zero_zero int), skv_5 ) 22.87/22.94 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ( 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) ) 22.87/22.94 ( (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) (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)) ) 22.87/22.94 ( (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (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))) ) 22.87/22.94 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun nat bool) (ord_less nat) Ma))) (= (or (hBOOL (hAPP nat bool _let_0 Na)) (= Ma Na)) (hBOOL (hAPP nat bool _let_0 (hAPP nat nat suc Na))))) ) 22.87/22.94 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((P_5 $$unsorted) (R_3 $$unsorted) (S_3 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (times_times int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (product_Pair int int))) (or (= _let_1 (ti int Q_3)) (= _let_1 (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_3) S_3)))) (= (hAPP int int (hAPP int _let_0 _let_2 R_3) Q_3) (hAPP int int (hAPP int _let_0 _let_2 P_5) S_3))))))))) ) 22.87/22.94 ( (one_one int), (zero_zero int), v, v ) 22.87/22.94 ( (zero_zero int), (one_one int), s1, s1 ) 22.87/22.94 ( (zero_zero int), (zero_zero int), s1, s1 ) 22.87/22.94 ( s, s, m, r ) 22.87/22.94 ( s, s, r, r ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) X) (zero_zero int)))) (not (forall ((N_1 $$unsorted)) (not (= (ti int X) (hAPP int int (uminus_uminus int) (hAPP nat int (semiring_1_of_nat int) (hAPP nat nat suc N_1))))) ))) ) 22.87/22.94 ( (one_one int) ) 22.87/22.94 ( min ) 22.87/22.94 ( (zero_zero int) ) 22.87/22.94 ( s ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.94 ( t ) 22.87/22.94 ( m1 ) 22.87/22.94 ( skv_4 ) 22.87/22.94 ( skv_5 ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143345 $$unsorted) (BOUND_VARIABLE_143346 $$unsorted) (BOUND_VARIABLE_143347 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_143346))) (or (not (comm_ring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_143347))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_143345))) (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_143347) BOUND_VARIABLE_143345))))) ) 22.87/22.94 ( int, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143368 $$unsorted) (BOUND_VARIABLE_143369 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_143368)) (hAPP int int (number_number_of int) BOUND_VARIABLE_143369))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_143368) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_143369))))) ) 22.87/22.94 ( int, min, pls ) 22.87/22.94 ( int, (zero_zero int), pls ) 22.87/22.94 ( int, (zero_zero int), (hAPP int int bit1 pls) ) 22.87/22.94 ( int, (zero_zero int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.94 ( int, (zero_zero int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.87/22.94 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.94 ( real, skv_10, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) Xa)) (not (forall ((Y_1 $$unsorted)) (not (= Xa (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat)))) Y_1))) ))) ) 22.87/22.94 ( (zero_zero nat) ) 22.87/22.94 ( (one_one nat) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143422 $$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_143422) (zero_zero X_a))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_143422))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_143422)) _let_2))))))) ) 22.87/22.94 ( int, (one_one int) ) 22.87/22.94 ( int, min ) 22.87/22.94 ( int, (zero_zero int) ) 22.87/22.94 ( int, t ) 22.87/22.94 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.87/22.94 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.87/22.94 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.87/22.94 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.87/22.94 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.94 ( 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)))) ) 22.87/22.94 ( real, (zero_zero real) ) 22.87/22.94 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( real, skv_10 ) 22.87/22.94 ( complex, ii ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Na $$unsorted)) (= (= (zero_zero nat) Na) (= (zero_zero real) (hAPP nat real (real_1 nat) Na))) ) 22.87/22.94 ( (zero_zero nat) ) 22.87/22.94 ( (one_one nat) ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((Na $$unsorted) (Va $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) (hAPP int int pred Va)))) (let ((_let_1 (hBOOL (hAPP int bool nat_neg _let_0)))) (= (and (or _let_1 (= Na (hAPP int nat nat_1 _let_0))) (not _let_1)) (= (hAPP int nat (number_number_of nat) Va) (hAPP nat nat suc Na))))) ) 22.87/22.94 ( (zero_zero nat), pls ) 22.87/22.94 ( (hAPP nat nat suc (zero_zero nat)), min ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP nat real (real_1 nat) (hAPP int nat nat_1 X)) (hAPP int real (real_1 int) X))) ) 22.87/22.94 ( pls ) 22.87/22.94 ( (one_one int) ) 22.87/22.94 ( min ) 22.87/22.94 ( (zero_zero int) ) 22.87/22.94 ( s ) 22.87/22.94 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.94 ( t ) 22.87/22.94 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.94 ( skv_4 ) 22.87/22.94 ( skv_5 ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) K_4) pls) (ti int K_4)) ) 22.87/22.94 ( pls ) 22.87/22.94 ( min ) 22.87/22.94 ( s ) 22.87/22.94 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.94 ( s1 ) 22.87/22.94 ( m ) 22.87/22.94 ( t ) 22.87/22.94 ( v ) 22.87/22.94 ( w ) 22.87/22.94 ( y ) 22.87/22.94 ( sa ) 22.87/22.94 ( x ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 22.87/22.94 ( r ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 22.87/22.94 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.87/22.94 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 22.87/22.94 ( m1 ) 22.87/22.94 ( (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))) m1))) ) 22.87/22.94 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 22.87/22.94 ( skv_14 ) 22.87/22.94 ( skv_20 ) 22.87/22.94 ) 22.87/22.94 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP int real (number_number_of real) N))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X)) (hAPP int nat (number_number_of nat) N)))) ) 22.87/22.94 ( (one_one real), (hAPP int int bit1 pls) ) 22.87/22.94 ) 22.87/22.95 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) (one_one real))))) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) N) (one_one int)) (hAPP real int (archimedean_ceiling real) X)))))) ) 22.87/22.95 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( (zero_zero int), pi ) 22.87/22.95 ( (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)))) ) 22.87/22.95 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( (zero_zero int), skv_2 ) 22.87/22.95 ( (zero_zero int), skv_9 ) 22.87/22.95 ( (zero_zero int), skv_12 ) 22.87/22.95 ) 22.87/22.95 (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))) ) 22.87/22.95 ( pls, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 22.87/22.95 ( pls, (hAPP int (fun int bool) (ord_less int) pls), pls ) 22.87/22.95 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 22.87/22.95 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 22.87/22.95 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 22.87/22.95 ( (one_one int), nat_neg, (one_one int) ) 22.87/22.95 ( (one_one int), nat_is_nat, (one_one int) ) 22.87/22.95 ( (one_one int), (even_odd_even int), (one_one int) ) 22.87/22.95 ( min, (hAPP int (fun int bool) (ord_less int) min), min ) 22.87/22.95 ( min, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 22.87/22.95 ( min, (hAPP int (fun int bool) (ord_less int) pls), min ) 22.87/22.95 ( min, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 22.87/22.95 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 22.87/22.95 ( (zero_zero int), nat_neg, (zero_zero int) ) 22.87/22.95 ( (zero_zero int), nat_is_nat, (zero_zero int) ) 22.87/22.95 ( (zero_zero int), (even_odd_even int), (zero_zero int) ) 22.87/22.95 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (hAPP int int (number_number_of int) min), (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) ) 22.87/22.95 ( (hAPP int int (number_number_of int) min), nat_neg, (hAPP int int (number_number_of int) min) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 22.87/22.95 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 22.87/22.95 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 22.87/22.95 ( (hAPP 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)), (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) (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)) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))), twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 22.87/22.95 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 22.87/22.95 ( skv_5, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((M $$unsorted) (N $$unsorted) (P_5 $$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)))) (hBOOL (hAPP int bool _let_0 N)) (hBOOL (hAPP int bool _let_0 M)))) ) 22.87/22.95 ( (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))), skv_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))) ) 22.87/22.95 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143594 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (inverse_inverse X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_143594)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_143594)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_143594)))))) ) 22.87/22.95 ( int, pls ) 22.87/22.95 ( int, (one_one int) ) 22.87/22.95 ( int, min ) 22.87/22.95 ( int, s ) 22.87/22.95 ( int, s1 ) 22.87/22.95 ( int, m ) 22.87/22.95 ( int, t ) 22.87/22.95 ( int, v ) 22.87/22.95 ( int, w ) 22.87/22.95 ( int, y ) 22.87/22.95 ( int, sa ) 22.87/22.95 ( int, x ) 22.87/22.95 ( int, r ) 22.87/22.95 ( int, m1 ) 22.87/22.95 ( int, skv_14 ) 22.87/22.95 ( int, skv_20 ) 22.87/22.95 ( (fun int int), bit1 ) 22.87/22.95 ( (fun int int), bit0 ) 22.87/22.95 ( (fun int int), succ ) 22.87/22.95 ( (fun int int), pred ) 22.87/22.95 ( (fun int int), (fact_fact int) ) 22.87/22.95 ( (fun int int), zfact ) 22.87/22.95 ( nat, n ) 22.87/22.95 ( nat, tn ) 22.87/22.95 ( bool, fTrue ) 22.87/22.95 ( bool, fFalse ) 22.87/22.95 ( real, pi ) 22.87/22.95 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( real, (one_one real) ) 22.87/22.95 ( real, (zero_zero real) ) 22.87/22.95 ( 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) ) 22.87/22.95 ( (fun nat real), (real_1 nat) ) 22.87/22.95 ( (fun nat real), cos_coeff ) 22.87/22.95 ( (fun nat real), sin_coeff ) 22.87/22.95 ( (fun real real), sin ) 22.87/22.95 ( (fun real real), cos ) 22.87/22.95 ( (fun real real), sqrt ) 22.87/22.95 ( (fun real real), tan ) 22.87/22.95 ( (fun real real), ln ) 22.87/22.95 ( (fun real real), arctan ) 22.87/22.95 ( (fun real real), arcsin ) 22.87/22.95 ( (fun real real), arccos ) 22.87/22.95 ( (fun nat nat), suc ) 22.87/22.95 ( (fun nat nat), (fact_fact nat) ) 22.87/22.95 ( (fun nat nat), nat_size ) 22.87/22.95 ( (fun nat nat), (size_size nat) ) 22.87/22.95 ( (fun nat nat), fact ) 22.87/22.95 ( (filter nat), sequentially ) 22.87/22.95 ( (fun int (fun int rat)), fract ) 22.87/22.95 ( complex, ii ) 22.87/22.95 ( complex, (one_one complex) ) 22.87/22.95 ( (fun int bool), zOdd ) 22.87/22.95 ( (fun int bool), zprime ) 22.87/22.95 ( (fun int bool), zEven ) 22.87/22.95 ( (fun int bool), nat_neg ) 22.87/22.95 ( (fun int bool), nat_is_nat ) 22.87/22.95 ( (fun int bool), (even_odd_even int) ) 22.87/22.95 ( (fun int bool), twoSqu1091635170sum2sq ) 22.87/22.95 ( (fun int (fun int int)), legacy_zgcd ) 22.87/22.95 ( (fun int (fun int int)), (gcd_gcd int) ) 22.87/22.95 ( (fun int (fun int int)), inv ) 22.87/22.95 ( (fun int (fun int int)), multInv ) 22.87/22.95 ( (fun int (fun int int)), legendre ) 22.87/22.95 ( (fun int (fun int int)), standardRes ) 22.87/22.95 ( (fun int (fun int int)), nat_tsub ) 22.87/22.95 ( (fun int (fun int int)), z3div ) 22.87/22.95 ( (fun int (fun int int)), z3mod ) 22.87/22.95 ( (fun int (fun int int)), int_lcm ) 22.87/22.95 ( (fun int (fun int int)), int_gcd ) 22.87/22.95 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.87/22.95 ( (fun bool bool), fNot ) 22.87/22.95 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.87/22.95 ( (fun bool (fun bool bool)), fconj ) 22.87/22.95 ( (fun bool (fun bool bool)), fdisj ) 22.87/22.95 ( (fun bool (fun bool bool)), fimplies ) 22.87/22.95 ( (fun int (fun int bool)), quadRes ) 22.87/22.95 ( (fun int (fun int bool)), d22set ) 22.87/22.95 ( (fun int (fun int bool)), norRRset ) 22.87/22.95 ( (fun int (fun int bool)), sRStar ) 22.87/22.95 ( (fun int (fun int bool)), sr ) 22.87/22.95 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.87/22.95 ( (fun nat bool), (even_odd_even nat) ) 22.87/22.95 ( (fun nat bool), prime ) 22.87/22.95 ( (fun real complex), cis ) 22.87/22.95 ( (fun nat (fun nat bool)), coprime ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.87/22.95 ( (fun (product_prod int int) bool), frac_1 ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.87/22.95 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.87/22.95 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.87/22.95 ( (fun (fun int bool) bool), nat_nat_set ) 22.87/22.95 ( (fun nat (fun real real)), root ) 22.87/22.95 ( (fun real (fun real real)), log ) 22.87/22.95 ( (fun real (fun real real)), powr ) 22.87/22.95 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.87/22.95 ( (fun complex complex), cnj ) 22.87/22.95 ( (fun complex complex), expi ) 22.87/22.95 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.87/22.95 ( (fun nat (fun nat nat)), nat_gcd ) 22.87/22.95 ( (fun nat (fun nat nat)), nat_lcm ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.87/22.95 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.87/22.95 ( (fun int (fun (fun int bool) bool)), resSet ) 22.87/22.95 ( (fun int nat), nat_1 ) 22.87/22.95 ( (fun int nat), phi ) 22.87/22.95 ( (fun complex real), re ) 22.87/22.95 ( (fun complex real), im ) 22.87/22.95 ( (fun complex real), arg ) 22.87/22.95 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.87/22.95 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.87/22.95 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.87/22.95 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.87/22.95 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.87/22.95 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.87/22.95 ( (fun (product_prod nat nat) bool), pred_nat ) 22.87/22.95 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.87/22.95 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.87/22.95 ( (fun (fun int bool) int), (the int) ) 22.87/22.95 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.87/22.95 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.87/22.95 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.87/22.95 ( (fun real (fun real complex)), rcis ) 22.87/22.95 ( (fun real (fun real complex)), complex_1 ) 22.87/22.95 ( (fun int (fun int (fun int bool))), zcong ) 22.87/22.95 ( (fun int (fun int (fun int bool))), wset ) 22.87/22.95 ( (fun int (fun int (fun int bool))), noXRRset ) 22.87/22.95 ( (fun int (fun int (fun int bool))), bnorRset ) 22.87/22.95 ( (fun int (fun int (fun int bool))), zcongm ) 22.87/22.95 ( (fun real nat), natceiling ) 22.87/22.95 ( (fun real nat), natfloor ) 22.87/22.95 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.87/22.95 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.87/22.95 ( (fun int real), (real_1 int) ) 22.87/22.95 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.87/22.95 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.87/22.95 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.87/22.95 ( (fun complex nat), (size_size complex) ) 22.87/22.95 ( (fun complex nat), complex_size ) 22.87/22.95 ( (fun (fun nat rat) bool), vanishes ) 22.87/22.95 ( (fun (product_prod int int) rat), frct ) 22.87/22.95 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.87/22.95 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.87/22.95 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.87/22.95 ( (fun rat real), ratreal ) 22.87/22.95 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.87/22.95 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.87/22.95 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.87/22.95 ( (fun rat (product_prod int int)), quotient_of ) 22.87/22.95 ( (fun int (fun nat nat)), nat_aux ) 22.87/22.95 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.87/22.95 ( (fun int (list int)), quickc666637781d_zero ) 22.87/22.95 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.87/22.95 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.87/22.95 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.87/22.95 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.87/22.95 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.87/22.95 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.87/22.95 ( (fun code_code_numeral int), code_int_of ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (dvd_dvd nat) P_5) (hAPP nat nat suc (zero_zero nat)))))) ) 22.87/22.95 ( (zero_zero nat) ) 22.87/22.95 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( (hAPP nat nat suc (zero_zero nat)) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143643 $$unsorted)) (let ((_let_0 (fun X_a (fun X_a X_a)))) (or (not (semiring_1 X_a)) (= (hAPP X_a X_a (hAPP nat (fun X_a X_a) (hAPP (fun X_a X_a) (fun nat (fun X_a X_a)) (semiri532925092at_aux X_a) (hAPP X_a (fun X_a X_a) (hAPP _let_0 _let_0 (combc X_a X_a X_a) (plus_plus X_a)) (one_one X_a))) BOUND_VARIABLE_143643) (zero_zero X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_143643)))) ) 22.87/22.95 ( int, (zero_zero nat) ) 22.87/22.95 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( int, (one_one nat) ) 22.87/22.95 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.95 ( int, n ) 22.87/22.95 ( real, (zero_zero nat) ) 22.87/22.95 ( real, (one_one nat) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 X_c))) (let ((_let_2 (fun X_b X_c))) (let ((_let_3 (fun X_a _let_2))) (let ((_let_4 (fun X_b _let_0))) (let ((_let_5 (fun X_a _let_4))) (let ((_let_6 (fun _let_4 _let_2))) (= (hAPP _let_3 _let_1 (product_prod_case X_a X_b X_c) (hAPP _let_5 _let_3 (hAPP _let_6 (fun _let_5 _let_3) (combb _let_4 _let_2 X_a) (hAPP _let_1 _let_6 (combb _let_0 X_c X_b) F)) (product_Pair X_a X_b))) (ti _let_1 F))))))))) ) 22.87/22.95 ( int, int, rat, frct ) 22.87/22.95 ( int, int, int, twoSqu1094008024sum2sq ) 22.87/22.95 ( int, int, bool, frac_1 ) 22.87/22.95 ( int, int, (product_prod int int), normalize ) 22.87/22.95 ( int, int, (product_prod int int), negateSnd ) 22.87/22.95 ( int, int, (fun (product_prod int int) bool), upto_rel ) 22.87/22.95 ( int, int, (fun (product_prod int int) bool), posDivAlg_rel ) 22.87/22.95 ( int, int, (fun (product_prod int int) bool), negDivAlg_rel ) 22.87/22.95 ( int, int, (fun (product_prod int int) bool), lazy_small_lazy_rel ) 22.87/22.95 ( int, int, (fun (product_prod int int) bool), norm_frac_rel ) 22.87/22.95 ( nat, nat, bool, pred_nat ) 22.87/22.95 ( nat, nat, (fun (product_prod nat nat) bool), nat_gcd_rel ) 22.87/22.95 ( (product_prod int int), (product_prod int int), bool, ratrel ) 22.87/22.95 ( (product_prod nat nat), (product_prod nat nat), bool, pair_less ) 22.87/22.95 ( (product_prod nat nat), (product_prod nat nat), bool, pair_leq ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((N $$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))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) N) (hAPP nat nat _let_1 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (one_one nat)))) (hAPP nat nat _let_1 N))))) ) 22.87/22.95 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( n ) 22.87/22.95 ( tn ) 22.87/22.95 ( (hAPP int nat nat_1 t) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 Xa))) (not (hBOOL (hAPP int bool _let_0 Ya))) (= (= (hAPP int nat nat_1 Ya) (hAPP int nat nat_1 Xa)) (= (ti int Ya) (ti int Xa))))) ) 22.87/22.95 ( pls, (one_one int) ) 22.87/22.95 ( (one_one int), pls ) 22.87/22.95 ( (one_one int), (one_one int) ) 22.87/22.95 ( min, min ) 22.87/22.95 ( min, s ) 22.87/22.95 ( s, min ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( (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))) ) 22.87/22.95 ( skv_4, skv_4 ) 22.87/22.95 ( skv_4, skv_5 ) 22.87/22.95 ( skv_5, skv_4 ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int rat))) (= (hAPP rat rat (inverse_inverse rat) (hAPP int rat (hAPP int _let_0 fract A_1) B)) (hAPP int rat (hAPP int _let_0 fract B) A_1))) ) 22.87/22.95 ( (one_one int), (one_one int) ) 22.87/22.95 ( (one_one int), (zero_zero int) ) 22.87/22.95 ( (zero_zero int), (one_one int) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (uminus_uminus real))) (= (hAPP real real _let_0 (hAPP real real sin X)) (hAPP real real sin (hAPP real real _let_0 X)))) ) 22.87/22.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (minus_minus nat))) (let ((_let_3 (power_power nat))) (= (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) X) Y)) (hAPP nat nat (hAPP nat _let_0 _let_2 X) Y)) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 _let_3 X) _let_1)) (hAPP nat nat (hAPP nat _let_0 _let_3 Y) _let_1))))))) ) 22.87/22.95 ( (one_one nat), (one_one nat) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X $$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))) (not (= (hAPP real real ln X) (hAPP real real (hAPP real (fun real real) (minus_minus real) X) _let_0))) (= _let_0 X))) ) 22.87/22.95 ( pi ) 22.87/22.95 ( (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)))) ) 22.87/22.95 ( (one_one real) ) 22.87/22.95 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 22.87/22.95 ( skv_2 ) 22.87/22.95 ( skv_9 ) 22.87/22.95 ( skv_12 ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143769 $$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_143769)) (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_143769))))))) ) 22.87/22.95 ( int, pls ) 22.87/22.95 ( int, (hAPP int int bit1 pls) ) 22.87/22.95 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( nat, pls ) 22.87/22.95 ( nat, (hAPP int int bit1 pls) ) 22.87/22.95 ( real, (hAPP int int bit1 pls) ) 22.87/22.95 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.87/22.95 ( complex, (hAPP int int bit1 pls) ) 22.87/22.95 ( quickcheck_code_int, pls ) 22.87/22.95 ( code_code_numeral, pls ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143816 $$unsorted) (BOUND_VARIABLE_143817 $$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_143816) BOUND_VARIABLE_143817)) (or (= (ti X_a BOUND_VARIABLE_143816) (ti X_a BOUND_VARIABLE_143817)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_143816) BOUND_VARIABLE_143817)))))) ) 22.87/22.95 ( int, (one_one int), t ) 22.87/22.95 ( int, min, pls ) 22.87/22.95 ( int, min, min ) 22.87/22.95 ( int, min, (zero_zero int) ) 22.87/22.95 ( int, (zero_zero int), pls ) 22.87/22.95 ( int, (zero_zero int), (one_one int) ) 22.87/22.95 ( int, (zero_zero int), min ) 22.87/22.95 ( int, (zero_zero int), s ) 22.87/22.95 ( 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))) ) 22.87/22.95 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.95 ( int, (zero_zero int), skv_4 ) 22.87/22.95 ( int, (zero_zero int), skv_5 ) 22.87/22.95 ( 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))) ) 22.87/22.95 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( 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))) ) 22.87/22.95 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( 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))) ) 22.87/22.95 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.87/22.95 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.87/22.95 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( nat, (zero_zero nat), n ) 22.87/22.95 ( nat, (zero_zero nat), tn ) 22.87/22.95 ( real, pi, (zero_zero real) ) 22.87/22.95 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.87/22.95 ( real, (hAPP real real (hAPP 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))) ) 22.87/22.95 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( real, (zero_zero real), pi ) 22.87/22.95 ( 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)))) ) 22.87/22.95 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( real, (zero_zero real), skv_2 ) 22.87/22.95 ( real, (zero_zero real), skv_9 ) 22.87/22.95 ( real, (zero_zero real), skv_10 ) 22.87/22.95 ( real, (zero_zero real), skv_11 ) 22.87/22.95 ( real, (zero_zero real), skv_12 ) 22.87/22.95 ( real, (zero_zero real), skv_15 ) 22.87/22.95 ( real, (zero_zero real), skv_18 ) 22.87/22.95 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.87/22.95 ( 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) ) 22.87/22.95 ( 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 ) 22.87/22.95 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143838 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) pls) BOUND_VARIABLE_143838)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_143838))))) ) 22.87/22.95 ( int, pls ) 22.87/22.95 ( int, (hAPP int int bit1 pls) ) 22.87/22.95 ( int, min ) 22.87/22.95 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.87/22.95 ( nat, pls ) 22.87/22.95 ( nat, (hAPP int int bit1 pls) ) 22.87/22.95 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.87/22.95 ( real, min ) 22.87/22.95 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.87/22.95 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.87/22.95 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 22.87/22.95 ( complex, min ) 22.87/22.95 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.87/22.95 ( quickcheck_code_int, pls ) 22.87/22.95 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.87/22.95 ( quickcheck_code_int, (one_one int) ) 22.87/22.95 ( code_code_numeral, pls ) 22.87/22.95 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (one_one real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Ya))) (hBOOL (hAPP real bool _let_0 Ya))))) ) 22.87/22.95 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_143872 $$unsorted) (BOUND_VARIABLE_143873 $$unsorted) (BOUND_VARIABLE_143874 $$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_143874) (zero_zero X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143872) (hAPP X_a X_a (hAPP X_a _let_2 (inverse_divide X_a) BOUND_VARIABLE_143873) BOUND_VARIABLE_143874))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_143873) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_143872) BOUND_VARIABLE_143874)))))))) ) 22.87/22.95 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.87/22.95 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.87/22.95 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.87/22.95 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.87/22.95 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Y))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (= Y (hAPP real real tan X_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X_1) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) (zero_zero real)) X_1))))) ))) ) 22.87/22.95 ( pi ) 22.87/22.95 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.87/22.95 ( skv_10 ) 22.87/22.95 ( skv_11 ) 22.87/22.95 ( skv_15 ) 22.87/22.95 ( skv_18 ) 22.87/22.95 ) 22.87/22.95 (instantiation (forall ((K_4 $$unsorted) (M $$unsorted) (N $$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)))) (not (hBOOL (hAPP int bool _let_0 N))) (hBOOL (hAPP int bool _let_0 M)))) ) 22.87/22.95 ( (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 nat int (hAPP 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) ) 22.87/22.95 ) 22.98/22.99 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (hAPP real real cos X))) (or (= (zero_zero real) _let_3) (= (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real (inverse_inverse real) _let_3)) _let_2) (hAPP real real (hAPP real (fun real real) (plus_plus real) (one_one real)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP real real tan X)) _let_2)))))))) ) 22.98/22.99 ( pi ) 22.98/22.99 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.98/22.99 ( (zero_zero real) ) 22.98/22.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.98/22.99 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.98/22.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.98/22.99 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex cis A_1) (hAPP real complex (hAPP real (fun real complex) rcis (one_one real)) A_1)) ) 22.98/22.99 ( (zero_zero real) ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((K $$unsorted) (Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (plus_plus nat) K))) (= (= (hAPP nat nat _let_0 Ma) (hAPP nat nat _let_0 Na)) (= Ma Na))) ) 22.98/22.99 ( (one_one nat), (one_one nat), (one_one nat) ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144043 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (times_times X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (one_one X_a))) (let ((_let_5 (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_144043))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_4) _let_4)) (hAPP _let_0 X_a (hAPP (fun nat X_a) (fun _let_0 X_a) (big_co1399186613setsum nat X_a) (semiring_1_of_nat X_a)) (hAPP nat _let_0 (hAPP nat (fun nat _let_0) (ord_atLeastAtMost nat) (one_one nat)) BOUND_VARIABLE_144043))) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 _let_5) (hAPP X_a X_a (hAPP X_a _let_1 _let_3 _let_5) _let_4)))))))))) ) 22.98/22.99 ( int, (zero_zero nat) ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.98/22.99 ( int, (one_one nat) ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.98/22.99 ( int, n ) 22.98/22.99 ( real, (zero_zero nat) ) 22.98/22.99 ( real, (one_one nat) ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144116 $$unsorted) (BOUND_VARIABLE_144117 $$unsorted) (BOUND_VARIABLE_144118 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_144117))) (or (not (comm_semiring_1 X_a)) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_144118))) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_144116) BOUND_VARIABLE_144118))))) ) 22.98/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), skv_21 ) 22.98/22.99 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (gcd_gcd nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) M) N)) N)))) ) 22.98/22.99 ( (one_one nat), (one_one nat) ) 22.98/22.99 ) 22.98/22.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144157 $$unsorted) (BOUND_VARIABLE_144158 $$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_144158) BOUND_VARIABLE_144157))) (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_144158))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144158) (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_144158) _let_2)) _let_2)))))) ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 22.98/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 22.98/22.99 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.98/22.99 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.98/22.99 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.98/22.99 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.99/22.99 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.99/22.99 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.99/22.99 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.99/22.99 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.99/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 22.99/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 22.99/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 22.99/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 22.99/22.99 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 22.99/22.99 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (one_one X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) _let_0) _let_0) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.99/22.99 ( rat ) 22.99/22.99 ( int ) 22.99/22.99 ( (fun int int) ) 22.99/22.99 ( nat ) 22.99/22.99 ( bool ) 22.99/22.99 ( real ) 22.99/22.99 ( (fun nat real) ) 22.99/22.99 ( (fun real real) ) 22.99/22.99 ( complex ) 22.99/22.99 ( (fun int bool) ) 22.99/22.99 ( (product_prod int int) ) 22.99/22.99 ( (fun (product_prod int int) int) ) 22.99/22.99 ( (fun int (fun int bool)) ) 22.99/22.99 ( (fun nat bool) ) 22.99/22.99 ( (fun (product_prod int int) bool) ) 22.99/22.99 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.99/22.99 ( (fun real bool) ) 22.99/22.99 ( quickcheck_code_int ) 22.99/22.99 ( code_code_numeral ) 22.99/22.99 ( (fun int (fun int (fun int bool))) ) 22.99/22.99 ( (fun int real) ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((S $$unsorted)) (or (not (hBOOL (hAPP (fun nat bool) bool (finite_finite_1 nat) S))) (not (forall ((K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (not (hBOOL (hAPP _let_0 bool (hAPP _let_0 (fun _let_0 bool) (ord_less_eq _let_0) S) (hAPP nat _let_0 (ord_lessThan nat) K_1))))) ))) ) 22.99/22.99 ( (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 _let_0 normalize (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_1) B)) (hAPP rat _let_0 quotient_of (hAPP int rat (hAPP int (fun int rat) fract A_1) B)))) ) 22.99/22.99 ( (one_one int), (one_one int) ) 22.99/22.99 ( (zero_zero int), (one_one int) ) 22.99/22.99 ( s, (one_one int) ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144283 $$unsorted) (BOUND_VARIABLE_144284 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_144284))) (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_144283)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_144284)))) (not (hBOOL (hAPP X_a bool _let_1 (zero_zero X_a)))) (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_144283))))) ) 22.99/22.99 ( int, pls, (zero_zero int) ) 22.99/22.99 ( int, (one_one int), (zero_zero int) ) 22.99/22.99 ( int, min, min ) 22.99/22.99 ( int, min, (zero_zero int) ) 22.99/22.99 ( int, (zero_zero int), min ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 22.99/22.99 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 22.99/22.99 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.99/22.99 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.99/22.99 ( int, t, (one_one int) ) 22.99/22.99 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.99/22.99 ( nat, n, (zero_zero nat) ) 22.99/22.99 ( nat, tn, (zero_zero nat) ) 22.99/22.99 ( real, pi, (zero_zero real) ) 22.99/22.99 ( 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)) ) 22.99/22.99 ( 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)))) ) 22.99/22.99 ( 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)))), (zero_zero real) ) 22.99/22.99 ( real, (zero_zero real), pi ) 22.99/22.99 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/22.99 ( 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))))) ) 22.99/22.99 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.99/22.99 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/22.99 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.99/22.99 ( real, skv_2, (zero_zero real) ) 22.99/22.99 ( real, skv_9, (zero_zero real) ) 22.99/22.99 ( real, skv_12, (zero_zero real) ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (hAPP nat int (semiring_1_of_nat int) N))) (= _let_0 (hAPP int int (ring_1_of_int int) _let_0))) ) 22.99/22.99 ( (zero_zero nat) ) 22.99/22.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/22.99 ( (one_one nat) ) 22.99/22.99 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/22.99 ( n ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((X_a $$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))) ) 22.99/22.99 ( rat ) 22.99/22.99 ( int ) 22.99/22.99 ( nat ) 22.99/22.99 ( real ) 22.99/22.99 ( complex ) 22.99/22.99 ( quickcheck_code_int ) 22.99/22.99 ( code_code_numeral ) 22.99/22.99 ) 22.99/22.99 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144335 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_144335) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_144335) (zero_zero X_a)))) ) 22.99/22.99 ( int, pls ) 22.99/22.99 ( int, (one_one int) ) 22.99/22.99 ( int, min ) 22.99/22.99 ( int, s ) 22.99/23.00 ( 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)))) ) 22.99/23.00 ( int, s1 ) 22.99/23.00 ( int, m ) 22.99/23.00 ( 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) ) 22.99/23.00 ( int, t ) 22.99/23.00 ( int, v ) 22.99/23.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, w ) 22.99/23.00 ( int, y ) 22.99/23.00 ( int, sa ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.99/23.00 ( int, x ) 22.99/23.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.99/23.00 ( int, r ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.99/23.00 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 22.99/23.00 ( int, m1 ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 22.99/23.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, skv_14 ) 22.99/23.00 ( int, skv_20 ) 22.99/23.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( (fun int int), bit1 ) 22.99/23.00 ( (fun int int), bit0 ) 22.99/23.00 ( (fun int int), succ ) 22.99/23.00 ( (fun int int), pred ) 22.99/23.00 ( (fun int int), (fact_fact int) ) 22.99/23.00 ( (fun int int), zfact ) 22.99/23.00 ( nat, (one_one nat) ) 22.99/23.00 ( nat, n ) 22.99/23.00 ( nat, tn ) 22.99/23.00 ( bool, fTrue ) 22.99/23.00 ( bool, fFalse ) 22.99/23.00 ( real, pi ) 22.99/23.00 ( (fun nat real), (real_1 nat) ) 22.99/23.00 ( (fun nat real), cos_coeff ) 22.99/23.00 ( (fun nat real), sin_coeff ) 22.99/23.00 ( (fun real real), sin ) 22.99/23.00 ( (fun real real), cos ) 22.99/23.00 ( (fun real real), sqrt ) 22.99/23.00 ( (fun real real), tan ) 22.99/23.00 ( (fun real real), ln ) 22.99/23.00 ( (fun real real), arctan ) 22.99/23.00 ( (fun real real), arcsin ) 22.99/23.00 ( (fun real real), arccos ) 22.99/23.00 ( (fun nat nat), suc ) 22.99/23.00 ( (fun nat nat), (fact_fact nat) ) 22.99/23.00 ( (fun nat nat), nat_size ) 22.99/23.00 ( (fun nat nat), (size_size nat) ) 22.99/23.00 ( (fun nat nat), fact ) 22.99/23.00 ( (filter nat), sequentially ) 22.99/23.00 ( (fun int (fun int rat)), fract ) 22.99/23.00 ( complex, ii ) 22.99/23.00 ( (fun int bool), zOdd ) 22.99/23.00 ( (fun int bool), zprime ) 22.99/23.00 ( (fun int bool), zEven ) 22.99/23.00 ( (fun int bool), nat_neg ) 22.99/23.00 ( (fun int bool), nat_is_nat ) 22.99/23.00 ( (fun int bool), (even_odd_even int) ) 22.99/23.00 ( (fun int bool), twoSqu1091635170sum2sq ) 22.99/23.00 ( (fun int (fun int int)), legacy_zgcd ) 22.99/23.00 ( (fun int (fun int int)), (gcd_gcd int) ) 22.99/23.00 ( (fun int (fun int int)), inv ) 22.99/23.00 ( (fun int (fun int int)), multInv ) 22.99/23.00 ( (fun int (fun int int)), legendre ) 22.99/23.00 ( (fun int (fun int int)), standardRes ) 22.99/23.00 ( (fun int (fun int int)), nat_tsub ) 22.99/23.00 ( (fun int (fun int int)), z3div ) 22.99/23.00 ( (fun int (fun int int)), z3mod ) 22.99/23.00 ( (fun int (fun int int)), int_lcm ) 22.99/23.00 ( (fun int (fun int int)), int_gcd ) 22.99/23.00 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 22.99/23.00 ( (fun bool bool), fNot ) 22.99/23.00 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 22.99/23.00 ( (fun bool (fun bool bool)), fconj ) 22.99/23.00 ( (fun bool (fun bool bool)), fdisj ) 22.99/23.00 ( (fun bool (fun bool bool)), fimplies ) 22.99/23.00 ( (fun int (fun int bool)), quadRes ) 22.99/23.00 ( (fun int (fun int bool)), d22set ) 22.99/23.00 ( (fun int (fun int bool)), norRRset ) 22.99/23.00 ( (fun int (fun int bool)), sRStar ) 22.99/23.00 ( (fun int (fun int bool)), sr ) 22.99/23.00 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 22.99/23.00 ( (fun nat bool), (even_odd_even nat) ) 22.99/23.00 ( (fun nat bool), prime ) 22.99/23.00 ( (fun real complex), cis ) 22.99/23.00 ( (fun nat (fun nat bool)), coprime ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 22.99/23.00 ( (fun (product_prod int int) bool), frac_1 ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 22.99/23.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 22.99/23.00 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 22.99/23.00 ( (fun (fun int bool) bool), nat_nat_set ) 22.99/23.00 ( (fun nat (fun real real)), root ) 22.99/23.00 ( (fun real (fun real real)), log ) 22.99/23.00 ( (fun real (fun real real)), powr ) 22.99/23.00 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 22.99/23.00 ( (fun complex complex), cnj ) 22.99/23.00 ( (fun complex complex), expi ) 22.99/23.00 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 22.99/23.00 ( (fun nat (fun nat nat)), nat_gcd ) 22.99/23.00 ( (fun nat (fun nat nat)), nat_lcm ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 22.99/23.00 ( (fun int (fun (fun int bool) bool)), rsetR ) 22.99/23.00 ( (fun int (fun (fun int bool) bool)), resSet ) 22.99/23.00 ( (fun int nat), nat_1 ) 22.99/23.00 ( (fun int nat), phi ) 22.99/23.00 ( (fun complex real), re ) 22.99/23.00 ( (fun complex real), im ) 22.99/23.00 ( (fun complex real), arg ) 22.99/23.00 ( (fun int (fun int (product_prod int int))), divmod_int ) 22.99/23.00 ( (fun int (fun int (product_prod int int))), posDivAlg ) 22.99/23.00 ( (fun int (fun int (product_prod int int))), negDivAlg ) 22.99/23.00 ( (fun int (fun int (product_prod int int))), pdivmod ) 22.99/23.00 ( (fun int (fun int (product_prod int int))), norm_frac ) 22.99/23.00 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 22.99/23.00 ( (fun (product_prod nat nat) bool), pred_nat ) 22.99/23.00 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 22.99/23.00 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 22.99/23.00 ( (fun (fun int bool) int), (the int) ) 22.99/23.00 ( (fun int quickcheck_code_int), quickcheck_of_int ) 22.99/23.00 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 22.99/23.00 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 22.99/23.00 ( (fun real (fun real complex)), rcis ) 22.99/23.00 ( (fun real (fun real complex)), complex_1 ) 22.99/23.00 ( (fun int (fun int (fun int bool))), zcong ) 22.99/23.00 ( (fun int (fun int (fun int bool))), wset ) 22.99/23.00 ( (fun int (fun int (fun int bool))), noXRRset ) 22.99/23.00 ( (fun int (fun int (fun int bool))), bnorRset ) 22.99/23.00 ( (fun int (fun int (fun int bool))), zcongm ) 22.99/23.00 ( (fun real nat), natceiling ) 22.99/23.00 ( (fun real nat), natfloor ) 22.99/23.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 22.99/23.00 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 22.99/23.00 ( (fun int real), (real_1 int) ) 22.99/23.00 ( (fun quickcheck_code_int int), quickcheck_int_of ) 22.99/23.00 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 22.99/23.00 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 22.99/23.00 ( (fun complex nat), (size_size complex) ) 22.99/23.00 ( (fun complex nat), complex_size ) 22.99/23.00 ( (fun (fun nat rat) bool), vanishes ) 22.99/23.00 ( (fun (product_prod int int) rat), frct ) 22.99/23.00 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 22.99/23.00 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 22.99/23.00 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 22.99/23.00 ( (fun rat real), ratreal ) 22.99/23.00 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 22.99/23.00 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 22.99/23.00 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 22.99/23.00 ( (fun rat (product_prod int int)), quotient_of ) 22.99/23.00 ( (fun int (fun nat nat)), nat_aux ) 22.99/23.00 ( (fun nat (fun nat (product_prod int int))), bezw ) 22.99/23.00 ( (fun int (list int)), quickc666637781d_zero ) 22.99/23.00 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 22.99/23.00 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 22.99/23.00 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 22.99/23.00 ( (fun code_code_numeral nat), code_c271388182l_size ) 22.99/23.00 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 22.99/23.00 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 22.99/23.00 ( (fun code_code_numeral int), code_int_of ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144377 $$unsorted) (BOUND_VARIABLE_144378 $$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_144377) BOUND_VARIABLE_144378) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144378) BOUND_VARIABLE_144377))))) ) 22.99/23.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 22.99/23.00 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( 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 ) 22.99/23.00 ( 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))), m1 ) 22.99/23.00 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 22.99/23.00 ( 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_21 ) 22.99/23.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 22.99/23.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 22.99/23.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 22.99/23.00 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one 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int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( int, x, v ) 22.99/23.00 ( int, x, w ) 22.99/23.00 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.99/23.00 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( int, r, v ) 22.99/23.00 ( int, r, w ) 22.99/23.00 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 22.99/23.00 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 22.99/23.00 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 22.99/23.00 ( int, (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 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int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.99/23.00 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.99/23.00 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.00 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 22.99/23.00 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( int, skv_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))) ) 22.99/23.00 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( 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))))) ) 22.99/23.00 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.99/23.00 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.99/23.00 ( 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)))))) ) 22.99/23.00 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( 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))))), pi ) 22.99/23.00 ( 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)))) ) 22.99/23.00 ( complex, ii, ii ) 22.99/23.00 ( 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)) ) 22.99/23.00 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 22.99/23.00 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( 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)), ii ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144433 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_144433)) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_144433)))) ) 22.99/23.00 ( int, pls ) 22.99/23.00 ( int, (one_one int) ) 22.99/23.00 ( int, min ) 22.99/23.00 ( int, v ) 22.99/23.00 ( int, w ) 22.99/23.00 ( int, skv_14 ) 22.99/23.00 ( int, skv_20 ) 22.99/23.00 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( real, (one_one real) ) 22.99/23.00 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.99/23.00 ( complex, ii ) 22.99/23.00 ( complex, (one_one complex) ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (hAPP int nat nat_1 Xa))) (or (not (= (hAPP int int (hAPP int _let_0 (times_times int) A_3) B_2) (hAPP nat int (hAPP int (fun nat int) (power_power int) C) _let_2))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) _let_2))) (not (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) Xa) zOdd))) (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd A_3) B_2))) (not (forall ((K_1 $$unsorted)) (not (= (ti int A_3) (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) _let_2))) )))))) ) 22.99/23.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s1, (one_one int) ) 22.99/23.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w), w, t ) 22.99/23.00 ( y, v, y, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.00 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), s, (zero_zero int) ) 22.99/23.00 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), v, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (= (hAPP nat _let_0 (ord_less_eq nat) (hAPP nat nat suc X_1)) (hAPP nat _let_0 (ord_less nat) X_1))) ) 22.99/23.00 ( (zero_zero nat) ) 22.99/23.00 ( (hAPP nat nat suc (zero_zero nat)) ) 22.99/23.00 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144575 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (divisi14063676e_zero X_a)) (not (real_n1866405975lgebra X_a)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_144575)) (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_144575))))) ) 22.99/23.00 ( real, (zero_zero real) ) 22.99/23.00 ( complex, ii ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (or (not (= (hAPP int int (hAPP int _let_0 (times_times int) A_1) B) (hAPP nat int (hAPP int (fun nat int) (power_power int) C_1) N))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) N))) (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd A_1) B))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP int int (abs_abs int) A_1) (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) N))) )))) ) 22.99/23.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (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 int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w), w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( y, v, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( y, w, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( sa, v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( sa, w, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( x, v, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( x, w, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( r, w, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real complex cis A_1) (hAPP real complex (hAPP real (fun real complex) complex_1 (hAPP real real cos A_1)) (hAPP real real sin A_1))) ) 22.99/23.00 ( pi ) 22.99/23.00 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( (zero_zero real) ) 22.99/23.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 22.99/23.00 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 22.99/23.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.99/23.00 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 22.99/23.00 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 22.99/23.00 ( skv_10 ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((Na $$unsorted)) (= (hBOOL (hAPP nat bool (even_odd_even nat) Na)) (not (forall ((M_2 $$unsorted)) (not (= Na (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) M_2))) ))) ) 22.99/23.00 ( (zero_zero nat) ) 22.99/23.00 ( (one_one nat) ) 22.99/23.00 ) 22.99/23.00 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144701 $$unsorted) (BOUND_VARIABLE_144702 $$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_144701) BOUND_VARIABLE_144702)) (= (ti X_a BOUND_VARIABLE_144702) (ti X_a BOUND_VARIABLE_144701)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144702) BOUND_VARIABLE_144701))))) ) 22.99/23.00 ( int, pls, (zero_zero int) ) 22.99/23.00 ( int, (one_one int), (zero_zero int) ) 22.99/23.00 ( int, (one_one int), t ) 22.99/23.00 ( int, min, min ) 22.99/23.00 ( int, min, (zero_zero int) ) 22.99/23.00 ( int, (zero_zero int), pls ) 22.99/23.00 ( int, (zero_zero int), (one_one int) ) 22.99/23.00 ( int, (zero_zero int), min ) 22.99/23.00 ( 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))) ) 22.99/23.00 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( 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))) ) 22.99/23.00 ( 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))), (zero_zero int) ) 22.99/23.00 ( 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 ) 22.99/23.00 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( 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 ) 22.99/23.00 ( 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 ) 22.99/23.00 ( 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_5 ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.00 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 22.99/23.00 ( int, t, (one_one int) ) 22.99/23.00 ( 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))) ) 22.99/23.00 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.00 ( 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))) ) 22.99/23.00 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.00 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.00 ( nat, (zero_zero nat), n ) 22.99/23.00 ( nat, (zero_zero nat), tn ) 22.99/23.00 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 22.99/23.00 ( nat, n, (zero_zero nat) ) 22.99/23.01 ( nat, tn, (zero_zero nat) ) 22.99/23.01 ( real, pi, (zero_zero real) ) 22.99/23.01 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( 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)) ) 22.99/23.01 ( 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)))) ) 22.99/23.01 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( 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) ) 22.99/23.01 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( real, (zero_zero real), pi ) 22.99/23.01 ( 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)))) ) 22.99/23.01 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( 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))))) ) 22.99/23.01 ( real, (zero_zero real), skv_2 ) 22.99/23.01 ( real, (zero_zero real), skv_9 ) 22.99/23.01 ( real, (zero_zero real), skv_12 ) 22.99/23.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.99/23.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.99/23.01 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.01 ( 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) ) 22.99/23.01 ( 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 ) 22.99/23.01 ( real, skv_2, (zero_zero real) ) 22.99/23.01 ( real, skv_9, (zero_zero real) ) 22.99/23.01 ( real, skv_12, (zero_zero real) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((P_4 $$unsorted)) (= (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (one_one int)) P_4)) (forall ((M_2 $$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 zprime P_4))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( t ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (dvd_dvd int))) (or (not (hBOOL (hAPP int bool _let_1 M))) (not (hBOOL (hAPP int bool _let_1 N))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 M) N))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_2 N) M))) (= (ti int N) (ti int M)))))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 22.99/23.01 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 22.99/23.01 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.01 ( (hAPP 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)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (div_mod int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) (zero_zero int)) Ma))) (= (= (hAPP int int (hAPP int _let_0 _let_2 A_3) Ma) (hAPP int int (hAPP int _let_0 _let_2 B_2) Ma)) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong A_3) B_2) Ma))))))) ) 22.99/23.01 ( (hAPP nat int (hAPP 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))) ) 22.99/23.01 ( (hAPP nat int (hAPP 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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( s1, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144771 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_144771)) (zero_zero int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_144771) (hAPP int X_a (number_number_of X_a) min))))) ) 22.99/23.01 ( int, (one_one int) ) 22.99/23.01 ( int, min ) 22.99/23.01 ( int, (zero_zero int) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 22.99/23.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( real, (zero_zero real) ) 22.99/23.01 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( real, skv_10 ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (hAPP int (fun int int) (times_times int) (hAPP nat int (semiring_1_of_nat int) K_4)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I_1) J_2))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) K_4))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int _let_2 I_1)) (hAPP int int _let_2 J_2))))))) ) 22.99/23.01 ( (zero_zero nat), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144835 $$unsorted) (BOUND_VARIABLE_144836 $$unsorted) (BOUND_VARIABLE_144837 $$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 (times_times X_a))) (or (not (ordered_ring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144836) BOUND_VARIABLE_144837))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_144835) (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 _let_3 BOUND_VARIABLE_144837) BOUND_VARIABLE_144835)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_144836) BOUND_VARIABLE_144835)))))))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_144938 $$unsorted) (BOUND_VARIABLE_144939 $$unsorted) (BOUND_VARIABLE_144940 $$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 (hAPP int int (hAPP int (fun int int) (times_times int) BOUND_VARIABLE_144938) BOUND_VARIABLE_144939))) BOUND_VARIABLE_144940) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_144938)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 BOUND_VARIABLE_144939)) BOUND_VARIABLE_144940))))))) ) 22.99/23.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))) ) 22.99/23.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 22.99/23.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 22.99/23.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.99/23.01 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 22.99/23.01 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (mono nat X_a))) (or (not (order X_a)) (= _let_0 (ti (fun (fun nat (fun nat bool)) (fun (fun nat X_a) bool)) _let_0)))) ) 22.99/23.01 ( rat ) 22.99/23.01 ( int ) 22.99/23.01 ( (fun int int) ) 22.99/23.01 ( nat ) 22.99/23.01 ( bool ) 22.99/23.01 ( real ) 22.99/23.01 ( (fun real real) ) 22.99/23.01 ( (fun nat nat) ) 22.99/23.01 ( complex ) 22.99/23.01 ( (product_prod int int) ) 22.99/23.01 ( (fun bool bool) ) 22.99/23.01 ( (fun nat bool) ) 22.99/23.01 ( (fun nat (fun nat bool)) ) 22.99/23.01 ( quickcheck_code_int ) 22.99/23.01 ( code_code_numeral ) 22.99/23.01 ( (fun nat (product_prod int int)) ) 22.99/23.01 ( (product_prod real real) ) 22.99/23.01 ( (product_prod nat nat) ) 22.99/23.01 ( (fun (product_prod nat nat) bool) ) 22.99/23.01 ( (fun nat (fun (product_prod nat nat) bool)) ) 22.99/23.01 ( (fun nat (product_prod nat nat)) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((N $$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)))) (or (not (= (hAPP int nat _let_1 (hAPP int int bit1 (hAPP int int bit1 pls))) (hAPP nat nat (hAPP nat _let_0 (div_mod nat) N) (hAPP int nat _let_1 (hAPP int int bit0 _let_2))))) (not (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) (one_one nat))) (hAPP int nat _let_1 _let_2))))))))) ) 22.99/23.01 ( (hAPP int nat nat_1 t) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int (number_number_of int) K_4) (ti int K_4)) ) 22.99/23.01 ( pls ) 22.99/23.01 ( (hAPP int int bit1 pls) ) 22.99/23.01 ( min ) 22.99/23.01 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.01 ( s ) 22.99/23.01 ( s1 ) 22.99/23.01 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( m ) 22.99/23.01 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.01 ( t ) 22.99/23.01 ( v ) 22.99/23.01 ( w ) 22.99/23.01 ( y ) 22.99/23.01 ( sa ) 22.99/23.01 ( x ) 22.99/23.01 ( r ) 22.99/23.01 ( m1 ) 22.99/23.01 ( skv_14 ) 22.99/23.01 ( skv_20 ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((A_1 $$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)))) ) 22.99/23.01 ( s ) 22.99/23.01 ( s1 ) 22.99/23.01 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.01 ( v ) 22.99/23.01 ( w ) 22.99/23.01 ( y ) 22.99/23.01 ( x ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 22.99/23.01 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.99/23.01 ( skv_6 ) 22.99/23.01 ( skv_7 ) 22.99/23.01 ( skv_14 ) 22.99/23.01 ( skv_16 ) 22.99/23.01 ( skv_20 ) 22.99/23.01 ( skv_23 ) 22.99/23.01 ( skv_24 ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145093 $$unsorted) (BOUND_VARIABLE_145094 $$unsorted)) (or (not (comm_semiring_1 X_a)) (and (not (= (one_one X_a) (ti X_a BOUND_VARIABLE_145093))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_145094)))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_145093) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_145093) BOUND_VARIABLE_145094)))) ) 22.99/23.01 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X $$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)))) (not (hBOOL (hAPP real bool _let_2 X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X)))))) ) 22.99/23.01 ( (one_one real) ) 22.99/23.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((W $$unsorted) (V $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int int _let_2 V))) (let ((_let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 W)) _let_3))) (let ((_let_5 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_4)))) (let ((_let_6 (hAPP int (fun int _let_1) negDivAlg (hAPP int int _let_2 W)))) (let ((_let_7 (hAPP int _let_1 _let_6 _let_3))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) _let_3))) (and (or (not _let_5) (= _let_7 (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) (hAPP int int _let_2 min)) _let_4))) (or _let_5 (= _let_7 (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust _let_3) (hAPP int _let_1 _let_6 (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_3))))))))))))))) ) 22.99/23.01 ( (hAPP int int bit1 pls), pls ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) X))) (= (hAPP int nat nat_1 (hAPP int int (fact_fact int) X)) (hAPP nat nat (fact_fact nat) (hAPP int nat nat_1 X)))) ) 22.99/23.01 ( pls ) 22.99/23.01 ( (one_one int) ) 22.99/23.01 ( min ) 22.99/23.01 ( (zero_zero int) ) 22.99/23.01 ( s ) 22.99/23.01 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.01 ( skv_4 ) 22.99/23.01 ( skv_5 ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$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)))) ) 22.99/23.01 ( int ) 22.99/23.01 ( (fun int int) ) 22.99/23.01 ( nat ) 22.99/23.01 ( bool ) 22.99/23.01 ( real ) 22.99/23.01 ( (fun nat real) ) 22.99/23.01 ( (fun real real) ) 22.99/23.01 ( complex ) 22.99/23.01 ( (fun int bool) ) 22.99/23.01 ( (product_prod int int) ) 22.99/23.01 ( (fun (product_prod int int) int) ) 22.99/23.01 ( (fun int (fun int bool)) ) 22.99/23.01 ( (fun nat bool) ) 22.99/23.01 ( (fun (product_prod int int) bool) ) 22.99/23.01 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.99/23.01 ( (fun real bool) ) 22.99/23.01 ( quickcheck_code_int ) 22.99/23.01 ( code_code_numeral ) 22.99/23.01 ( (fun int (fun int (fun int bool))) ) 22.99/23.01 ( (fun int real) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145258 $$unsorted) (BOUND_VARIABLE_145268 $$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_145258))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_145268))) (or (not (linordered_idom X_a)) (not (number_ring 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 _let_0 _let_4) (hAPP X_a X_a (uminus_uminus X_a) _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))))))))))) ) 22.99/23.01 ( int, pls, pls ) 22.99/23.01 ( int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.99/23.01 ( int, min, min ) 22.99/23.01 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.01 ( nat, pls, pls ) 22.99/23.01 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.99/23.01 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.01 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.01 ( real, min, min ) 22.99/23.01 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( 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))) ) 22.99/23.01 ( 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)))))))) ) 22.99/23.01 ( complex, min, min ) 22.99/23.01 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.01 ( quickcheck_code_int, pls, pls ) 22.99/23.01 ( quickcheck_code_int, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.99/23.01 ( quickcheck_code_int, (one_one int), (one_one int) ) 22.99/23.01 ( code_code_numeral, pls, pls ) 22.99/23.01 ( code_code_numeral, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((N $$unsorted)) (= (hAPP int real (real_1 int) (hAPP nat int (semiring_1_of_nat int) N)) (hAPP nat real (real_1 nat) N)) ) 22.99/23.01 ( (zero_zero nat) ) 22.99/23.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( (one_one nat) ) 22.99/23.01 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.01 ( n ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145296 $$unsorted) (BOUND_VARIABLE_145297 $$unsorted)) (or (not (dense_linorder X_a)) (not (forall ((X_1 $$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_1) BOUND_VARIABLE_145297))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) X_1) BOUND_VARIABLE_145296)))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_145297) BOUND_VARIABLE_145296))) ) 22.99/23.01 ( int, pls, min ) 22.99/23.01 ( int, pls, (zero_zero int) ) 22.99/23.01 ( int, (one_one int), (zero_zero int) ) 22.99/23.01 ( int, min, min ) 22.99/23.01 ( int, min, (zero_zero int) ) 22.99/23.01 ( int, s, (zero_zero int) ) 22.99/23.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.99/23.01 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.99/23.01 ( int, t, (one_one int) ) 22.99/23.01 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.99/23.01 ( int, skv_4, (zero_zero int) ) 22.99/23.01 ( int, skv_5, (zero_zero int) ) 22.99/23.01 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.01 ( real, pi, (zero_zero real) ) 22.99/23.01 ( 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)))) ) 22.99/23.01 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.99/23.01 ( 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) ) 22.99/23.01 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.01 ( real, skv_10, (zero_zero real) ) 22.99/23.01 ( real, skv_11, (zero_zero real) ) 22.99/23.01 ( real, skv_15, (zero_zero real) ) 22.99/23.01 ( real, skv_18, (zero_zero real) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145333 $$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_145333)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_145333)))))) ) 22.99/23.01 ( int, pls ) 22.99/23.01 ( int, (one_one int) ) 22.99/23.01 ( int, min ) 22.99/23.01 ( 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)))) ) 22.99/23.01 ( real, (one_one real) ) 22.99/23.01 ( real, (zero_zero real) ) 22.99/23.01 ( 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) ) 22.99/23.01 ( complex, ii ) 22.99/23.01 ( complex, (one_one complex) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (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_3 (fun real bool))) (let ((_let_4 (ord_less real))) (let ((_let_5 (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))) (or (not (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 (hAPP real real (uminus_uminus real) _let_2)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_3 _let_4 X) _let_2))) (= (hAPP real real tan X) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin _let_5)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real cos _let_5)) (one_one real))))))))))) ) 22.99/23.01 ( pi ) 22.99/23.01 ( (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)))) ) 22.99/23.01 ( (one_one real) ) 22.99/23.01 ( (zero_zero real) ) 22.99/23.01 ( (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))))) ) 22.99/23.01 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( (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))))) ) 22.99/23.01 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 22.99/23.01 ( (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))))) ) 22.99/23.01 ( (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)))) ) 22.99/23.01 ( (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)) ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((R_3 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) R_3))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (real_1 int))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) R_3) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) N_1) (one_one int)))))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) (hAPP int real _let_0 N_1)) R_3)))))) ))) ) 22.99/23.01 ( pi ) 22.99/23.01 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.01 ( skv_10 ) 22.99/23.01 ( skv_11 ) 22.99/23.01 ( skv_15 ) 22.99/23.01 ( skv_18 ) 22.99/23.01 ) 22.99/23.01 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145399 $$unsorted) (BOUND_VARIABLE_145400 $$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)) (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) (plus_plus X_a) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145399) _let_0)) (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_145400) _let_0))) (zero_zero X_a)))))))) ) 22.99/23.01 ( int, v, w ) 22.99/23.01 ( int, x, y ) 22.99/23.01 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 22.99/23.02 ( int, skv_6, skv_7 ) 22.99/23.02 ( int, skv_23, skv_24 ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) Y))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natfloor X)) (hAPP real nat natfloor Y)))) ) 22.99/23.02 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.99/23.02 ( (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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( (zero_zero real), pi ) 22.99/23.02 ( (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)))) ) 22.99/23.02 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( (zero_zero real), skv_10 ) 22.99/23.02 ( (zero_zero real), skv_11 ) 22.99/23.02 ( (zero_zero real), skv_15 ) 22.99/23.02 ( (zero_zero real), skv_18 ) 22.99/23.02 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.02 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (deriv X_a))) (or (not (real_normed_field X_a)) (= _let_0 (ti (fun (fun X_a X_a) (fun X_a (fun X_a bool))) _let_0)))) ) 22.99/23.02 ( int ) 22.99/23.02 ( (fun int int) ) 22.99/23.02 ( nat ) 22.99/23.02 ( bool ) 22.99/23.02 ( real ) 22.99/23.02 ( (fun nat real) ) 22.99/23.02 ( (fun real real) ) 22.99/23.02 ( (filter nat) ) 22.99/23.02 ( complex ) 22.99/23.02 ( (fun int bool) ) 22.99/23.02 ( (product_prod int int) ) 22.99/23.02 ( (fun (product_prod int int) int) ) 22.99/23.02 ( (fun int (fun int bool)) ) 22.99/23.02 ( (fun nat bool) ) 22.99/23.02 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 22.99/23.02 ( (fun (product_prod int int) bool) ) 22.99/23.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.99/23.02 ( (fun real bool) ) 22.99/23.02 ( code_code_numeral ) 22.99/23.02 ( (product_prod real real) ) 22.99/23.02 ( (filter real) ) 22.99/23.02 ( (product_prod nat nat) ) 22.99/23.02 ( (fun nat rat) ) 22.99/23.02 ( (fun int (fun int (fun int bool))) ) 22.99/23.02 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 22.99/23.02 ( (fun int real) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145513 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_145513)) (hAPP int X_a _let_0 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_145513))))) ) 22.99/23.02 ( int, pls ) 22.99/23.02 ( int, (hAPP int int bit1 pls) ) 22.99/23.02 ( int, (one_one int) ) 22.99/23.02 ( int, min ) 22.99/23.02 ( nat, pls ) 22.99/23.02 ( nat, min ) 22.99/23.02 ( real, (one_one int) ) 22.99/23.02 ( complex, (one_one int) ) 22.99/23.02 ( quickcheck_code_int, pls ) 22.99/23.02 ( quickcheck_code_int, min ) 22.99/23.02 ( code_code_numeral, pls ) 22.99/23.02 ( code_code_numeral, min ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145647 $$unsorted) (BOUND_VARIABLE_145648 $$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_145648) BOUND_VARIABLE_145647)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_145647) BOUND_VARIABLE_145648)))))) ) 22.99/23.02 ( int, pls, min ) 22.99/23.02 ( int, pls, (zero_zero int) ) 22.99/23.02 ( int, (one_one int), (zero_zero int) ) 22.99/23.02 ( int, (one_one int), t ) 22.99/23.02 ( int, min, min ) 22.99/23.02 ( int, min, (zero_zero int) ) 22.99/23.02 ( int, (zero_zero int), pls ) 22.99/23.02 ( int, (zero_zero int), (one_one int) ) 22.99/23.02 ( int, (zero_zero int), min ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.02 ( int, s, (zero_zero int) ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 22.99/23.02 ( int, t, (one_one int) ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 22.99/23.02 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.02 ( int, skv_4, (zero_zero int) ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( int, skv_5, (zero_zero int) ) 22.99/23.02 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 22.99/23.02 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( nat, (zero_zero nat), n ) 22.99/23.02 ( nat, (zero_zero nat), tn ) 22.99/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( real, pi, (zero_zero real) ) 22.99/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( 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)))) ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( 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)))), (zero_zero real) ) 22.99/23.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( real, (zero_zero real), pi ) 22.99/23.02 ( 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)))) ) 22.99/23.02 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( real, (zero_zero real), skv_2 ) 22.99/23.02 ( real, (zero_zero real), skv_9 ) 22.99/23.02 ( real, (zero_zero real), skv_12 ) 22.99/23.02 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.02 ( 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) ) 22.99/23.02 ( 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 ) 22.99/23.02 ( real, skv_10, (zero_zero real) ) 22.99/23.02 ( real, skv_11, (zero_zero real) ) 22.99/23.02 ( real, skv_15, (zero_zero real) ) 22.99/23.02 ( real, skv_18, (zero_zero real) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (zero_zero X_a)) (ring_1_Ints X_a))))) ) 22.99/23.02 ( rat ) 22.99/23.02 ( int ) 22.99/23.02 ( nat ) 22.99/23.02 ( real ) 22.99/23.02 ( complex ) 22.99/23.02 ( quickcheck_code_int ) 22.99/23.02 ( code_code_numeral ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$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)))) ) 22.99/23.02 ( rat ) 22.99/23.02 ( int ) 22.99/23.02 ( nat ) 22.99/23.02 ( real ) 22.99/23.02 ( complex ) 22.99/23.02 ( quickcheck_code_int ) 22.99/23.02 ( code_code_numeral ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_145770 $$unsorted)) (let ((_let_0 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_145770))) (or (not (division_ring X_b)) (not (number X_b)) (= (hAPP X_b X_b (inverse_inverse X_b) _let_0) (hAPP X_b X_b (hAPP X_b (fun X_b X_b) (inverse_divide X_b) (one_one X_b)) _let_0)))) ) 22.99/23.02 ( int, pls ) 22.99/23.02 ( int, (hAPP int int bit1 pls) ) 22.99/23.02 ( int, min ) 22.99/23.02 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.02 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.02 ( nat, pls ) 22.99/23.02 ( nat, (hAPP int int bit1 pls) ) 22.99/23.02 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.02 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.02 ( real, min ) 22.99/23.02 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.02 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.02 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.02 ( 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)))))))) ) 22.99/23.02 ( complex, min ) 22.99/23.02 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 22.99/23.02 ( quickcheck_code_int, pls ) 22.99/23.02 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 22.99/23.02 ( quickcheck_code_int, (one_one int) ) 22.99/23.02 ( code_code_numeral, pls ) 22.99/23.02 ( code_code_numeral, (hAPP int int bit1 pls) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (nat_rec X_a))) (= _let_0 (ti (fun X_a (fun (fun nat (fun X_a X_a)) (fun nat X_a))) _let_0))) ) 22.99/23.02 ( int ) 22.99/23.02 ( (fun int int) ) 22.99/23.02 ( nat ) 22.99/23.02 ( bool ) 22.99/23.02 ( real ) 22.99/23.02 ( (fun nat real) ) 22.99/23.02 ( (fun real real) ) 22.99/23.02 ( complex ) 22.99/23.02 ( (fun int bool) ) 22.99/23.02 ( (product_prod int int) ) 22.99/23.02 ( (fun (product_prod int int) int) ) 22.99/23.02 ( (fun int (fun int bool)) ) 22.99/23.02 ( (fun nat bool) ) 22.99/23.02 ( (fun (product_prod int int) bool) ) 22.99/23.02 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 22.99/23.02 ( (fun real bool) ) 22.99/23.02 ( code_code_numeral ) 22.99/23.02 ( (fun int (fun int (fun int bool))) ) 22.99/23.02 ( (fun int real) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145788 $$unsorted) (BOUND_VARIABLE_145789 $$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_145788) BOUND_VARIABLE_145789))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_145788) (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_145789))))) ) 22.99/23.02 ( int, (one_one int), zEven ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((K $$unsorted) (L $$unsorted)) (= (= (hAPP int int bit1 K) (hAPP int int bit1 L)) (= (ti int K) (ti int L))) ) 22.99/23.02 ( pls, pls ) 22.99/23.02 ( pls, (hAPP int int bit1 pls) ) 22.99/23.02 ( (hAPP int int bit1 pls), pls ) 22.99/23.02 ( (hAPP int int bit1 pls), min ) 22.99/23.02 ( min, pls ) 22.99/23.02 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (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)))))) ) 22.99/23.02 ( (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 22.99/23.02 ( (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)))) ) 22.99/23.02 ( (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 pls)) ) 22.99/23.02 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 22.99/23.02 ( (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 pls)) ) 22.99/23.02 ( (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 bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 22.99/23.02 ( (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 bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 22.99/23.02 ( (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 bit1 pls)) ) 22.99/23.02 ( (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 bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145818 $$unsorted) (BOUND_VARIABLE_145819 $$unsorted) (BOUND_VARIABLE_145820 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_145818))) (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_145819) BOUND_VARIABLE_145820))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145819))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145820)))) ) 22.99/23.02 ( int, (one_one int), (one_one int), t ) 22.99/23.02 ( int, min, (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.02 ( int, (zero_zero int), (zero_zero int), (one_one int) ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (zero_zero int), pls ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), min, min ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), min, pls ) 22.99/23.02 ( 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) ) 22.99/23.02 ( 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 real real (hAPP 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))) ) 22.99/23.02 ( 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)))) ) 22.99/23.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 22.99/23.02 ( real, skv_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)))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((Nat_1 $$unsorted)) (let ((_let_0 (size_size nat))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP nat nat _let_0 Nat_1)) (hAPP nat nat suc (zero_zero nat))) (hAPP nat nat _let_0 (hAPP nat nat suc Nat_1)))) ) 22.99/23.02 ( (zero_zero nat) ) 22.99/23.02 ( (hAPP nat nat suc (zero_zero nat)) ) 22.99/23.02 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145846 $$unsorted) (BOUND_VARIABLE_145847 $$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_145847)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145846)) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_145846) BOUND_VARIABLE_145847)))))) ) 22.99/23.02 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (times_times int) (one_one int)) Z_1)) ) 22.99/23.02 ( pls ) 22.99/23.02 ( min ) 22.99/23.02 ( s ) 22.99/23.02 ( s1 ) 22.99/23.02 ( m ) 22.99/23.02 ( t ) 22.99/23.02 ( v ) 22.99/23.02 ( w ) 22.99/23.02 ( y ) 22.99/23.02 ( sa ) 22.99/23.02 ( x ) 22.99/23.02 ( r ) 22.99/23.02 ( m1 ) 22.99/23.02 ( skv_14 ) 22.99/23.02 ( skv_20 ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145915 $$unsorted) (BOUND_VARIABLE_145916 $$unsorted) (BOUND_VARIABLE_145917 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_145915))) (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_145916) BOUND_VARIABLE_145917))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145916))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_145917)))) ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.02 ( int, min, (zero_zero int), pls ) 22.99/23.02 ( int, (zero_zero int), (zero_zero int), (one_one int) ) 22.99/23.02 ( int, s, min, pls ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), min, min ) 22.99/23.02 ( int, t, (one_one int), t ) 22.99/23.02 ( int, m1, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 22.99/23.02 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 22.99/23.02 ( int, skv_5, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( real, pi, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( 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 real real (hAPP 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))) ) 22.99/23.02 ( real, (one_one 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)))) ) 22.99/23.02 ( real, (zero_zero real), (zero_zero real), pi ) 22.99/23.02 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( 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))))), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 22.99/23.02 ( 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)), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145944 $$unsorted) (BOUND_VARIABLE_145945 $$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_145945))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_145944) _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_145945) BOUND_VARIABLE_145944)) _let_2)))))) ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 22.99/23.02 ( 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)))) ) 22.99/23.02 ( 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))) ) 22.99/23.02 ( 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)))) ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 22.99/23.02 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 22.99/23.02 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 22.99/23.02 ( 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) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP real int (archim2085082626_floor real) X) (ti int N))))) ) 22.99/23.02 ( (zero_zero int), pi ) 22.99/23.02 ( (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)))) ) 22.99/23.02 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( (zero_zero int), skv_10 ) 22.99/23.02 ( (zero_zero int), skv_11 ) 22.99/23.02 ( (zero_zero int), skv_15 ) 22.99/23.02 ( (zero_zero int), skv_18 ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_145992 $$unsorted) (BOUND_VARIABLE_145993 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_145992) BOUND_VARIABLE_145993) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_145993)) (hBOOL (hAPP _let_1 bool (bseq X_a) (hAPP _let_1 _let_1 (hAPP (fun X_a X_a) (fun _let_1 _let_1) (combb X_a X_a nat) (inverse_inverse X_a)) BOUND_VARIABLE_145992)))))) ) 22.99/23.02 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((N $$unsorted)) (= (hAPP int int (uminus_uminus int) N) (hAPP real int (archim2085082626_floor real) (hAPP real real (uminus_uminus real) (hAPP int real (real_1 int) N)))) ) 22.99/23.02 ( pls ) 22.99/23.02 ( (one_one int) ) 22.99/23.02 ( min ) 22.99/23.02 ( (zero_zero int) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP nat nat suc (zero_zero nat))) N))) (hBOOL (hAPP nat bool prime N)) (not (forall ((M_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP nat _let_0 _let_1 (hAPP nat nat suc (zero_zero nat))))) (or (not (hBOOL (hAPP nat bool _let_2 M_2))) (not (hBOOL (hAPP nat bool _let_2 K_1))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 M_2) N))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 K_1) N))) (not (= N (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M_2) K_1))))))) ))) ) 22.99/23.02 ( (zero_zero nat) ) 22.99/23.02 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ( (hAPP nat nat suc (zero_zero nat)) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146059 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_146059)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_146059) (hAPP int int bit1 pls)))))) ) 22.99/23.02 ( int, (hAPP int int bit1 pls) ) 22.99/23.02 ( nat, (hAPP int int bit1 pls) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146082 $$unsorted) (BOUND_VARIABLE_146083 $$unsorted) (BOUND_VARIABLE_146084 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_146082))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_146083) BOUND_VARIABLE_146084))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_146082))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146082) (one_one X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_146084)) (hAPP nat X_a _let_2 BOUND_VARIABLE_146083))))))) ) 22.99/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP complex (fun complex complex) (times_times complex) ii))) (= (hAPP complex complex _let_0 (hAPP complex complex _let_0 X)) (hAPP complex complex (uminus_uminus complex) X))) ) 22.99/23.02 ( ii ) 22.99/23.02 ( (one_one complex) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146141 $$unsorted) (BOUND_VARIABLE_146142 $$unsorted)) (let ((_let_0 (ring_1_of_int X_a))) (or (not (ring_1 X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_146141)) (hAPP int X_a _let_0 BOUND_VARIABLE_146142)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) BOUND_VARIABLE_146141) BOUND_VARIABLE_146142))))) ) 22.99/23.02 ( real, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (hAPP complex real re Y) (hAPP complex real re X))) (not (= (hAPP complex real im X) (hAPP complex real im Y))) (= X Y)) ) 22.99/23.02 ( (zero_zero complex), (one_one complex) ) 22.99/23.02 ( ii, (zero_zero complex) ) 22.99/23.02 ( (one_one complex), (zero_zero complex) ) 22.99/23.02 ( (one_one complex), ii ) 22.99/23.02 ( (one_one complex), (one_one complex) ) 22.99/23.02 ) 22.99/23.02 (instantiation (forall ((Xa $$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)) Xa))) (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) Xa))) (zero_zero real)) sequentially))))) ) 22.99/23.02 ( (hAPP int real (number_number_of real) min) ) 22.99/23.02 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 22.99/23.02 ( (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)))) ) 22.99/23.02 ) 23.02/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146170 $$unsorted) (BOUND_VARIABLE_146171 $$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_146170) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_146171))) (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_146170)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146171) _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_146170) BOUND_VARIABLE_146171)) _let_2)))))))) ) 23.02/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.02/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.02/23.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.02/23.02 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( 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))))))))) ) 23.02/23.02 ( 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))) ) 23.02/23.02 ( 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))) ) 23.02/23.02 ( 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))) ) 23.02/23.02 ) 23.02/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146204 $$unsorted) (BOUND_VARIABLE_146205 $$unsorted) (BOUND_VARIABLE_146206 $$unsorted) (BOUND_VARIABLE_146207 $$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))) (or (not (ordere223160158up_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146206) BOUND_VARIABLE_146207))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146204) BOUND_VARIABLE_146205))) (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_146206) BOUND_VARIABLE_146204)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_146207) BOUND_VARIABLE_146205)))))))) ) 23.02/23.02 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one 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) ) 23.02/23.02 ) 23.02/23.02 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP int int (abs_abs int) X))) (= _let_0 (hAPP nat int (semiring_1_of_nat int) (hAPP int nat nat_1 _let_0)))) ) 23.02/23.02 ( v ) 23.02/23.02 ( w ) 23.02/23.02 ( skv_14 ) 23.02/23.02 ( skv_20 ) 23.02/23.02 ) 23.02/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146285 $$unsorted) (BOUND_VARIABLE_146286 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_146285))) (or (not (power X_a)) (= (hAPP nat X_a _let_0 (hAPP nat nat suc BOUND_VARIABLE_146286)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_146285) (hAPP nat X_a _let_0 BOUND_VARIABLE_146286))))) ) 23.02/23.02 ( int, s, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, s1, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, v, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, w, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, y, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, x, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, skv_6, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, skv_7, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, skv_16, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, skv_23, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( int, skv_24, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ( complex, ii, (hAPP nat nat suc (zero_zero nat)) ) 23.02/23.02 ) 23.02/23.02 (instantiation (forall ((Sb $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (zero_zero real))) (let ((_let_4 (fun nat _let_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_3) Sb))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto nat real) (hAPP real _let_0 (hAPP _let_4 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_4 (hAPP (fun real _let_1) (fun _let_0 _let_4) (combb real _let_1 nat) powr) (real_1 nat))) (hAPP real real (uminus_uminus real) Sb))) _let_3) sequentially)))))))) ) 23.02/23.02 ( pi ) 23.02/23.02 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( (one_one real) ) 23.02/23.02 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.02/23.02 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.02/23.02 ( skv_2 ) 23.02/23.02 ( skv_9 ) 23.02/23.02 ( skv_12 ) 23.02/23.02 ) 23.02/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146394 $$unsorted) (BOUND_VARIABLE_146395 $$unsorted) (BOUND_VARIABLE_146396 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (minus_minus X_a))) (let ((_let_2 (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_146394))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_146395)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_146396)) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146395) BOUND_VARIABLE_146396))))))) ) 23.02/23.02 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.02/23.02 ( int, y, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, y, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, sa, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, sa, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, x, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, x, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, r, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, r, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.02/23.02 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.02 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.02 ) 23.03/23.02 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP real real sin A_1) (hAPP complex real im (hAPP real complex cis A_1))) ) 23.03/23.02 ( pi ) 23.03/23.02 ( (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)))) ) 23.03/23.02 ( (zero_zero real) ) 23.03/23.02 ( (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))))) ) 23.03/23.02 ( (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) ) 23.03/23.02 ( (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))))) ) 23.03/23.02 ( (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)))) ) 23.03/23.02 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.03/23.02 ) 23.03/23.02 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146437 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (or (not (group_add X_a)) (= (ti X_a BOUND_VARIABLE_146437) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_0 BOUND_VARIABLE_146437))))) ) 23.03/23.02 ( int, pls ) 23.03/23.02 ( int, (one_one int) ) 23.03/23.02 ( int, min ) 23.03/23.02 ( int, s ) 23.03/23.02 ( int, s1 ) 23.03/23.02 ( int, m ) 23.03/23.02 ( int, t ) 23.03/23.02 ( int, v ) 23.03/23.02 ( int, w ) 23.03/23.02 ( int, y ) 23.03/23.02 ( int, sa ) 23.03/23.02 ( int, x ) 23.03/23.02 ( int, r ) 23.03/23.02 ( int, m1 ) 23.03/23.02 ( int, skv_14 ) 23.03/23.02 ( int, skv_20 ) 23.03/23.02 ( (fun int int), bit1 ) 23.03/23.02 ( (fun int int), bit0 ) 23.03/23.02 ( (fun int int), succ ) 23.03/23.02 ( (fun int int), pred ) 23.03/23.02 ( (fun int int), (fact_fact int) ) 23.03/23.02 ( (fun int int), zfact ) 23.03/23.02 ( nat, n ) 23.03/23.02 ( nat, tn ) 23.03/23.02 ( bool, fTrue ) 23.03/23.02 ( bool, fFalse ) 23.03/23.02 ( real, pi ) 23.03/23.02 ( 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)))) ) 23.03/23.02 ( real, (one_one real) ) 23.03/23.02 ( 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) ) 23.03/23.02 ( (fun nat real), (real_1 nat) ) 23.03/23.02 ( (fun nat real), cos_coeff ) 23.03/23.02 ( (fun nat real), sin_coeff ) 23.03/23.02 ( (fun real real), sin ) 23.03/23.02 ( (fun real real), cos ) 23.03/23.02 ( (fun real real), sqrt ) 23.03/23.02 ( (fun real real), tan ) 23.03/23.02 ( (fun real real), ln ) 23.03/23.02 ( (fun real real), arctan ) 23.03/23.02 ( (fun real real), arcsin ) 23.03/23.02 ( (fun real real), arccos ) 23.03/23.02 ( (fun nat nat), suc ) 23.03/23.02 ( (fun nat nat), (fact_fact nat) ) 23.03/23.02 ( (fun nat nat), nat_size ) 23.03/23.02 ( (fun nat nat), (size_size nat) ) 23.03/23.02 ( (fun nat nat), fact ) 23.03/23.02 ( (filter nat), sequentially ) 23.03/23.02 ( (fun int (fun int rat)), fract ) 23.03/23.02 ( complex, ii ) 23.03/23.02 ( complex, (one_one complex) ) 23.03/23.02 ( (fun int bool), zOdd ) 23.03/23.02 ( (fun int bool), zprime ) 23.03/23.02 ( (fun int bool), zEven ) 23.03/23.03 ( (fun int bool), nat_neg ) 23.03/23.03 ( (fun int bool), nat_is_nat ) 23.03/23.03 ( (fun int bool), (even_odd_even int) ) 23.03/23.03 ( (fun int bool), twoSqu1091635170sum2sq ) 23.03/23.03 ( (fun int (fun int int)), legacy_zgcd ) 23.03/23.03 ( (fun int (fun int int)), (gcd_gcd int) ) 23.03/23.03 ( (fun int (fun int int)), inv ) 23.03/23.03 ( (fun int (fun int int)), multInv ) 23.03/23.03 ( (fun int (fun int int)), legendre ) 23.03/23.03 ( (fun int (fun int int)), standardRes ) 23.03/23.03 ( (fun int (fun int int)), nat_tsub ) 23.03/23.03 ( (fun int (fun int int)), z3div ) 23.03/23.03 ( (fun int (fun int int)), z3mod ) 23.03/23.03 ( (fun int (fun int int)), int_lcm ) 23.03/23.03 ( (fun int (fun int int)), int_gcd ) 23.03/23.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.03/23.03 ( (fun bool bool), fNot ) 23.03/23.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.03/23.03 ( (fun bool (fun bool bool)), fconj ) 23.03/23.03 ( (fun bool (fun bool bool)), fdisj ) 23.03/23.03 ( (fun bool (fun bool bool)), fimplies ) 23.03/23.03 ( (fun int (fun int bool)), quadRes ) 23.03/23.03 ( (fun int (fun int bool)), d22set ) 23.03/23.03 ( (fun int (fun int bool)), norRRset ) 23.03/23.03 ( (fun int (fun int bool)), sRStar ) 23.03/23.03 ( (fun int (fun int bool)), sr ) 23.03/23.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.03/23.03 ( (fun nat bool), (even_odd_even nat) ) 23.03/23.03 ( (fun nat bool), prime ) 23.03/23.03 ( (fun real complex), cis ) 23.03/23.03 ( (fun nat (fun nat bool)), coprime ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.03/23.03 ( (fun (product_prod int int) bool), frac_1 ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.03/23.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.03/23.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.03/23.03 ( (fun (fun int bool) bool), nat_nat_set ) 23.03/23.03 ( (fun nat (fun real real)), root ) 23.03/23.03 ( (fun real (fun real real)), log ) 23.03/23.03 ( (fun real (fun real real)), powr ) 23.03/23.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.03/23.03 ( (fun complex complex), cnj ) 23.03/23.03 ( (fun complex complex), expi ) 23.03/23.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.03/23.03 ( (fun nat (fun nat nat)), nat_gcd ) 23.03/23.03 ( (fun nat (fun nat nat)), nat_lcm ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.03/23.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.03/23.03 ( (fun int (fun (fun int bool) bool)), resSet ) 23.03/23.03 ( (fun int nat), nat_1 ) 23.03/23.03 ( (fun int nat), phi ) 23.03/23.03 ( (fun complex real), re ) 23.03/23.03 ( (fun complex real), im ) 23.03/23.03 ( (fun complex real), arg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.03/23.03 ( (fun (product_prod nat nat) bool), pred_nat ) 23.03/23.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.03/23.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.03/23.03 ( (fun (fun int bool) int), (the int) ) 23.03/23.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.03/23.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.03/23.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.03/23.03 ( (fun real (fun real complex)), rcis ) 23.03/23.03 ( (fun real (fun real complex)), complex_1 ) 23.03/23.03 ( (fun int (fun int (fun int bool))), zcong ) 23.03/23.03 ( (fun int (fun int (fun int bool))), wset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), noXRRset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), bnorRset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), zcongm ) 23.03/23.03 ( (fun real nat), natceiling ) 23.03/23.03 ( (fun real nat), natfloor ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.03/23.03 ( (fun int real), (real_1 int) ) 23.03/23.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.03/23.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.03/23.03 ( (fun complex nat), (size_size complex) ) 23.03/23.03 ( (fun complex nat), complex_size ) 23.03/23.03 ( (fun (fun nat rat) bool), vanishes ) 23.03/23.03 ( (fun (product_prod int int) rat), frct ) 23.03/23.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.03/23.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.03/23.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.03/23.03 ( (fun rat real), ratreal ) 23.03/23.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.03/23.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.03/23.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.03/23.03 ( (fun rat (product_prod int int)), quotient_of ) 23.03/23.03 ( (fun int (fun nat nat)), nat_aux ) 23.03/23.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.03/23.03 ( (fun int (list int)), quickc666637781d_zero ) 23.03/23.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.03/23.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.03/23.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.03/23.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.03/23.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.03/23.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.03/23.03 ( (fun code_code_numeral int), code_int_of ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP int int (hAPP int (fun int int) (plus_plus int) (zero_zero int)) Z_1) (ti int Z_1)) ) 23.03/23.03 ( pls ) 23.03/23.03 ( min ) 23.03/23.03 ( s ) 23.03/23.03 ( s1 ) 23.03/23.03 ( m ) 23.03/23.03 ( t ) 23.03/23.03 ( v ) 23.03/23.03 ( w ) 23.03/23.03 ( y ) 23.03/23.03 ( sa ) 23.03/23.03 ( x ) 23.03/23.03 ( r ) 23.03/23.03 ( m1 ) 23.03/23.03 ( skv_14 ) 23.03/23.03 ( skv_20 ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((L_4 $$unsorted)) (let ((_let_0 (hAPP int (fun int int) (minus_minus int) min))) (= (hAPP int int bit0 (hAPP int int _let_0 L_4)) (hAPP int int _let_0 (hAPP int int bit1 L_4)))) ) 23.03/23.03 ( pls ) 23.03/23.03 ( (hAPP int int bit1 pls) ) 23.03/23.03 ( min ) 23.03/23.03 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.03/23.03 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.03/23.03 ( (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)))))) ) 23.03/23.03 ( (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))))))) ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146455 $$unsorted) (BOUND_VARIABLE_146456 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun nat X_a))) (let ((_let_4 (fun _let_1 X_a))) (or (not (topological_space X_a)) (not (comm_monoid_add X_a)) (= (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_3 (fun X_a _let_0) (tendsto nat X_a) (hAPP _let_2 _let_3 (hAPP _let_4 (fun _let_2 _let_3) (combb _let_1 X_a nat) (hAPP _let_3 _let_4 (big_co1399186613setsum nat X_a) BOUND_VARIABLE_146455)) (hAPP nat _let_2 (ord_atLeastLessThan nat) (zero_zero nat)))) BOUND_VARIABLE_146456) sequentially)) (hBOOL (hAPP X_a bool (hAPP _let_3 (fun X_a bool) (sums X_a) BOUND_VARIABLE_146455) BOUND_VARIABLE_146456))))))))) ) 23.03/23.03 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real re X)) (hAPP complex real re Y))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP complex real im X)) (hAPP complex real im Y))) (hAPP complex real re (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) X) Y))))) ) 23.03/23.03 ( ii, ii ) 23.03/23.03 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.03/23.03 ( (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi)), ii ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_146501 $$unsorted) (BOUND_VARIABLE_146502 $$unsorted) (BOUND_VARIABLE_146503 $$unsorted) (BOUND_VARIABLE_146504 $$unsorted) (BOUND_VARIABLE_146505 $$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_146504))) (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_146505))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_146504)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (norm_norm X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) X_1) BOUND_VARIABLE_146504))) BOUND_VARIABLE_146505))) (= (hAPP X_a X_b BOUND_VARIABLE_146503 X_1) (hAPP X_a X_b BOUND_VARIABLE_146502 X_1))) )) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_146503) BOUND_VARIABLE_146501) _let_5))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 _let_3 _let_4 BOUND_VARIABLE_146502) BOUND_VARIABLE_146501) _let_5))))))))) ) 23.03/23.03 ( real, real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146587 $$unsorted) (BOUND_VARIABLE_146588 $$unsorted) (BOUND_VARIABLE_146589 $$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_146588)))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_146589))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) _let_5) BOUND_VARIABLE_146588))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_146588) _let_1)))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_146587) _let_6))) (or _let_4 (and (or _let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_1) _let_5))) (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_6) BOUND_VARIABLE_146587)))))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_146587) BOUND_VARIABLE_146588)) _let_5)))))))))))) ) 23.03/23.03 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( int, skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), pls ) 23.03/23.03 ( 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)) ) 23.03/23.03 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ( real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_146634 $$unsorted) (BOUND_VARIABLE_146635 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (fun X_a X_b))) (let ((_let_3 (fun X_a real))) (let ((_let_4 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_146635))) (or (not (topological_space X_a)) (not (real_normed_vector X_b)) (not (hBOOL (hAPP _let_0 bool (hAPP real _let_1 (hAPP _let_3 (fun real _let_1) (tendsto X_a real) (hAPP _let_2 _let_3 (hAPP (fun X_b real) (fun _let_2 _let_3) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_146634)) (zero_zero real)) _let_4))) (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP _let_2 (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_146634) (zero_zero X_b)) _let_4)))))))) ) 23.03/23.03 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146656 $$unsorted) (BOUND_VARIABLE_146657 $$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 X_a) BOUND_VARIABLE_146656) BOUND_VARIABLE_146657)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_146656) (hAPP X_a _let_0 (ord_lessThan X_a) BOUND_VARIABLE_146657)))))) ) 23.03/23.03 ( int, (one_one int), t ) 23.03/23.03 ( int, min, min ) 23.03/23.03 ( int, min, (zero_zero int) ) 23.03/23.03 ( int, (zero_zero int), pls ) 23.03/23.03 ( int, (zero_zero int), (one_one int) ) 23.03/23.03 ( int, (zero_zero int), min ) 23.03/23.03 ( 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))) ) 23.03/23.03 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.03 ( 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))) ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.03 ( 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))) ) 23.03/23.03 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.03 ( 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))) ) 23.03/23.03 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.03 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.03 ( nat, (zero_zero nat), n ) 23.03/23.03 ( nat, (zero_zero nat), tn ) 23.03/23.03 ( real, pi, (zero_zero real) ) 23.03/23.03 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.03 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( real, (zero_zero real), pi ) 23.03/23.03 ( 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)))) ) 23.03/23.03 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( real, (zero_zero real), skv_2 ) 23.03/23.03 ( real, (zero_zero real), skv_9 ) 23.03/23.03 ( real, (zero_zero real), skv_12 ) 23.03/23.03 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.03/23.03 ( 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) ) 23.03/23.03 ( 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 ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (semiring_1_of_nat int))) (= (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) X) Y)) (hAPP int int (hAPP int (fun int int) nat_tsub (hAPP nat int _let_0 X)) (hAPP nat int _let_0 Y)))) ) 23.03/23.03 ( (hAPP int nat nat_1 t), (one_one nat) ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C $$unsorted) (D_1 $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (one_one int))) (let ((_let_2 (fun int bool))) (let ((_let_3 (times_times int))) (let ((_let_4 (hAPP int nat nat_1 Xa))) (or (not (= (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_3 A_3) B_2)) C) (hAPP nat int (hAPP int (fun nat int) (power_power int) D_1) _let_4))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (one_one nat)) _let_4))) (not (hBOOL (hAPP _let_2 bool (hAPP int (fun _let_2 bool) (member int) Xa) zOdd))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd A_3) B_2))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd B_2) C))) (not (= _let_1 (hAPP int int (hAPP int _let_0 legacy_zgcd C) A_3))) (and (not (forall ((K_1 $$unsorted)) (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) K_1) _let_4) (ti int A_3))) )) (not (forall ((M_2 $$unsorted)) (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) M_2) _let_4) (ti int C))) )) (not (forall ((L_3 $$unsorted)) (not (= (hAPP nat int (hAPP int (fun nat int) (power_power int) L_3) _let_4) (ti int B_2))) ))))))))) ) 23.03/23.03 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), s1, (one_one int) ) 23.03/23.03 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (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))) m1))), v, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.03 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), y, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.03 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), s, (zero_zero int) ) 23.03/23.03 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), w, t ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146933 $$unsorted)) (let ((_let_0 (ti X_a BOUND_VARIABLE_146933))) (or (not (linord219039673up_add X_a)) (= (= (zero_zero X_a) _let_0) (= _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_146933))))) ) 23.03/23.03 ( int, pls ) 23.03/23.03 ( int, (one_one int) ) 23.03/23.03 ( int, min ) 23.03/23.03 ( int, s ) 23.03/23.03 ( int, s1 ) 23.03/23.03 ( int, m ) 23.03/23.03 ( int, t ) 23.03/23.03 ( int, v ) 23.03/23.03 ( int, w ) 23.03/23.03 ( int, y ) 23.03/23.03 ( int, sa ) 23.03/23.03 ( int, x ) 23.03/23.03 ( int, r ) 23.03/23.03 ( int, m1 ) 23.03/23.03 ( int, skv_14 ) 23.03/23.03 ( int, skv_20 ) 23.03/23.03 ( (fun int int), bit1 ) 23.03/23.03 ( (fun int int), bit0 ) 23.03/23.03 ( (fun int int), succ ) 23.03/23.03 ( (fun int int), pred ) 23.03/23.03 ( (fun int int), (fact_fact int) ) 23.03/23.03 ( (fun int int), zfact ) 23.03/23.03 ( nat, n ) 23.03/23.03 ( nat, tn ) 23.03/23.03 ( bool, fTrue ) 23.03/23.03 ( bool, fFalse ) 23.03/23.03 ( real, pi ) 23.03/23.03 ( 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)))) ) 23.03/23.03 ( real, (one_one real) ) 23.03/23.03 ( 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) ) 23.03/23.03 ( (fun nat real), (real_1 nat) ) 23.03/23.03 ( (fun nat real), cos_coeff ) 23.03/23.03 ( (fun nat real), sin_coeff ) 23.03/23.03 ( (fun real real), sin ) 23.03/23.03 ( (fun real real), cos ) 23.03/23.03 ( (fun real real), sqrt ) 23.03/23.03 ( (fun real real), tan ) 23.03/23.03 ( (fun real real), ln ) 23.03/23.03 ( (fun real real), arctan ) 23.03/23.03 ( (fun real real), arcsin ) 23.03/23.03 ( (fun real real), arccos ) 23.03/23.03 ( (fun nat nat), suc ) 23.03/23.03 ( (fun nat nat), (fact_fact nat) ) 23.03/23.03 ( (fun nat nat), nat_size ) 23.03/23.03 ( (fun nat nat), (size_size nat) ) 23.03/23.03 ( (fun nat nat), fact ) 23.03/23.03 ( (filter nat), sequentially ) 23.03/23.03 ( (fun int (fun int rat)), fract ) 23.03/23.03 ( complex, ii ) 23.03/23.03 ( complex, (one_one complex) ) 23.03/23.03 ( (fun int bool), zOdd ) 23.03/23.03 ( (fun int bool), zprime ) 23.03/23.03 ( (fun int bool), zEven ) 23.03/23.03 ( (fun int bool), nat_neg ) 23.03/23.03 ( (fun int bool), nat_is_nat ) 23.03/23.03 ( (fun int bool), (even_odd_even int) ) 23.03/23.03 ( (fun int bool), twoSqu1091635170sum2sq ) 23.03/23.03 ( (fun int (fun int int)), legacy_zgcd ) 23.03/23.03 ( (fun int (fun int int)), (gcd_gcd int) ) 23.03/23.03 ( (fun int (fun int int)), inv ) 23.03/23.03 ( (fun int (fun int int)), multInv ) 23.03/23.03 ( (fun int (fun int int)), legendre ) 23.03/23.03 ( (fun int (fun int int)), standardRes ) 23.03/23.03 ( (fun int (fun int int)), nat_tsub ) 23.03/23.03 ( (fun int (fun int int)), z3div ) 23.03/23.03 ( (fun int (fun int int)), z3mod ) 23.03/23.03 ( (fun int (fun int int)), int_lcm ) 23.03/23.03 ( (fun int (fun int int)), int_gcd ) 23.03/23.03 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.03/23.03 ( (fun bool bool), fNot ) 23.03/23.03 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.03/23.03 ( (fun bool (fun bool bool)), fconj ) 23.03/23.03 ( (fun bool (fun bool bool)), fdisj ) 23.03/23.03 ( (fun bool (fun bool bool)), fimplies ) 23.03/23.03 ( (fun int (fun int bool)), quadRes ) 23.03/23.03 ( (fun int (fun int bool)), d22set ) 23.03/23.03 ( (fun int (fun int bool)), norRRset ) 23.03/23.03 ( (fun int (fun int bool)), sRStar ) 23.03/23.03 ( (fun int (fun int bool)), sr ) 23.03/23.03 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.03/23.03 ( (fun nat bool), (even_odd_even nat) ) 23.03/23.03 ( (fun nat bool), prime ) 23.03/23.03 ( (fun real complex), cis ) 23.03/23.03 ( (fun nat (fun nat bool)), coprime ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.03/23.03 ( (fun (product_prod int int) bool), frac_1 ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.03/23.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.03/23.03 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.03/23.03 ( (fun (fun int bool) bool), nat_nat_set ) 23.03/23.03 ( (fun nat (fun real real)), root ) 23.03/23.03 ( (fun real (fun real real)), log ) 23.03/23.03 ( (fun real (fun real real)), powr ) 23.03/23.03 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.03/23.03 ( (fun complex complex), cnj ) 23.03/23.03 ( (fun complex complex), expi ) 23.03/23.03 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.03/23.03 ( (fun nat (fun nat nat)), nat_gcd ) 23.03/23.03 ( (fun nat (fun nat nat)), nat_lcm ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.03/23.03 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.03/23.03 ( (fun int (fun (fun int bool) bool)), resSet ) 23.03/23.03 ( (fun int nat), nat_1 ) 23.03/23.03 ( (fun int nat), phi ) 23.03/23.03 ( (fun complex real), re ) 23.03/23.03 ( (fun complex real), im ) 23.03/23.03 ( (fun complex real), arg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.03/23.03 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.03/23.03 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.03/23.03 ( (fun (product_prod nat nat) bool), pred_nat ) 23.03/23.03 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.03/23.03 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.03/23.03 ( (fun (fun int bool) int), (the int) ) 23.03/23.03 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.03/23.03 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.03/23.03 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.03/23.03 ( (fun real (fun real complex)), rcis ) 23.03/23.03 ( (fun real (fun real complex)), complex_1 ) 23.03/23.03 ( (fun int (fun int (fun int bool))), zcong ) 23.03/23.03 ( (fun int (fun int (fun int bool))), wset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), noXRRset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), bnorRset ) 23.03/23.03 ( (fun int (fun int (fun int bool))), zcongm ) 23.03/23.03 ( (fun real nat), natceiling ) 23.03/23.03 ( (fun real nat), natfloor ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.03/23.03 ( (fun int real), (real_1 int) ) 23.03/23.03 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.03/23.03 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.03/23.03 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.03/23.03 ( (fun complex nat), (size_size complex) ) 23.03/23.03 ( (fun complex nat), complex_size ) 23.03/23.03 ( (fun (fun nat rat) bool), vanishes ) 23.03/23.03 ( (fun (product_prod int int) rat), frct ) 23.03/23.03 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.03/23.03 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.03/23.03 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.03/23.03 ( (fun rat real), ratreal ) 23.03/23.03 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.03/23.03 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.03/23.03 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.03/23.03 ( (fun rat (product_prod int int)), quotient_of ) 23.03/23.03 ( (fun int (fun nat nat)), nat_aux ) 23.03/23.03 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.03/23.03 ( (fun int (list int)), quickc666637781d_zero ) 23.03/23.03 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.03/23.03 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.03/23.03 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.03/23.03 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.03/23.03 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.03/23.03 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.03/23.03 ( (fun code_code_numeral int), code_int_of ) 23.03/23.03 ) 23.03/23.03 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146956 $$unsorted) (BOUND_VARIABLE_146957 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (plus_plus X_a))) (let ((_let_3 (inverse_inverse X_a))) (let ((_let_4 (zero_zero X_a))) (let ((_let_5 (hAPP X_a X_a _let_3 BOUND_VARIABLE_146957))) (let ((_let_6 (hAPP X_a X_a _let_3 BOUND_VARIABLE_146956))) (or (not (field X_a)) (= _let_4 (ti X_a BOUND_VARIABLE_146957)) (= _let_4 (ti X_a BOUND_VARIABLE_146956)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_2 _let_5) _let_6) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (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_146957) BOUND_VARIABLE_146956)) _let_5)) _let_6)))))))))) ) 23.03/23.03 ( 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)))) ) 23.03/23.03 ( 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) ) 23.03/23.03 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.03/23.03 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.03/23.03 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.03 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.03 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.03/23.03 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.03 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.03/23.04 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.03/23.04 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.03/23.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( nat, (one_one nat), (one_one nat) ) 23.03/23.04 ) 23.03/23.04 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_146993 $$unsorted) (BOUND_VARIABLE_146994 $$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_146994))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_146993))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_146993) (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_146994) BOUND_VARIABLE_146993)) BOUND_VARIABLE_146994)))))) ) 23.03/23.04 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.03/23.04 ( 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))) ) 23.03/23.04 ( int, v, y ) 23.03/23.04 ( int, v, sa ) 23.03/23.04 ( int, v, x ) 23.03/23.04 ( int, v, r ) 23.03/23.04 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.04 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.04 ( int, w, y ) 23.03/23.04 ( int, w, sa ) 23.03/23.04 ( int, w, x ) 23.03/23.04 ( int, w, r ) 23.03/23.04 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.04 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.04 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.03/23.04 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.04 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.04 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.03/23.04 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.04 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.04 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.04 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.07 ( int, skv_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))) ) 23.03/23.08 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( 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))))) ) 23.03/23.08 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( 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)))) ) 23.03/23.08 ( complex, ii, ii ) 23.03/23.08 ( 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)) ) 23.03/23.08 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147027 $$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) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_147027))) (zero_zero X_a)))) ) 23.03/23.08 ( int, v ) 23.03/23.08 ( int, w ) 23.03/23.08 ( int, skv_14 ) 23.03/23.08 ( int, skv_20 ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147150 $$unsorted) (BOUND_VARIABLE_147151 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_147150) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_147151))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_147150)) BOUND_VARIABLE_147151)))) ) 23.03/23.08 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147243 $$unsorted) (BOUND_VARIABLE_147256 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (sgn_sgn X_a))) (let ((_let_2 (one_one X_a))) (let ((_let_3 (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) _let_0) BOUND_VARIABLE_147243)))) (let ((_let_4 (hAPP X_a X_a _let_1 BOUND_VARIABLE_147243))) (or (not (sgn_if X_a)) (and (or (= _let_0 (ti X_a BOUND_VARIABLE_147243)) (and (or _let_3 (= (hAPP X_a X_a (uminus_uminus X_a) _let_2) _let_4)) (or (not _let_3) (= _let_2 _let_4)))) (or (not (= _let_0 (ti X_a BOUND_VARIABLE_147256))) (= _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_147256)))))))))) ) 23.03/23.08 ( int, pls, pls ) 23.03/23.08 ( int, min, min ) 23.03/23.08 ( int, s, s ) 23.03/23.08 ( int, s1, s1 ) 23.03/23.08 ( int, m, m ) 23.03/23.08 ( int, t, t ) 23.03/23.08 ( int, v, v ) 23.03/23.08 ( int, w, w ) 23.03/23.08 ( int, y, y ) 23.03/23.08 ( int, sa, sa ) 23.03/23.08 ( int, x, x ) 23.03/23.08 ( int, r, r ) 23.03/23.08 ( int, m1, m1 ) 23.03/23.08 ( int, skv_14, skv_14 ) 23.03/23.08 ( int, skv_20, skv_20 ) 23.03/23.08 ( (fun int int), bit1, bit1 ) 23.03/23.08 ( (fun int int), bit0, bit0 ) 23.03/23.08 ( (fun int int), succ, succ ) 23.03/23.08 ( (fun int int), pred, pred ) 23.03/23.08 ( (fun int int), (fact_fact int), (fact_fact int) ) 23.03/23.08 ( (fun int int), zfact, zfact ) 23.03/23.08 ( nat, n, n ) 23.03/23.08 ( nat, tn, tn ) 23.03/23.08 ( bool, fTrue, fTrue ) 23.03/23.08 ( bool, fFalse, fFalse ) 23.03/23.08 ( real, pi, pi ) 23.03/23.08 ( (fun nat real), (real_1 nat), (real_1 nat) ) 23.03/23.08 ( (fun nat real), cos_coeff, cos_coeff ) 23.03/23.08 ( (fun nat real), sin_coeff, sin_coeff ) 23.03/23.08 ( (fun real real), sin, sin ) 23.03/23.08 ( (fun real real), cos, cos ) 23.03/23.08 ( (fun real real), sqrt, sqrt ) 23.03/23.08 ( (fun real real), tan, tan ) 23.03/23.08 ( (fun real real), ln, ln ) 23.03/23.08 ( (fun real real), arctan, arctan ) 23.03/23.08 ( (fun real real), arcsin, arcsin ) 23.03/23.08 ( (fun real real), arccos, arccos ) 23.03/23.08 ( (fun nat nat), suc, suc ) 23.03/23.08 ( (fun nat nat), (fact_fact nat), (fact_fact nat) ) 23.03/23.08 ( (fun nat nat), nat_size, nat_size ) 23.03/23.08 ( (fun nat nat), (size_size nat), (size_size nat) ) 23.03/23.08 ( (fun nat nat), fact, fact ) 23.03/23.08 ( (filter nat), sequentially, sequentially ) 23.03/23.08 ( (fun int (fun int rat)), fract, fract ) 23.03/23.08 ( complex, ii, ii ) 23.03/23.08 ( (fun int bool), zOdd, zOdd ) 23.03/23.08 ( (fun int bool), zprime, zprime ) 23.03/23.08 ( (fun int bool), zEven, zEven ) 23.03/23.08 ( (fun int bool), nat_neg, nat_neg ) 23.03/23.08 ( (fun int bool), nat_is_nat, nat_is_nat ) 23.03/23.08 ( (fun int bool), (even_odd_even int), (even_odd_even int) ) 23.03/23.08 ( (fun int bool), twoSqu1091635170sum2sq, twoSqu1091635170sum2sq ) 23.03/23.08 ( (fun int (fun int int)), legacy_zgcd, legacy_zgcd ) 23.03/23.08 ( (fun int (fun int int)), (gcd_gcd int), (gcd_gcd int) ) 23.03/23.08 ( (fun int (fun int int)), inv, inv ) 23.03/23.08 ( (fun int (fun int int)), multInv, multInv ) 23.03/23.08 ( (fun int (fun int int)), legendre, legendre ) 23.03/23.08 ( (fun int (fun int int)), standardRes, standardRes ) 23.03/23.08 ( (fun int (fun int int)), nat_tsub, nat_tsub ) 23.03/23.08 ( (fun int (fun int int)), z3div, z3div ) 23.03/23.08 ( (fun int (fun int int)), z3mod, z3mod ) 23.03/23.08 ( (fun int (fun int int)), int_lcm, int_lcm ) 23.03/23.08 ( (fun int (fun int int)), int_gcd, int_gcd ) 23.03/23.08 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq, twoSqu1094008024sum2sq ) 23.03/23.08 ( (fun bool bool), fNot, fNot ) 23.03/23.08 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset, is_RRset ) 23.03/23.08 ( (fun bool (fun bool bool)), fconj, fconj ) 23.03/23.08 ( (fun bool (fun bool bool)), fdisj, fdisj ) 23.03/23.08 ( (fun bool (fun bool bool)), fimplies, fimplies ) 23.03/23.08 ( (fun int (fun int bool)), quadRes, quadRes ) 23.03/23.08 ( (fun int (fun int bool)), d22set, d22set ) 23.03/23.08 ( (fun int (fun int bool)), norRRset, norRRset ) 23.03/23.08 ( (fun int (fun int bool)), sRStar, sRStar ) 23.03/23.08 ( (fun int (fun int bool)), sr, sr ) 23.03/23.08 ( (fun int (fun int bool)), quickc1265749348ro_rel, quickc1265749348ro_rel ) 23.03/23.08 ( (fun nat bool), (even_odd_even nat), (even_odd_even nat) ) 23.03/23.08 ( (fun nat bool), prime, prime ) 23.03/23.08 ( (fun real complex), cis, cis ) 23.03/23.08 ( (fun nat (fun nat bool)), coprime, coprime ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel, ratrel ) 23.03/23.08 ( (fun (product_prod int int) bool), frac_1, frac_1 ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel, upto_rel ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel, posDivAlg_rel ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel, negDivAlg_rel ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel, lazy_small_lazy_rel ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel, norm_frac_rel ) 23.03/23.08 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2, int_ge_less_than2 ) 23.03/23.08 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than, int_ge_less_than ) 23.03/23.08 ( (fun (fun int bool) bool), nat_nat_set, nat_nat_set ) 23.03/23.08 ( (fun nat (fun real real)), root, root ) 23.03/23.08 ( (fun real (fun real real)), log, log ) 23.03/23.08 ( (fun real (fun real real)), powr, powr ) 23.03/23.08 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd, xzgcd ) 23.03/23.08 ( (fun complex complex), cnj, cnj ) 23.03/23.08 ( (fun complex complex), expi, expi ) 23.03/23.08 ( (fun nat (fun nat nat)), (gcd_gcd nat), (gcd_gcd nat) ) 23.03/23.08 ( (fun nat (fun nat nat)), nat_gcd, nat_gcd ) 23.03/23.08 ( (fun nat (fun nat nat)), nat_lcm, nat_lcm ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize, normalize ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd, negateSnd ) 23.03/23.08 ( (fun int (fun (fun int bool) bool)), rsetR, rsetR ) 23.03/23.08 ( (fun int (fun (fun int bool) bool)), resSet, resSet ) 23.03/23.08 ( (fun int nat), nat_1, nat_1 ) 23.03/23.08 ( (fun int nat), phi, phi ) 23.03/23.08 ( (fun complex real), re, re ) 23.03/23.08 ( (fun complex real), im, im ) 23.03/23.08 ( (fun complex real), arg, arg ) 23.03/23.08 ( (fun int (fun int (product_prod int int))), divmod_int, divmod_int ) 23.03/23.08 ( (fun int (fun int (product_prod int int))), posDivAlg, posDivAlg ) 23.03/23.08 ( (fun int (fun int (product_prod int int))), negDivAlg, negDivAlg ) 23.03/23.08 ( (fun int (fun int (product_prod int int))), pdivmod, pdivmod ) 23.03/23.08 ( (fun int (fun int (product_prod int int))), norm_frac, norm_frac ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust, adjust ) 23.03/23.08 ( (fun (product_prod nat nat) bool), pred_nat, pred_nat ) 23.03/23.08 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux, code_nat_of_aux ) 23.03/23.08 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral, code_S1047413653umeral ) 23.03/23.08 ( (fun (fun int bool) int), (the int), (the int) ) 23.03/23.08 ( (fun int quickcheck_code_int), quickcheck_of_int, quickcheck_of_int ) 23.03/23.08 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat, divmod_nat ) 23.03/23.08 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral, code_d418564891umeral ) 23.03/23.08 ( (fun real (fun real complex)), rcis, rcis ) 23.03/23.08 ( (fun real (fun real complex)), complex_1, complex_1 ) 23.03/23.08 ( (fun int (fun int (fun int bool))), zcong, zcong ) 23.03/23.08 ( (fun int (fun int (fun int bool))), wset, wset ) 23.03/23.08 ( (fun int (fun int (fun int bool))), noXRRset, noXRRset ) 23.03/23.08 ( (fun int (fun int (fun int bool))), bnorRset, bnorRset ) 23.03/23.08 ( (fun int (fun int (fun int bool))), zcongm, zcongm ) 23.03/23.08 ( (fun real nat), natceiling, natceiling ) 23.03/23.08 ( (fun real nat), natfloor, natfloor ) 23.03/23.08 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less, pair_less ) 23.03/23.08 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq, pair_leq ) 23.03/23.08 ( (fun int real), (real_1 int), (real_1 int) ) 23.03/23.08 ( (fun quickcheck_code_int int), quickcheck_int_of, quickcheck_int_of ) 23.03/23.08 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int, quickc495462417de_int ) 23.03/23.08 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel, nat_gcd_rel ) 23.03/23.08 ( (fun complex nat), (size_size complex), (size_size complex) ) 23.03/23.08 ( (fun complex nat), complex_size, complex_size ) 23.03/23.08 ( (fun (fun nat rat) bool), vanishes, vanishes ) 23.03/23.08 ( (fun (product_prod int int) rat), frct, frct ) 23.03/23.08 ( (fun int (fun int (fun (fun int bool) bool))), setS, setS ) 23.03/23.08 ( (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 ) 23.03/23.08 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat), (ord_gr676655987ssThan nat) ) 23.03/23.08 ( (fun rat real), ratreal, ratreal ) 23.03/23.08 ( (fun int (fun int (fun int (fun int bool)))), multInvPair, multInvPair ) 23.03/23.08 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR, rRset2norRR ) 23.03/23.08 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect, bolzano_bisect ) 23.03/23.08 ( (fun rat (product_prod int int)), quotient_of, quotient_of ) 23.03/23.08 ( (fun int (fun nat nat)), nat_aux, nat_aux ) 23.03/23.08 ( (fun nat (fun nat (product_prod int int))), bezw, bezw ) 23.03/23.08 ( (fun int (list int)), quickc666637781d_zero, quickc666637781d_zero ) 23.03/23.08 ( (fun quickcheck_code_int nat), quickcheck_nat_of, quickcheck_nat_of ) 23.03/23.08 ( (fun (fun real bool) real), (complete_Sup_Sup real), (complete_Sup_Sup real) ) 23.03/23.08 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel, divmod_int_rel ) 23.03/23.08 ( (fun code_code_numeral nat), code_c271388182l_size, code_c271388182l_size ) 23.03/23.08 ( (fun code_code_numeral nat), (size_size code_code_numeral), (size_size code_code_numeral) ) 23.03/23.08 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel, divmod_nat_rel ) 23.03/23.08 ( (fun code_code_numeral int), code_int_of, code_int_of ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real ln (hAPP real real (inverse_inverse real) X)) (hAPP real real (uminus_uminus real) (hAPP real real ln X)))) ) 23.03/23.08 ( pi ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (zero_zero real) ) 23.03/23.08 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( skv_2 ) 23.03/23.08 ( skv_9 ) 23.03/23.08 ( skv_12 ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147325 $$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_147325) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_147325) (one_one X_a))))) ) 23.03/23.08 ( int, (one_one int) ) 23.03/23.08 ( int, min ) 23.03/23.08 ( int, (zero_zero int) ) 23.03/23.08 ( int, s ) 23.03/23.08 ( 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)))) ) 23.03/23.08 ( 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) ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( int, t ) 23.03/23.08 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.08 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.03/23.08 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.03/23.08 ( int, m1 ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.03/23.08 ( int, skv_4 ) 23.03/23.08 ( int, skv_5 ) 23.03/23.08 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( nat, (zero_zero nat) ) 23.03/23.08 ( nat, (one_one nat) ) 23.03/23.08 ( real, pi ) 23.03/23.08 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( real, (one_one real) ) 23.03/23.08 ( real, (zero_zero real) ) 23.03/23.08 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( 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))))) ) 23.03/23.08 ( 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)) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((Wa $$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 Wa)) (hAPP int nat nat_1 Z))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Wa) Z)))))) ) 23.03/23.08 ( (one_one int), t ) 23.03/23.08 ( min, min ) 23.03/23.08 ( min, (zero_zero int) ) 23.03/23.08 ( (zero_zero int), pls ) 23.03/23.08 ( (zero_zero int), (one_one int) ) 23.03/23.08 ( (zero_zero int), min ) 23.03/23.08 ( (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))) ) 23.03/23.08 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( 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))) ) 23.03/23.08 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.08 ( 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))) ) 23.03/23.08 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( 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))) ) 23.03/23.08 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147371 $$unsorted) (BOUND_VARIABLE_147372 $$unsorted) (BOUND_VARIABLE_147373 $$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_147373)) (= (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_147371) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_147372) BOUND_VARIABLE_147373))) BOUND_VARIABLE_147373) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147372) (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_147371) BOUND_VARIABLE_147373))))))) ) 23.03/23.08 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), y, w ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), sa, w ) 23.03/23.08 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147406 $$unsorted) (BOUND_VARIABLE_147407 $$unsorted) (BOUND_VARIABLE_147408 $$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 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147407) BOUND_VARIABLE_147408))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_147406))) (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_147407) BOUND_VARIABLE_147406)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_147408) BOUND_VARIABLE_147406)))))))) ) 23.03/23.08 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147468 $$unsorted) (BOUND_VARIABLE_147469 $$unsorted) (BOUND_VARIABLE_147470 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_147468))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_147469) BOUND_VARIABLE_147470))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_147468))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_147469)) (hAPP nat X_a _let_2 BOUND_VARIABLE_147470))))))) ) 23.03/23.08 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147498 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (ring_1 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_147498)) (ring_1_Ints X_a))))) ) 23.03/23.08 ( int, (zero_zero nat) ) 23.03/23.08 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( int, (one_one nat) ) 23.03/23.08 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.08 ( int, n ) 23.03/23.08 ( real, (zero_zero nat) ) 23.03/23.08 ( real, (one_one nat) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147517 $$unsorted) (BOUND_VARIABLE_147518 $$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_147517) BOUND_VARIABLE_147518))) (= (ti X_a BOUND_VARIABLE_147517) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_147517) BOUND_VARIABLE_147518))) ) 23.03/23.08 ( int, (one_one int), t ) 23.03/23.08 ( int, min, pls ) 23.03/23.08 ( int, min, min ) 23.03/23.08 ( int, (zero_zero int), pls ) 23.03/23.08 ( int, (zero_zero int), (one_one int) ) 23.03/23.08 ( int, (zero_zero int), min ) 23.03/23.08 ( int, (zero_zero int), s ) 23.03/23.08 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.08 ( int, (zero_zero int), skv_4 ) 23.03/23.08 ( int, (zero_zero int), skv_5 ) 23.03/23.08 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.03/23.08 ( real, (hAPP real real (hAPP 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))) ) 23.03/23.08 ( real, (zero_zero real), pi ) 23.03/23.08 ( 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)))) ) 23.03/23.08 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( real, (zero_zero real), skv_10 ) 23.03/23.08 ( real, (zero_zero real), skv_11 ) 23.03/23.08 ( real, (zero_zero real), skv_15 ) 23.03/23.08 ( real, (zero_zero real), skv_18 ) 23.03/23.08 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.03/23.08 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (minus_minus nat) M))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP nat nat _let_0 (one_one nat))) N) (hAPP nat nat _let_0 (hAPP nat nat suc N)))) ) 23.03/23.08 ( (hAPP int nat nat_1 t), (zero_zero nat) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) B_2) (hAPP int _let_0 d22set A_3)))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) A_3)))) ) 23.03/23.08 ( (one_one int), t ) 23.03/23.08 ( min, pls ) 23.03/23.08 ( min, min ) 23.03/23.08 ( (zero_zero int), pls ) 23.03/23.08 ( (zero_zero int), (one_one int) ) 23.03/23.08 ( (zero_zero int), min ) 23.03/23.08 ( (zero_zero int), s ) 23.03/23.08 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.08 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.08 ( (zero_zero int), skv_4 ) 23.03/23.08 ( (zero_zero int), skv_5 ) 23.03/23.08 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP real _let_0 _let_1 (zero_zero real)))) (or (not (hBOOL (hAPP real bool _let_2 X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real tan X))))))) ) 23.03/23.08 ( pi ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (one_one real) ) 23.03/23.08 ( (zero_zero real) ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.03/23.08 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (inverse_divide X_a))) (or (not (inverse X_a)) (not (real_normed_vector X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 23.03/23.08 ( rat ) 23.03/23.08 ( int ) 23.03/23.08 ( (fun int int) ) 23.03/23.08 ( nat ) 23.03/23.08 ( bool ) 23.03/23.08 ( real ) 23.03/23.08 ( (fun nat real) ) 23.03/23.08 ( (fun real real) ) 23.03/23.08 ( complex ) 23.03/23.08 ( (fun int bool) ) 23.03/23.08 ( (product_prod int int) ) 23.03/23.08 ( (fun (product_prod int int) int) ) 23.03/23.08 ( (fun int (fun int bool)) ) 23.03/23.08 ( (fun nat bool) ) 23.03/23.08 ( (fun (product_prod int int) bool) ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.03/23.08 ( (fun real bool) ) 23.03/23.08 ( code_code_numeral ) 23.03/23.08 ( (fun int (fun int (fun int bool))) ) 23.03/23.08 ( (fun int real) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X))) (hBOOL (hAPP int bool _let_0 Y)) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y)))))) ) 23.03/23.08 ( (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)))) ) 23.03/23.08 ( (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) ) 23.03/23.08 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.03/23.08 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.03/23.08 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.08 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.03/23.08 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.03/23.08 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.03/23.08 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.03/23.08 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.03/23.08 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.03/23.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (abs_abs real) X)) _let_0))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) _let_0)))))) ) 23.03/23.08 ( (hAPP int real (number_number_of real) min) ) 23.03/23.08 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((Ta $$unsorted) (B_1 $$unsorted) (D $$unsorted) (BOUND_VARIABLE_147685 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ti int Ta))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) B_1))) (not (forall ((Xa_1 $$unsorted) (BOUND_VARIABLE_147653 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa_1) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_147653) B_1))) (not (= (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_147653) Xa_1) (ti int BOUND_VARIABLE_147685)))))) )) (= _let_1 (ti int BOUND_VARIABLE_147685)) (not (= _let_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_147685) D)))))) ) 23.03/23.08 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun X_a (fun X_a bool)))) (or (not (linorder X_a)) (= (ord_min 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)))))) ) 23.03/23.08 ( rat ) 23.03/23.08 ( int ) 23.03/23.08 ( (fun int int) ) 23.03/23.08 ( nat ) 23.03/23.08 ( bool ) 23.03/23.08 ( real ) 23.03/23.08 ( (fun nat real) ) 23.03/23.08 ( (fun real real) ) 23.03/23.08 ( (filter nat) ) 23.03/23.08 ( complex ) 23.03/23.08 ( (fun int bool) ) 23.03/23.08 ( (product_prod int int) ) 23.03/23.08 ( (fun (product_prod int int) int) ) 23.03/23.08 ( (fun int (fun int bool)) ) 23.03/23.08 ( (fun nat bool) ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.03/23.08 ( (fun (product_prod int int) bool) ) 23.03/23.08 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.03/23.08 ( (fun real bool) ) 23.03/23.08 ( quickcheck_code_int ) 23.03/23.08 ( code_code_numeral ) 23.03/23.08 ( (product_prod real real) ) 23.03/23.08 ( (filter real) ) 23.03/23.08 ( (product_prod nat nat) ) 23.03/23.08 ( (fun nat rat) ) 23.03/23.08 ( (fun int (fun int (fun int bool))) ) 23.03/23.08 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.03/23.08 ( (fun int real) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (of_real complex) (hAPP real real (exp real) (hAPP complex real re Z_1)))) (hAPP real complex cis (hAPP complex real im Z_1))) (hAPP complex complex expi Z_1)) ) 23.03/23.08 ( (zero_zero complex) ) 23.03/23.08 ( ii ) 23.03/23.08 ( (one_one complex) ) 23.03/23.08 ( (let ((_let_0 (fun complex complex))) (let ((_let_1 (times_times complex))) (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP complex complex (hAPP complex _let_0 _let_1 (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real complex (of_real complex) pi))) ii))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147867 $$unsorted)) (or (not (field_inverse_zero X_a)) (not (number_ring X_a)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_147867) (hAPP int X_a (number_number_of X_a) pls)))) ) 23.03/23.08 ( real, pi ) 23.03/23.08 ( real, (one_one real) ) 23.03/23.08 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.08 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.08 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$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)))) ) 23.03/23.08 ( rat ) 23.03/23.08 ( int ) 23.03/23.08 ( nat ) 23.03/23.08 ( real ) 23.03/23.08 ( complex ) 23.03/23.08 ( quickcheck_code_int ) 23.03/23.08 ( code_code_numeral ) 23.03/23.08 ) 23.03/23.08 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (semiring_1_of_nat X_a))) (or (not (semiring_1 X_a)) (= _let_0 (ti (fun nat X_a) _let_0)))) ) 23.03/23.08 ( rat ) 23.03/23.08 ( int ) 23.03/23.08 ( (fun int int) ) 23.03/23.08 ( nat ) 23.03/23.08 ( bool ) 23.03/23.08 ( real ) 23.03/23.08 ( (fun real real) ) 23.03/23.09 ( (fun nat nat) ) 23.03/23.09 ( complex ) 23.03/23.09 ( (product_prod int int) ) 23.03/23.09 ( (fun bool bool) ) 23.03/23.09 ( (fun nat bool) ) 23.03/23.09 ( (fun nat (fun nat bool)) ) 23.03/23.09 ( quickcheck_code_int ) 23.03/23.09 ( code_code_numeral ) 23.03/23.09 ( (fun nat (product_prod int int)) ) 23.03/23.09 ( (product_prod real real) ) 23.03/23.09 ( (product_prod nat nat) ) 23.03/23.09 ( (fun (product_prod nat nat) bool) ) 23.03/23.09 ( (fun nat (fun (product_prod nat nat) bool)) ) 23.03/23.09 ( (fun nat (product_prod nat nat)) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$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)))))))))))) ) 23.03/23.09 ( int, int, (fequal int) ) 23.03/23.09 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun int _let_1))) (let ((_let_7 (fun _let_0 _let_6))) (let ((_let_8 (fun int _let_6))) (let ((_let_9 (fun _let_6 _let_6))) (hAPP _let_6 _let_6 (hAPP _let_5 _let_9 (combb _let_1 _let_1 int) (hAPP _let_4 _let_5 (combs int bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_3) (fun _let_1 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_1 (ord_less int) (zero_zero int))))) (hAPP int _let_6 (hAPP _let_8 _let_8 (combc int int _let_1) (hAPP _let_8 _let_8 (hAPP _let_9 (fun _let_8 _let_8) (combb _let_6 _let_6 int) (combc int int bool)) (hAPP _let_2 _let_8 (hAPP _let_7 (fun _let_2 _let_8) (combb _let_0 _let_6 int) (hAPP _let_6 _let_7 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 23.03/23.09 ( 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))) ) 23.03/23.09 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (fun _let_2 _let_4))) (let ((_let_11 (fun _let_2 _let_1))) (let ((_let_12 (fun _let_3 _let_11))) (let ((_let_13 (hAPP (fun int _let_1) _let_12 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_10 (hAPP (fun bool _let_4) (fun (fun _let_2 bool) _let_10) (combb bool _let_4 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_4 _let_7 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_11 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_3 _let_11 _let_13 _let_5)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_3))) (let ((_let_16 (fun _let_3 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_11))) (let ((_let_19 (fun _let_3 _let_3))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_3 _let_15))) (let ((_let_22 (fun _let_2 _let_0))) (let ((_let_23 (hAPP _let_3 _let_22 (hAPP (fun int _let_0) (fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb _let_3 _let_11 _let_2) _let_13) (hAPP _let_3 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_3 _let_3) (hAPP _let_22 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_22 _let_20) (combb _let_0 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_5)))) (hAPP _let_3 _let_15 (hAPP _let_24 _let_21 (combb int _let_3 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_5))))))))))))))))))))))))))))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted) (C $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (or (= (zero_zero real) C) (= (= (hAPP real real (hAPP real _let_0 _let_1 B_2) C) (hAPP real real (hAPP real _let_0 _let_1 A_3) C)) (= A_3 B_2))))) ) 23.03/23.09 ( (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 ) 23.03/23.09 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.03/23.09 ( (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)))))) ) 23.03/23.09 ( (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))))), pi ) 23.03/23.09 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.03/23.09 ( (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))), pi ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_147972 $$unsorted) (BOUND_VARIABLE_147973 $$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_147972)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_147973))) (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_147972) BOUND_VARIABLE_147973)))))))) ) 23.03/23.09 ( 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) ) 23.03/23.09 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.09 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.09 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.09 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.03/23.09 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.03/23.09 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.09 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.03/23.09 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.03/23.09 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((K_4 $$unsorted)) (= (zero_zero rat) (hAPP int rat (hAPP int (fun int rat) fract K_4) (zero_zero int))) ) 23.03/23.09 ( (one_one int) ) 23.03/23.09 ( (zero_zero int) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (not (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP real real (inverse_inverse real) (hAPP nat real (real_1 nat) (hAPP nat nat suc N_1)))) X))) ))) ) 23.03/23.09 ( pi ) 23.03/23.09 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( skv_2 ) 23.03/23.09 ( skv_9 ) 23.03/23.09 ( skv_12 ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP real real cos Xa))) (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) Xa) (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)))))))))) ) 23.03/23.09 ( pi ) 23.03/23.09 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( (zero_zero real) ) 23.03/23.09 ( (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 bit0 (hAPP int int bit1 pls))))) ) 23.03/23.09 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.03/23.09 ( (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 (hAPP int int bit1 pls))))) ) 23.03/23.09 ( (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)))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148012 $$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_148012) (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_148012))) ) 23.03/23.09 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( real, (zero_zero real) ) 23.03/23.09 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( 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))))))))) ) 23.03/23.09 ( complex, ii ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_148030 $$unsorted) (BOUND_VARIABLE_148031 $$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_148031))) (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_148030) (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_148030)) (zero_zero real)) _let_4)))))))) ) 23.03/23.09 ( 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)))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148066 $$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_148066) (zero_zero X_a)))) (= (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_148066) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_148066))) ) 23.03/23.09 ( int, pls ) 23.03/23.09 ( int, (one_one int) ) 23.03/23.09 ( int, min ) 23.03/23.09 ( int, (zero_zero int) ) 23.03/23.09 ( int, v ) 23.03/23.09 ( int, w ) 23.03/23.09 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.03/23.09 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.03/23.09 ( int, skv_14 ) 23.03/23.09 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.03/23.09 ( int, skv_20 ) 23.03/23.09 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.03/23.09 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( 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)))) ) 23.03/23.09 ( real, (one_one real) ) 23.03/23.09 ( real, (zero_zero real) ) 23.03/23.09 ( 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) ) 23.03/23.09 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( real, skv_10 ) 23.03/23.09 ( complex, ii ) 23.03/23.09 ( complex, (one_one complex) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_1))) (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_0 (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_1 (ord_less int) _let_3) P_5))) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int _let_2 zcong A_1) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_1 quadRes P_5) A_1)) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int _let_2 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_0 (div_div int) _let_4) _let_3)))) P_5)))))))) ) 23.03/23.09 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((Ma $$unsorted) (Na $$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) Na)) (or (and (= _let_0 Na) (= _let_1 Ma)) (and (= _let_1 Na) (= _let_0 Ma)))))) ) 23.03/23.09 ( (one_one nat), (one_one nat) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP int bool nat_is_nat X))) (not (hBOOL (hAPP int bool nat_is_nat Y))) (hBOOL (hAPP int bool nat_is_nat (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)))) ) 23.03/23.09 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.03/23.09 ( 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))) ) 23.03/23.09 ( v, y ) 23.03/23.09 ( v, sa ) 23.03/23.09 ( v, x ) 23.03/23.09 ( v, r ) 23.03/23.09 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.09 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.09 ( w, y ) 23.03/23.09 ( w, sa ) 23.03/23.09 ( w, x ) 23.03/23.09 ( w, r ) 23.03/23.09 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.09 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.09 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.03/23.09 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.03/23.09 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( skv_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))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148137 $$unsorted) (BOUND_VARIABLE_148138 $$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_148137))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148138) _let_2)))) (or (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_148138))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148137) _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_148138) BOUND_VARIABLE_148137)) _let_2))))))) ) 23.03/23.09 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.03/23.09 ( 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))) ) 23.03/23.09 ( int, v, y ) 23.03/23.09 ( int, v, sa ) 23.03/23.09 ( int, v, x ) 23.03/23.09 ( int, v, r ) 23.03/23.09 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.09 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.09 ( int, w, y ) 23.03/23.09 ( int, w, sa ) 23.03/23.09 ( int, w, x ) 23.03/23.09 ( int, w, r ) 23.03/23.09 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.09 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.09 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.03/23.09 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.09 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( int, skv_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))) ) 23.03/23.09 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( 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))))) ) 23.03/23.09 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ( 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)))) ) 23.03/23.09 ( complex, ii, ii ) 23.03/23.09 ( 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)) ) 23.03/23.09 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148176 $$unsorted) (BOUND_VARIABLE_148177 $$unsorted) (BOUND_VARIABLE_148178 $$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_148176) BOUND_VARIABLE_148178) (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_148176) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_148177) BOUND_VARIABLE_148178))) BOUND_VARIABLE_148178))))) ) 23.03/23.09 ( int, (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), y, w ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), sa, w ) 23.03/23.09 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.03/23.09 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148204 $$unsorted) (BOUND_VARIABLE_148205 $$unsorted) (BOUND_VARIABLE_148206 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_148204))) (or (not (order X_a)) (not (= (ti X_a BOUND_VARIABLE_148206) (ti X_a BOUND_VARIABLE_148205))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_148206))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_148205)))) ) 23.03/23.09 ( int, (one_one int), v, v ) 23.03/23.09 ( int, min, m, m ) 23.03/23.09 ( int, (zero_zero int), s1, s1 ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)), r, r ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)), min, min ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), s, s ) 23.03/23.09 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), m1, m1 ) 23.03/23.09 ( real, (zero_zero real), pi, pi ) 23.03/23.09 ) 23.03/23.09 (instantiation (forall ((N $$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)) K_4)))) ) 23.03/23.09 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.03/23.09 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.03/23.09 ( 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))) ) 23.03/23.09 ( v, y ) 23.03/23.09 ( v, sa ) 23.03/23.09 ( v, x ) 23.03/23.09 ( v, r ) 23.03/23.09 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.09 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.09 ( w, y ) 23.03/23.09 ( w, sa ) 23.03/23.09 ( w, x ) 23.03/23.09 ( w, r ) 23.03/23.10 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.10 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.10 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.03/23.10 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.10 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.03/23.10 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( skv_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))) ) 23.03/23.10 ) 23.03/23.10 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X)) A_1) (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (hAPP nat real (real_1 nat) A_1))))) ) 23.03/23.10 ( (one_one nat), (one_one real) ) 23.03/23.10 ) 23.03/23.10 (instantiation (forall ((X $$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))) (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))))))) (hBOOL (hAPP real bool _let_2 (hAPP real real cos X))))))) ) 23.03/23.10 ( pi ) 23.03/23.10 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (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)))) ) 23.03/23.10 ( (one_one real) ) 23.03/23.10 ( (zero_zero real) ) 23.03/23.10 ( (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 bit0 (hAPP int int bit1 pls))))) ) 23.03/23.10 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.03/23.10 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( (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))))) ) 23.03/23.10 ( (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 (hAPP int int bit1 pls))))) ) 23.03/23.10 ( (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)))) ) 23.03/23.10 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.03/23.10 ( (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)) ) 23.03/23.10 ( skv_10 ) 23.03/23.10 ) 23.03/23.10 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (= (hAPP real real sqrt (hAPP real real (hAPP real _let_0 _let_1 X) Y)) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sqrt X)) (hAPP real real sqrt Y))))) ) 23.03/23.10 ( (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.03/23.10 ) 23.03/23.10 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (hAPP nat _let_0 root Na))) (or (hBOOL (hAPP nat bool (even_odd_even nat) Na)) (= (zero_zero real) Xa) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (deriv real) _let_2) Xa) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) Na)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_2 Xa)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) (hAPP nat nat suc (zero_zero nat)))))))))))) ) 23.03/23.10 ( (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))) ) 23.03/23.10 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.03/23.10 ( (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))) ) 23.03/23.10 ) 23.03/23.10 (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)))) ) 23.03/23.10 ( (one_one int), pls ) 23.03/23.10 ( (hAPP nat int (hAPP 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) ) 23.03/23.10 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.10 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.10 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.10 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.03/23.10 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.03/23.10 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.03/23.10 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.03/23.10 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.03/23.10 ) 23.03/23.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148306 $$unsorted) (BOUND_VARIABLE_148307 $$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_148307) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_148306) _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_148307) BOUND_VARIABLE_148306)) _let_3))))))) ) 23.03/23.10 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.03/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.03/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.03/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.03/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.03/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.03/23.10 ( 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))) ) 23.03/23.10 ( int, v, y ) 23.03/23.10 ( int, v, sa ) 23.03/23.10 ( int, v, x ) 23.03/23.10 ( int, v, r ) 23.03/23.10 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.10 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.03/23.10 ( int, w, y ) 23.03/23.10 ( int, w, sa ) 23.03/23.10 ( int, w, x ) 23.03/23.10 ( int, w, r ) 23.03/23.10 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.03/23.10 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.10 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.11/23.10 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.11/23.10 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.10 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( int, skv_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))) ) 23.11/23.10 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( 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))))) ) 23.11/23.10 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ( 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)))) ) 23.11/23.10 ( complex, ii, ii ) 23.11/23.10 ( 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)) ) 23.11/23.10 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((X $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (hAPP nat real (real_1 nat) A_1)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling X)) A_1))) ) 23.11/23.10 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero nat) ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148350 $$unsorted) (BOUND_VARIABLE_148351 $$unsorted) (BOUND_VARIABLE_148352 $$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_148350)))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_148352)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148352) _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_148350)) BOUND_VARIABLE_148352))) (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_148351) BOUND_VARIABLE_148352))) (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_148351) _let_6))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_6) BOUND_VARIABLE_148351))))))))))))) ) 23.11/23.10 ( int, pls, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( int, pls, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( int, pls, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( int, pls, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.10 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.11/23.10 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.11/23.10 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148393 $$unsorted) (BOUND_VARIABLE_148394 $$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_148394) BOUND_VARIABLE_148393)) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_148393) BOUND_VARIABLE_148394))))))) ) 23.11/23.10 ( 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) ) 23.11/23.10 ( int, (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.10 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.10 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.11/23.10 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.10 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.11/23.10 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.11/23.10 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.11/23.10 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.11/23.10 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.11/23.10 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.11/23.10 ( nat, (one_one nat), (hAPP int nat nat_1 t) ) 23.11/23.10 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.11/23.10 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.11/23.10 ( 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 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.11/23.10 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.11/23.10 ( code_code_numeral, (one_one code_code_numeral), (zero_zero code_code_numeral) ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (real_algebra_1 X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_1)) K_2))) )) ))) ) 23.11/23.10 ( real ) 23.11/23.10 ( complex ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((N $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N))) (not (forall ((X_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (number_number_of nat))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (not (= (hAPP nat nat (hAPP nat _let_0 (power_power nat) N) (hAPP int nat _let_1 _let_2)) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat _let_1 (hAPP int int bit0 _let_2))) X_1)))))) ))) ) 23.11/23.10 ( (zero_zero nat) ) 23.11/23.10 ( (one_one nat) ) 23.11/23.10 ) 23.11/23.10 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (archimedean_ceiling X_a))) (or (not (archim1727834104eiling X_a)) (= _let_0 (ti (fun X_a int) _let_0)))) ) 23.11/23.10 ( rat ) 23.11/23.10 ( int ) 23.11/23.10 ( nat ) 23.11/23.10 ( real ) 23.11/23.10 ( (fun int bool) ) 23.11/23.10 ( (product_prod int int) ) 23.11/23.10 ( quickcheck_code_int ) 23.11/23.10 ( code_code_numeral ) 23.11/23.10 ) 23.11/23.11 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (fun _let_0 X_b))) (let ((_let_2 (fun _let_0 X_c))) (let ((_let_3 (fun X_b X_c))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun _let_0 X_d))) (let ((_let_6 (fun X_d _let_3))) (let ((_let_7 (fun _let_0 X_a))) (let ((_let_8 (fun X_a X_d))) (let ((_let_9 (fun X_a _let_3))) (= (hAPP _let_9 _let_2 (product_prod_case X_a X_b X_c) (hAPP _let_8 _let_9 (hAPP _let_6 (fun _let_8 _let_9) (combb X_d _let_3 X_a) F) G)) (hAPP _let_1 _let_2 (hAPP _let_4 (fun _let_1 _let_2) (combs _let_0 X_b X_c) (hAPP _let_5 _let_4 (hAPP _let_6 (fun _let_5 _let_4) (combb X_d _let_3 _let_0) F) (hAPP _let_7 _let_5 (hAPP _let_8 (fun _let_7 _let_5) (combb X_a X_d _let_0) G) (product_fst X_a X_b)))) (product_snd X_a X_b))))))))))))) ) 23.11/23.11 ( 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))))) ) 23.11/23.11 ( 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)))) ) 23.11/23.11 ( 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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 23.11/23.11 ( 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 ) 23.11/23.11 ( int, int, (fun int bool), (fun int (fun int bool)), (combc int int bool), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))))))) ) 23.11/23.11 ( 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))))))) ) 23.11/23.11 ( int, (fun int int), (fun int bool), (fun int bool), (combb int bool int), (fequal int) ) 23.11/23.11 ( int, bool, bool, bool, fconj, (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 23.11/23.11 ( int, real, real, real, (inverse_divide real), (real_1 int) ) 23.11/23.11 ( 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))))) ) 23.11/23.11 ( 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))))) ) 23.11/23.11 ( 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))))) ) 23.11/23.11 ( nat, nat, bool, nat, (let ((_let_0 (fun nat (fun nat bool)))) (hAPP _let_0 _let_0 (combc nat nat bool) (fequal nat))), suc ) 23.11/23.11 ( nat, real, real, real, (inverse_divide real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real))))) ) 23.11/23.11 ( nat, real, real, real, (times_times real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) ) 23.11/23.11 ( 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 real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (fun int (fun int bool)))) (let ((_let_6 (real_1 int))) (let ((_let_7 (fun real bool))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun int _let_3))) (let ((_let_10 (fun (fun int bool) _let_5))) (let ((_let_11 (fun int _let_2))) (let ((_let_12 (fun _let_11 _let_9))) (let ((_let_13 (fun _let_5 _let_11))) (let ((_let_14 (fun int real))) (let ((_let_15 (fun int _let_0))) (let ((_let_16 (fun _let_14 (fun int bool)))) (let ((_let_17 (fun real _let_5))) (let ((_let_18 (fun real _let_10))) (let ((_let_19 (fun real _let_9))) (let ((_let_20 (fun real _let_11))) (let ((_let_21 (fun int _let_14))) (let ((_let_22 (fun _let_21 _let_5))) (let ((_let_23 (fun real _let_22))) (let ((_let_24 (fun real _let_16))) (let ((_let_25 (fun _let_14 _let_14))) (let ((_let_26 (fun int _let_25))) (hAPP (fun int bool) _let_17 (hAPP _let_18 (fun (fun int bool) _let_17) (combc real (fun int bool) _let_5) (hAPP _let_19 _let_18 (hAPP (fun _let_9 _let_10) (fun _let_19 _let_18) (combb _let_9 _let_10 real) (combc int (fun int bool) (fun int bool))) (hAPP _let_20 _let_19 (hAPP _let_12 (fun _let_20 _let_19) (combb _let_11 _let_9 real) (hAPP (fun _let_2 _let_3) _let_12 (combb _let_2 _let_3 int) (combs int bool bool))) (hAPP _let_17 _let_20 (hAPP _let_13 (fun _let_17 _let_20) (combb _let_5 _let_11 real) (hAPP _let_4 _let_13 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_4 (combb bool _let_1 int) fconj))) (hAPP _let_21 _let_17 (hAPP _let_23 (fun _let_21 _let_17) (combc real _let_21 _let_5) (hAPP _let_24 _let_23 (hAPP (fun _let_16 _let_22) (fun _let_24 _let_23) (combb _let_16 _let_22 real) (combb _let_14 (fun int bool) int)) (hAPP _let_8 _let_24 (hAPP (fun _let_7 _let_16) (fun _let_8 _let_24) (combb _let_7 _let_16 real) (combb real bool int)) (fequal real)))) (hAPP _let_14 _let_21 (hAPP _let_26 (fun _let_14 _let_21) (combc int _let_14 _let_14) (hAPP _let_15 _let_26 (hAPP (fun _let_0 _let_25) (fun _let_15 _let_26) (combb _let_0 _let_25 int) (combb real real int)) (hAPP _let_14 _let_15 (hAPP (fun real _let_0) (fun _let_14 _let_15) (combb real _let_0 int) (inverse_divide real)) _let_6))) _let_6)))))) (hAPP (fun int bool) (fun int bool) (hAPP _let_1 _let_3 (combb bool bool int) fNot) (hAPP int (fun int bool) (hAPP _let_5 _let_5 (combc int int bool) (fequal int)) (zero_zero int))))))))))))))))))))))))))))))) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun nat (fun nat bool)))) (let ((_let_3 (fun real bool))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun (fun nat real) (fun nat real)))) (let ((_let_6 (fun nat _let_1))) (let ((_let_7 (fun (fun nat bool) (fun nat bool)))) (let ((_let_8 (fun (fun nat bool) _let_6))) (let ((_let_9 (fun int real))) (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_7))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun int _let_6))) (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_5))) (let ((_let_25 (fun int _let_0))) (hAPP (fun nat bool) _let_10 (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_6 _let_7) _let_17 (combb _let_6 _let_7 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_6 int) (hAPP (fun bool _let_1) _let_8 (combb bool _let_1 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_3 _let_22) (fun _let_4 _let_23) (combb _let_3 _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_25 _let_24 (hAPP (fun _let_0 _let_5) (fun _let_25 _let_24) (combb _let_0 _let_5 int) (combb real real nat)) (hAPP _let_9 _let_25 (hAPP (fun real _let_0) (fun _let_9 _let_25) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))) (hAPP (fun nat bool) (fun nat bool) (hAPP _let_1 _let_7 (combb bool bool nat) fNot) (hAPP nat (fun nat bool) (hAPP _let_2 _let_2 (combc nat nat bool) (fequal nat)) (zero_zero nat)))))))))))))))))))))))))))))) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (real_1 int))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_0))) (let ((_let_6 (fun _let_4 (fun int bool)))) (let ((_let_7 (fun real (fun int (fun int bool))))) (let ((_let_8 (fun int _let_4))) (let ((_let_9 (fun _let_8 (fun int (fun int bool))))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun real _let_6))) (let ((_let_12 (fun _let_4 _let_4))) (let ((_let_13 (fun int _let_12))) (hAPP _let_8 _let_7 (hAPP _let_10 (fun _let_8 _let_7) (combc real _let_8 (fun int (fun int bool))) (hAPP _let_11 _let_10 (hAPP (fun _let_6 _let_9) (fun _let_11 _let_10) (combb _let_6 _let_9 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_2 _let_6) (fun _let_3 _let_11) (combb _let_2 _let_6 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_8 (hAPP _let_13 (fun _let_4 _let_8) (combc int _let_4 _let_4) (hAPP _let_5 _let_13 (hAPP (fun _let_0 _let_12) (fun _let_5 _let_13) (combb _let_0 _let_12 int) (combb real real int)) (hAPP _let_4 _let_5 (hAPP (fun real _let_0) (fun _let_4 _let_5) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))))))))))) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) _let_2))) (let ((_let_4 (real_1 int))) (let ((_let_5 (fun real bool))) (let ((_let_6 (fun real _let_5))) (let ((_let_7 (fun int _let_2))) (let ((_let_8 (fun (fun int (fun int bool)) _let_7))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_0))) (let ((_let_11 (fun _let_9 (fun int bool)))) (let ((_let_12 (fun real (fun int (fun int bool))))) (let ((_let_13 (fun real _let_7))) (let ((_let_14 (fun int _let_9))) (let ((_let_15 (fun _let_14 (fun int (fun int bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun _let_9 _let_9))) (let ((_let_19 (fun int _let_18))) (hAPP _let_12 _let_13 (hAPP _let_8 (fun _let_12 _let_13) (combb (fun int (fun int bool)) _let_7 real) (hAPP _let_3 _let_8 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj))) (hAPP _let_14 _let_12 (hAPP _let_16 (fun _let_14 _let_12) (combc real _let_14 (fun int (fun int bool))) (hAPP _let_17 _let_16 (hAPP (fun _let_11 _let_15) (fun _let_17 _let_16) (combb _let_11 _let_15 real) (combb _let_9 (fun int bool) int)) (hAPP _let_6 _let_17 (hAPP (fun _let_5 _let_11) (fun _let_6 _let_17) (combb _let_5 _let_11 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_14 (hAPP _let_19 (fun _let_9 _let_14) (combc int _let_9 _let_9) (hAPP _let_10 _let_19 (hAPP (fun _let_0 _let_18) (fun _let_10 _let_19) (combb _let_0 _let_18 int) (combb real real int)) (hAPP _let_9 _let_10 (hAPP (fun real _let_0) (fun _let_9 _let_10) (combb real _let_0 int) (inverse_divide real)) _let_4))) _let_4))))))))))))))))))))))) ) 23.11/23.11 ( real, int, (fun nat (fun bool bool)), (fun int (fun nat bool)), (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat _let_0))) (let ((_let_3 (fun _let_1 _let_2))) (hAPP _let_3 (fun (fun int _let_1) (fun int _let_2)) (combb _let_1 _let_2 int) (hAPP (fun bool _let_0) _let_3 (combb bool _let_0 nat) fconj)))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_1))) (let ((_let_3 (fun (fun nat real) (fun nat real)))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun real (fun int (fun nat bool))))) (let ((_let_6 (fun int (fun nat real)))) (let ((_let_7 (fun _let_6 (fun int (fun nat bool))))) (let ((_let_8 (fun real _let_7))) (let ((_let_9 (fun (fun nat real) (fun nat bool)))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun int _let_3))) (let ((_let_12 (fun int _let_0))) (hAPP _let_6 _let_5 (hAPP _let_8 (fun _let_6 _let_5) (combc real _let_6 (fun int (fun nat bool))) (hAPP _let_10 _let_8 (hAPP (fun _let_9 _let_7) (fun _let_10 _let_8) (combb _let_9 _let_7 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_2 _let_10 (hAPP (fun _let_1 _let_9) (fun _let_2 _let_10) (combb _let_1 _let_9 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_6 (hAPP _let_11 (fun (fun nat real) _let_6) (combc int (fun nat real) (fun nat real)) (hAPP _let_12 _let_11 (hAPP (fun _let_0 _let_3) (fun _let_12 _let_11) (combb _let_0 _let_3 int) (combb real real nat)) (hAPP _let_4 _let_12 (hAPP (fun real _let_0) (fun _let_4 _let_12) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat)))))))))))))))) ) 23.11/23.11 ( real, int, (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)), (fun int (fun nat (fun bool bool))), (let ((_let_0 (fun nat (fun bool bool)))) (let ((_let_1 (fun (fun nat bool) (fun nat bool)))) (hAPP (fun _let_0 _let_1) (fun (fun int _let_0) (fun int _let_1)) (combb _let_0 _let_1 int) (combs nat bool bool)))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun (fun nat bool) _let_5))) (let ((_let_7 (fun int real))) (let ((_let_8 (fun real (fun int (fun nat bool))))) (let ((_let_9 (fun int _let_5))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun (fun int (fun nat bool)) _let_9))) (let ((_let_12 (fun int (fun nat real)))) (let ((_let_13 (fun _let_12 (fun int (fun nat bool))))) (let ((_let_14 (fun real _let_13))) (let ((_let_15 (fun (fun nat real) (fun nat bool)))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun int _let_4))) (let ((_let_18 (fun int _let_0))) (hAPP _let_8 _let_10 (hAPP _let_11 (fun _let_8 _let_10) (combb (fun int (fun nat bool)) _let_9 real) (hAPP _let_6 _let_11 (combb (fun nat bool) _let_5 int) (hAPP (fun bool _let_1) _let_6 (combb bool _let_1 nat) fconj))) (hAPP _let_12 _let_8 (hAPP _let_14 (fun _let_12 _let_8) (combc real _let_12 (fun int (fun nat bool))) (hAPP _let_16 _let_14 (hAPP (fun _let_15 _let_13) (fun _let_16 _let_14) (combb _let_15 _let_13 real) (combb (fun nat real) (fun nat bool) int)) (hAPP _let_3 _let_16 (hAPP (fun _let_2 _let_15) (fun _let_3 _let_16) (combb _let_2 _let_15 real) (combb real bool nat)) (fequal real)))) (hAPP (fun nat real) _let_12 (hAPP _let_17 (fun (fun nat real) _let_12) (combc int (fun nat real) (fun nat real)) (hAPP _let_18 _let_17 (hAPP (fun _let_0 _let_4) (fun _let_18 _let_17) (combb _let_0 _let_4 int) (combb real real nat)) (hAPP _let_7 _let_18 (hAPP (fun real _let_0) (fun _let_7 _let_18) (combb real _let_0 int) (inverse_divide real)) (real_1 int)))) (real_1 nat))))))))))))))))))))))) ) 23.11/23.11 ( real, bool, bool, bool, fconj, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 23.11/23.11 ( 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))))) ) 23.11/23.11 ( real, real, bool, real, (fequal real), cos ) 23.11/23.11 ( real, real, real, real, (inverse_divide real), cos ) 23.11/23.11 ( real, (fun nat real), (fun nat bool), (fun real bool), (combb real bool nat), (fequal real) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) (fun int bool)))) (let ((_let_4 (fun (fun int bool) _let_2))) (let ((_let_5 (real_1 int))) (let ((_let_6 (fun real bool))) (let ((_let_7 (fun real _let_6))) (let ((_let_8 (fun int _let_3))) (let ((_let_9 (fun int _let_2))) (let ((_let_10 (fun _let_9 _let_8))) (let ((_let_11 (fun (fun int (fun int bool)) _let_9))) (let ((_let_12 (fun int real))) (let ((_let_13 (fun int _let_0))) (let ((_let_14 (fun _let_12 (fun int bool)))) (let ((_let_15 (fun real (fun int (fun int bool))))) (let ((_let_16 (fun real _let_8))) (let ((_let_17 (fun real _let_9))) (let ((_let_18 (fun int _let_12))) (let ((_let_19 (fun _let_18 (fun int (fun int bool))))) (let ((_let_20 (fun real _let_19))) (let ((_let_21 (fun real _let_14))) (let ((_let_22 (fun _let_12 _let_12))) (let ((_let_23 (fun int _let_22))) (hAPP _let_17 _let_16 (hAPP _let_10 (fun _let_17 _let_16) (combb _let_9 _let_8 real) (hAPP (fun _let_2 _let_3) _let_10 (combb 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_let_5)))))))))))))))))))))))))))) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun (fun nat real) (fun nat real)))) (let ((_let_5 (fun nat _let_1))) (let ((_let_6 (fun (fun nat bool) (fun nat bool)))) (let ((_let_7 (fun (fun nat bool) _let_5))) (let ((_let_8 (fun int real))) (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 int _let_5))) (let ((_let_13 (fun real _let_12))) (let ((_let_14 (fun _let_12 _let_10))) (let ((_let_15 (fun (fun int (fun nat bool)) _let_12))) (let ((_let_16 (fun int (fun nat real)))) (let ((_let_17 (fun _let_16 (fun int (fun nat bool))))) (let ((_let_18 (fun real _let_17))) (let ((_let_19 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23.11/23.11 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.11/23.11 ( quickcheck_code_int ) 23.11/23.11 ( code_code_numeral ) 23.11/23.11 ( (product_prod real real) ) 23.11/23.11 ( (filter real) ) 23.11/23.11 ( (product_prod nat nat) ) 23.11/23.11 ( (fun nat rat) ) 23.11/23.11 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.11/23.11 ) 23.11/23.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148544 $$unsorted) (BOUND_VARIABLE_148550 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) (zero_zero X_a)))) (let ((_let_2 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_148544))) (let ((_let_3 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_148550))) (or (not (semiring_0 X_a)) (not (power X_a)) (and (or (= _let_0 _let_2) (= (zero_zero X_a) (hAPP nat X_a _let_1 _let_2))) (or (not (= _let_0 _let_3)) (= (one_one X_a) (hAPP nat X_a _let_1 _let_3))))))))) ) 23.11/23.11 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 23.11/23.11 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.11/23.11 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.11 ( code_code_numeral, pls, pls ) 23.11/23.11 ) 23.11/23.11 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148579 $$unsorted) (BOUND_VARIABLE_148580 $$unsorted) (BOUND_VARIABLE_148581 $$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 (fun X_a X_a))) (let ((_let_4 (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_148580)))) (let ((_let_5 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148580) (zero_zero X_a))))) (let ((_let_6 (hAPP X_a X_a (hAPP X_a _let_3 (times_times X_a) BOUND_VARIABLE_148581) BOUND_VARIABLE_148580))) (or (not (linord1117847801e_zero X_a)) (= (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_148579))) (or _let_5 (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_148581))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148579) _let_6)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_3 (inverse_divide X_a) BOUND_VARIABLE_148579) BOUND_VARIABLE_148580)) BOUND_VARIABLE_148581))))))))))) ) 23.11/23.11 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( int, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( int, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( 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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.11 ( 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))) ) 23.11/23.11 ( real, (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.11 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ( 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)), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148624 $$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_148624) _let_0)))) ) 23.11/23.12 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.12 ( 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))) ) 23.11/23.12 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.12 ( int, y ) 23.11/23.12 ( int, sa ) 23.11/23.12 ( int, x ) 23.11/23.12 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.11/23.12 ( int, r ) 23.11/23.12 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.11/23.12 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.12 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.12 ( int, skv_13 ) 23.11/23.12 ( int, skv_19 ) 23.11/23.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.12 ( 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))))) ) 23.11/23.12 ( complex, ii ) 23.11/23.12 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ( 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)) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (product_prod X_b X_a))) (let ((_let_1 (ti X_a A_1))) (or (not (= (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) Y)) _let_1)) (= _let_1 (ti X_a Y))))) ) 23.11/23.12 ( int, int, (one_one int), (one_one int), v ) 23.11/23.12 ( int, int, (zero_zero int), (one_one int), s1 ) 23.11/23.12 ( int, int, s, (one_one int), r ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) B_2))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) Y_1)))) ))) )) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real F A_3)) (hAPP real real F B_2)))))) ) 23.11/23.12 ( cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.11/23.12 ( sqrt, (zero_zero real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (N $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) Y))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 X)) (hAPP real real _let_2 Y))))))) ) 23.11/23.12 ( (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))) ) 23.11/23.12 ( (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))) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148756 $$unsorted) (BOUND_VARIABLE_148757 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (t2_space X_a)) (not (comm_monoid_add X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_148756) BOUND_VARIABLE_148757))) (= (ti X_a BOUND_VARIABLE_148757) (hAPP _let_0 X_a (suminf X_a) BOUND_VARIABLE_148756)))) ) 23.11/23.12 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int real (number_number_of real) _let_1))) (let ((_let_3 (minus_minus real))) (let ((_let_4 (one_one real))) (let ((_let_5 (fun real bool))) (let ((_let_6 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_5 _let_6 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_5 _let_6 X) (hAPP real real (hAPP real _let_0 (inverse_divide real) _let_4) _let_2)))) (hBOOL (hAPP real bool (hAPP real _let_5 _let_6 (hAPP real real (hAPP real _let_0 _let_3 (hAPP real real (uminus_uminus real) X)) (hAPP real real (hAPP real _let_0 (times_times real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_1))))) (hAPP real real ln (hAPP real real (hAPP real _let_0 _let_3 _let_4) X)))))))))))) ) 23.11/23.12 ( (hAPP int real (number_number_of real) min) ) 23.11/23.12 ( pi ) 23.11/23.12 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.12 ( (one_one real) ) 23.11/23.12 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.12 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.11/23.12 ( (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)))) ) 23.11/23.12 ( skv_10 ) 23.11/23.12 ( skv_11 ) 23.11/23.12 ( skv_15 ) 23.11/23.12 ( skv_18 ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148863 $$unsorted) (BOUND_VARIABLE_148864 $$unsorted) (BOUND_VARIABLE_148865 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_148863))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_148864) BOUND_VARIABLE_148865))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_148863))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_148864)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_148865))))))) ) 23.11/23.12 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.11/23.12 ) 23.11/23.12 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148895 $$unsorted) (BOUND_VARIABLE_148896 $$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_148896))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_148895))) (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_148896) BOUND_VARIABLE_148895))))) ) 23.11/23.12 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.11/23.15 ( 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))) ) 23.11/23.15 ( int, v, y ) 23.11/23.15 ( int, v, sa ) 23.11/23.15 ( int, v, x ) 23.11/23.15 ( int, v, r ) 23.11/23.15 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.11/23.15 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.15 ( int, w, y ) 23.11/23.15 ( int, w, sa ) 23.11/23.15 ( int, w, x ) 23.11/23.15 ( int, w, r ) 23.11/23.15 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.11/23.15 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.15 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.11/23.15 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.11/23.15 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.11/23.15 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( int, skv_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))) ) 23.11/23.15 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( 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))))) ) 23.11/23.15 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( 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)))) ) 23.11/23.15 ( complex, ii, ii ) 23.11/23.15 ( 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)) ) 23.11/23.15 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ) 23.11/23.15 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_148944 $$unsorted) (BOUND_VARIABLE_148945 $$unsorted) (BOUND_VARIABLE_148946 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_148946))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_148946))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_148944) BOUND_VARIABLE_148945)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP nat X_a _let_1 BOUND_VARIABLE_148944)) (hAPP nat X_a _let_1 BOUND_VARIABLE_148945))))))) ) 23.11/23.15 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.15 ) 23.11/23.15 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun real complex))) (let ((_let_1 (uminus_uminus real))) (= (hAPP complex complex (uminus_uminus complex) (hAPP real complex (hAPP real _let_0 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_0 complex_1 (hAPP real real _let_1 A_1)) (hAPP real real _let_1 B))))) ) 23.11/23.15 ( (one_one real), (zero_zero real) ) 23.11/23.15 ( (zero_zero real), (one_one real) ) 23.11/23.15 ) 23.11/23.15 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun X_a bool))) (or (not (hBOOL (hAPP _let_1 bool (finite_finite_1 X_a) A_2))) (and (not (forall ((X_1 $$unsorted)) (not (hBOOL (hAPP _let_1 bool (hAPP X_a (fun _let_1 bool) (member X_a) X_1) A_2))) )) (not (= _let_0 (one_one nat)))) (= _let_0 (hAPP _let_1 nat (finite_card X_a) A_2))))) ) 23.11/23.15 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 23.11/23.15 ) 23.11/23.15 (instantiation (forall ((W $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) W)))) (= (zero_zero nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 W)))) ) 23.11/23.15 ( pls ) 23.11/23.15 ( (hAPP int int bit1 pls) ) 23.11/23.15 ( min ) 23.11/23.15 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.15 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.15 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.11/23.15 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.11/23.15 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.11/23.15 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))) ) 23.11/23.15 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))) ) 23.11/23.15 ) 23.11/23.15 (instantiation (forall ((W $$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))))) ) 23.11/23.15 ( pls ) 23.11/23.15 ( (hAPP int int bit1 pls) ) 23.11/23.15 ( min ) 23.11/23.16 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.11/23.16 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.11/23.16 ( (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)))))) ) 23.11/23.16 ( (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))))))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149069 $$unsorted) (BOUND_VARIABLE_149070 $$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_149069) BOUND_VARIABLE_149070)) (= (ti X_a BOUND_VARIABLE_149069) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_149070)))) ) 23.11/23.16 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.11/23.16 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.11/23.16 ( 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) ) 23.11/23.16 ( 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) ) 23.11/23.16 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.11/23.16 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.11/23.16 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.11/23.16 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.11/23.16 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( nat, (one_one nat), (one_one nat) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149088 $$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_149088) (zero_zero nat)))) ) 23.11/23.16 ( int, s ) 23.11/23.16 ( int, s1 ) 23.11/23.16 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( int, v ) 23.11/23.16 ( int, w ) 23.11/23.16 ( int, y ) 23.11/23.16 ( int, x ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.11/23.16 ( int, skv_6 ) 23.11/23.16 ( int, skv_7 ) 23.11/23.16 ( int, skv_16 ) 23.11/23.16 ( int, skv_23 ) 23.11/23.16 ( int, skv_24 ) 23.11/23.16 ( real, (hAPP int real (number_number_of real) min) ) 23.11/23.16 ( 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)))) ) 23.11/23.16 ( complex, ii ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((A_3 $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (hAPP nat real (real_1 nat) A_3))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling Xa)) A_3)))))) ) 23.11/23.16 ( (zero_zero nat), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zEven))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) Xa) Ya)) zEven)))))) ) 23.11/23.16 ( (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)))) ) 23.11/23.16 ( (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) ) 23.11/23.16 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.11/23.16 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.11/23.16 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.16 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.16 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.11/23.16 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.11/23.16 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.11/23.16 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.11/23.16 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun (filter nat) bool))) (let ((_let_3 (fun nat _let_1))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (tendsto nat real) A_3) (zero_zero real)) sequentially))) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) (hAPP nat real A_3 N_1))) )) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real A_3 (hAPP nat nat suc N_1))) (hAPP nat real A_3 N_1))) )) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_3 (hAPP (fun real _let_1) (fun _let_0 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3)))))))) ) 23.11/23.16 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149160 $$unsorted) (BOUND_VARIABLE_149161 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (hAPP int nat (number_number_of nat) BOUND_VARIABLE_149161))) (or (not (power X_a)) (not (no_zero_divisors X_a)) (not (zero_neq_one X_a)) (not (mult_zero X_a)) (= (and (not (= (zero_zero nat) _let_1)) (= _let_0 (ti X_a BOUND_VARIABLE_149160))) (= _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_149160) _let_1)))))) ) 23.11/23.16 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.11/23.16 ) 23.11/23.16 (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 $$unsorted) (N_1 $$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_1))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP nat nat F M_2)) (hAPP nat nat F N_1)))))) )) (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))))))) ) 23.11/23.16 ( (zero_zero nat), (one_one nat), fact ) 23.11/23.16 ( (one_one nat), (one_one nat), suc ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (zero_zero X_a) (hAPP int X_a (ring_1_of_int X_a) (zero_zero int)))) ) 23.11/23.16 ( rat ) 23.11/23.16 ( int ) 23.11/23.16 ( nat ) 23.11/23.16 ( real ) 23.11/23.16 ( complex ) 23.11/23.16 ( quickcheck_code_int ) 23.11/23.16 ( code_code_numeral ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((N $$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)))) (let ((_let_3 (one_one nat))) (or (not (= _let_3 (hAPP nat nat (hAPP nat _let_0 (div_mod nat) N) (hAPP int nat _let_1 (hAPP int int bit0 _let_2))))) (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP nat nat (hAPP nat _let_0 (div_div nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) _let_3)) (hAPP int nat _let_1 _let_2))))))))) ) 23.11/23.16 ( (hAPP int nat nat_1 t) ) 23.11/23.16 ) 23.11/23.16 (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 _let_1 _let_1 normalize (hAPP int _let_1 (hAPP int _let_2 _let_3 A_1) B)) (hAPP int _let_1 (hAPP int _let_2 _let_3 P_5) Q_3))) (= (hAPP int rat (hAPP int _let_0 fract A_1) B) (hAPP int rat (hAPP int _let_0 fract P_5) Q_3))))))) ) 23.11/23.16 ( (one_one int), (one_one int), (zero_zero int), (one_one int) ) 23.11/23.16 ( (zero_zero int), (one_one int), (one_one int), (one_one int) ) 23.11/23.16 ( (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 23.11/23.16 ( s, (one_one int), s, (one_one int) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) (hAPP real real ln X)))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) X))) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (one_one real)) X)))))) ) 23.11/23.16 ( pi ) 23.11/23.16 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (one_one real) ) 23.11/23.16 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( skv_2 ) 23.11/23.16 ( skv_9 ) 23.11/23.16 ( skv_12 ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (combk X_a nat) (zero_zero X_a)))))) ) 23.11/23.16 ( rat ) 23.11/23.16 ( int ) 23.11/23.16 ( (fun int int) ) 23.11/23.16 ( nat ) 23.11/23.16 ( bool ) 23.11/23.16 ( real ) 23.11/23.16 ( (fun real real) ) 23.11/23.16 ( (fun nat nat) ) 23.11/23.16 ( complex ) 23.11/23.16 ( (product_prod int int) ) 23.11/23.16 ( (fun bool bool) ) 23.11/23.16 ( (fun nat bool) ) 23.11/23.16 ( (fun nat (fun nat bool)) ) 23.11/23.16 ( quickcheck_code_int ) 23.11/23.16 ( code_code_numeral ) 23.11/23.16 ( (fun nat (product_prod int int)) ) 23.11/23.16 ( (product_prod real real) ) 23.11/23.16 ( (product_prod nat nat) ) 23.11/23.16 ( (fun (product_prod nat nat) bool) ) 23.11/23.16 ( (fun nat (fun (product_prod nat nat) bool)) ) 23.11/23.16 ( (fun nat (product_prod nat nat)) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) Xa) Ya)) zOdd)))))) ) 23.11/23.16 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.11/23.16 ( 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))) ) 23.11/23.16 ( v, y ) 23.11/23.16 ( v, sa ) 23.11/23.16 ( v, x ) 23.11/23.16 ( v, r ) 23.11/23.16 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.11/23.16 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.16 ( w, y ) 23.11/23.16 ( w, sa ) 23.11/23.16 ( w, x ) 23.11/23.16 ( w, r ) 23.11/23.16 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.11/23.16 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.11/23.16 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.11/23.16 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.11/23.16 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.11/23.16 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( skv_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))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (one_one X_a)) (zero_zero X_a))))) ) 23.11/23.16 ( rat ) 23.11/23.16 ( int ) 23.11/23.16 ( nat ) 23.11/23.16 ( bool ) 23.11/23.16 ( real ) 23.11/23.16 ( (filter nat) ) 23.11/23.16 ( complex ) 23.11/23.16 ( (fun int bool) ) 23.11/23.16 ( (product_prod int int) ) 23.11/23.16 ( (fun nat bool) ) 23.11/23.16 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.11/23.16 ( quickcheck_code_int ) 23.11/23.16 ( code_code_numeral ) 23.11/23.16 ( (product_prod real real) ) 23.11/23.16 ( (filter real) ) 23.11/23.16 ( (product_prod nat nat) ) 23.11/23.16 ( (fun nat rat) ) 23.11/23.16 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149296 $$unsorted) (BOUND_VARIABLE_149297 $$unsorted) (BOUND_VARIABLE_149298 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_149298))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_149298))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) BOUND_VARIABLE_149296) BOUND_VARIABLE_149297)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_149296)) (hAPP nat X_a _let_2 BOUND_VARIABLE_149297)))))))) ) 23.11/23.16 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool _let_0 X))) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root N) X))))) ) 23.11/23.16 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less_eq real))) (let ((_let_4 (plus_plus real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 X) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP real real (exp real) X)) (hAPP real real (hAPP real _let_0 _let_4 (hAPP real real (hAPP real _let_0 _let_4 _let_1) X)) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))))) ) 23.11/23.16 ( (hAPP int real (number_number_of real) min) ) 23.11/23.16 ( pi ) 23.11/23.16 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.16 ( (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)))) ) 23.11/23.16 ( skv_10 ) 23.11/23.16 ( skv_11 ) 23.11/23.16 ( skv_15 ) 23.11/23.16 ( skv_18 ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) N))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) _let_1) (hAPP int int (fact_fact int) N)))))) ) 23.11/23.16 ( pls ) 23.11/23.16 ( (one_one int) ) 23.11/23.16 ( min ) 23.11/23.16 ( (zero_zero int) ) 23.11/23.16 ( s ) 23.11/23.16 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.16 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.11/23.16 ( skv_4 ) 23.11/23.16 ( skv_5 ) 23.11/23.16 ) 23.11/23.16 (instantiation (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 (plus_plus int) A_1) B))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) _let_2) A_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) _let_3) _let_2))) (= _let_3 (hAPP int int (hAPP int _let_0 (div_mod int) A_1) B))))))) ) 23.11/23.16 ( (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)))) ) 23.11/23.16 ( (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) ) 23.11/23.16 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.11/23.16 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.11/23.17 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.17 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.11/23.17 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.11/23.17 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.11/23.17 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.11/23.17 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.11/23.17 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.11/23.17 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ) 23.11/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149503 $$unsorted) (BOUND_VARIABLE_149504 $$unsorted) (BOUND_VARIABLE_149505 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_149505))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149505) (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_149503)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_149504))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149504) BOUND_VARIABLE_149503))))))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ) 23.11/23.17 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP int real (real_1 int) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 _let_2) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_2) (one_one real))))) (= (ti int N) (hAPP real int (archim2085082626_floor real) X)))))) ) 23.11/23.17 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (zero_zero int), pi ) 23.11/23.17 ( (zero_zero int), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( (zero_zero int), skv_2 ) 23.11/23.17 ( (zero_zero int), skv_9 ) 23.11/23.17 ( (zero_zero int), skv_12 ) 23.11/23.17 ) 23.11/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149563 $$unsorted) (BOUND_VARIABLE_149564 $$unsorted) (BOUND_VARIABLE_149565 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (fun nat X_a))) (let ((_let_3 (power_power X_a))) (let ((_let_4 (abs_abs X_a))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_149565))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_4 BOUND_VARIABLE_149563)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_149564)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_149563) BOUND_VARIABLE_149565)) (hAPP nat X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_149564) BOUND_VARIABLE_149565))))))))) ) 23.11/23.17 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.11/23.17 ) 23.11/23.17 (instantiation (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (hAPP int _let_1 (dvd_dvd int) K_4))) (or (not (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd N) K_4))) (not (hBOOL (hAPP int bool _let_2 (hAPP int int (hAPP int _let_0 (times_times int) M) N)))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) M))) (hBOOL (hAPP int bool _let_2 M)))))) ) 23.11/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_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))) ) 23.11/23.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.11/23.17 ) 23.11/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149602 $$unsorted) (BOUND_VARIABLE_149603 $$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_149602) BOUND_VARIABLE_149603))) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP X_a real _let_0 BOUND_VARIABLE_149602)) (hAPP X_a real _let_0 BOUND_VARIABLE_149603)))))) ) 23.11/23.17 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.11/23.17 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.11/23.17 ( 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) ) 23.11/23.17 ( 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) ) 23.11/23.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.11/23.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.11/23.17 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.11/23.17 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.11/23.17 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.11/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.18/23.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( nat, (one_one nat), (one_one nat) ) 23.18/23.17 ) 23.18/23.17 (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 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) K) I_2))) (not (hBOOL (hAPP int bool P_1 I_2))) (hBOOL (hAPP int bool P_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) I_2) (one_one int))))) )) (hBOOL (hAPP int bool P_1 I))) ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int), t ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less int) min), min, min ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less int) min), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.17 ( nat_neg, (zero_zero int), pls ) 23.18/23.17 ( nat_is_nat, (zero_zero int), skv_4 ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less_eq int) pls), (zero_zero int), (one_one int) ) 23.18/23.17 ( (even_odd_even int), (zero_zero int), min ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less int) pls), (zero_zero int), s ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less_eq int) min), min, pls ) 23.18/23.17 ( (hAPP int (fun int bool) (ord_less_eq int) min), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((Ma $$unsorted)) (let ((_let_0 (fun int bool))) (= (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) (hAPP int _let_0 norRRset Ma))) ) 23.18/23.17 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( y ) 23.18/23.17 ( x ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.17 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.18/23.17 ( (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))) m1))) ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_0 (number_number_of int))) (let ((_let_1 (number_number_of rat))) (= (hAPP int rat (hAPP int (fun int rat) fract (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_1 K_4)) (hAPP int rat _let_1 L_4))))) ) 23.18/23.17 ( pls, (hAPP int int bit1 pls) ) 23.18/23.17 ( (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149657 $$unsorted) (BOUND_VARIABLE_149658 $$unsorted)) (let ((_let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_149657) BOUND_VARIABLE_149658))) (or (not (comm_semiring_1 X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_149657) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) BOUND_VARIABLE_149658)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) _let_0) _let_0)))) ) 23.18/23.17 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((K_4 $$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)))) ) 23.18/23.17 ( pls ) 23.18/23.17 ( (one_one int) ) 23.18/23.17 ( min ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ord_less_eq int))) (= (or (= _let_2 (ti int K)) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) I)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 I) _let_2))) (and (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 I) K)) (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_2) I)))) (= _let_2 (hAPP int int (hAPP int (fun int int) (div_div int) I) K))))))) ) 23.18/23.17 ( pls, (zero_zero int) ) 23.18/23.17 ( (one_one int), (zero_zero int) ) 23.18/23.17 ( (one_one int), t ) 23.18/23.17 ( min, min ) 23.18/23.17 ( min, (zero_zero int) ) 23.18/23.17 ( (zero_zero int), pls ) 23.18/23.17 ( (zero_zero int), (one_one int) ) 23.18/23.17 ( (zero_zero int), min ) 23.18/23.17 ( (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))) ) 23.18/23.17 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.18/23.17 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5 ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.18/23.17 ( t, (one_one int) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149727 $$unsorted) (BOUND_VARIABLE_149728 $$unsorted) (BOUND_VARIABLE_149729 $$unsorted) (BOUND_VARIABLE_149730 $$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)))) (let ((_let_3 (fun X_a X_a))) (let ((_let_4 (times_times X_a))) (or (not (ordered_semiring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149729) BOUND_VARIABLE_149730))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_149727) BOUND_VARIABLE_149728))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_149729))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_149727))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_149729) BOUND_VARIABLE_149727)) (hAPP X_a X_a (hAPP X_a _let_3 _let_4 BOUND_VARIABLE_149730) BOUND_VARIABLE_149728))))))))) ) 23.18/23.17 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) (zero_zero real)) Xa))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) ln) Xa)))) ) 23.18/23.17 ( pi ) 23.18/23.17 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( skv_2 ) 23.18/23.17 ( skv_9 ) 23.18/23.17 ( skv_12 ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_149778 $$unsorted) (BOUND_VARIABLE_149779 $$unsorted) (BOUND_VARIABLE_149780 $$unsorted)) (let ((_let_0 (fun bool bool))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (dvd_dvd nat))) (let ((_let_4 (fun nat _let_0))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun _let_1 _let_4))) (let ((_let_7 (fun nat _let_5))) (let ((_let_8 (fun _let_2 _let_2))) (let ((_let_9 (fun nat _let_4))) (let ((_let_10 (fun nat X_a))) (or (not (order X_a)) (not (hBOOL (hAPP _let_10 bool (hAPP _let_2 (fun _let_10 bool) (strict_mono nat X_a) (hAPP _let_2 _let_2 (hAPP _let_7 _let_8 (combs nat _let_1 _let_1) (hAPP _let_9 _let_7 (hAPP (fun _let_4 _let_5) (fun _let_9 _let_7) (combb _let_4 _let_5 nat) (combs nat bool bool)) (hAPP _let_2 _let_9 (hAPP _let_6 (fun _let_2 _let_9) (combb _let_1 _let_4 nat) (hAPP (fun bool _let_0) _let_6 (combb bool _let_0 nat) fconj)) _let_3))) (hAPP _let_2 _let_2 (hAPP _let_5 _let_8 (combb _let_1 _let_1 nat) (hAPP _let_0 _let_5 (combb bool bool nat) fNot)) (hAPP _let_2 _let_2 (combc nat nat bool) _let_3)))) BOUND_VARIABLE_149780))) (not (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_3 BOUND_VARIABLE_149778) BOUND_VARIABLE_149779))) (hBOOL (hAPP nat bool (hAPP nat _let_1 _let_3 BOUND_VARIABLE_149779) BOUND_VARIABLE_149778)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP nat X_a BOUND_VARIABLE_149780 BOUND_VARIABLE_149778)) (hAPP nat X_a BOUND_VARIABLE_149780 BOUND_VARIABLE_149779))))))))))))))) ) 23.18/23.17 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 23.18/23.17 ( 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))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (= (hAPP real X_a (of_real X_a) (one_one real)) (one_one X_a))) ) 23.18/23.17 ( rat ) 23.18/23.17 ( int ) 23.18/23.17 ( nat ) 23.18/23.17 ( real ) 23.18/23.17 ( complex ) 23.18/23.17 ( quickcheck_code_int ) 23.18/23.17 ( code_code_numeral ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) Xa) zEven))) (= (hAPP int int (hAPP int _let_0 (times_times int) _let_2) (hAPP int int (hAPP int _let_0 (div_div int) Xa) _let_2)) (ti int Xa)))))) ) 23.18/23.17 ( pls ) 23.18/23.17 ( (one_one int) ) 23.18/23.17 ( min ) 23.18/23.17 ( s ) 23.18/23.17 ( s1 ) 23.18/23.17 ( m ) 23.18/23.17 ( t ) 23.18/23.17 ( v ) 23.18/23.17 ( w ) 23.18/23.17 ( y ) 23.18/23.17 ( sa ) 23.18/23.17 ( x ) 23.18/23.17 ( r ) 23.18/23.17 ( m1 ) 23.18/23.17 ( skv_14 ) 23.18/23.17 ( skv_20 ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_149872 $$unsorted) (BOUND_VARIABLE_149873 $$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 X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_149872) (zero_zero X_b)) BOUND_VARIABLE_149873))) (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_149872)) (zero_zero real)) BOUND_VARIABLE_149873)))))) ) 23.18/23.17 ( nat, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 23.18/23.17 ( 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))))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_1 $$unsorted)) (or (hBOOL (hAPP nat bool (even_odd_even nat) X_1)) (= (zero_zero real) (hAPP nat real cos_coeff X_1))) ) 23.18/23.17 ( (zero_zero nat) ) 23.18/23.17 ( (one_one nat) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X_1))) (= (hAPP nat real cos_coeff X_1) (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)) (hAPP nat nat (hAPP nat (fun nat nat) (div_div nat) X_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) X_1))))) ) 23.18/23.17 ( (zero_zero nat) ) 23.18/23.17 ( (one_one nat) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted)) (or (not (real_algebra_1 X_a)) (not (real_normed_vector X_a)) (not (forall ((K_2 $$unsorted)) (or (not (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP real real (norm_norm real) X_1)) K_2))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2)))) ))) ) 23.18/23.17 ( real ) 23.18/23.17 ( complex ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((A_3 $$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_3) P_4))) (= (hAPP _let_0 nat (finite_card int) (hAPP int _let_0 (hAPP int (fun int _let_0) bnorRset A_3) P_4)) (hAPP int nat nat_1 A_3)))) ) 23.18/23.17 ( (one_one int), t ) 23.18/23.17 ( min, min ) 23.18/23.17 ( min, (zero_zero int) ) 23.18/23.17 ( (zero_zero int), pls ) 23.18/23.17 ( (zero_zero int), (one_one int) ) 23.18/23.17 ( (zero_zero int), min ) 23.18/23.17 ( (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))) ) 23.18/23.17 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150008 $$unsorted) (BOUND_VARIABLE_150009 $$unsorted)) (let ((_let_0 (uminus_uminus X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (division_ring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_150008)) BOUND_VARIABLE_150009) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_150008) BOUND_VARIABLE_150009))))))) ) 23.18/23.17 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.17 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.17 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.17 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.17 ( 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))))))))) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ( 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))) ) 23.18/23.17 ) 23.18/23.17 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150043 $$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_150043) _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_150043)) _let_2)))))) ) 23.18/23.17 ( int, min ) 23.18/23.17 ( int, (zero_zero int) ) 23.18/23.17 ( real, pi ) 23.18/23.17 ( real, (zero_zero real) ) 23.18/23.17 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( 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))))) ) 23.18/23.18 ( complex, ii ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150069 $$unsorted) (BOUND_VARIABLE_150070 $$unsorted)) (let ((_let_0 (fun nat X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 (fun X_a bool) (sums X_a) BOUND_VARIABLE_150069) BOUND_VARIABLE_150070))) (hBOOL (hAPP _let_0 bool (summable X_a) BOUND_VARIABLE_150069)))) ) 23.18/23.18 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (hAPP real _let_0 (power_power real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) suc))), (one_one real) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150239 $$unsorted) (BOUND_VARIABLE_150240 $$unsorted) (BOUND_VARIABLE_150241 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (division_ring X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_150241)) (not (= (ti X_a BOUND_VARIABLE_150240) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_150239) BOUND_VARIABLE_150241))) (= (ti X_a BOUND_VARIABLE_150239) (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_150240) BOUND_VARIABLE_150241)))) ) 23.18/23.18 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s1 ) 23.18/23.18 ( 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))), m1, m1 ) 23.18/23.18 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), v, v ) 23.18/23.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), pls, pls ) 23.18/23.18 ( int, y, min, min ) 23.18/23.18 ( int, sa, r, r ) 23.18/23.18 ( int, x, s, s ) 23.18/23.18 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), m, m ) 23.18/23.18 ( int, r, t, t ) 23.18/23.18 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), y, y ) 23.18/23.18 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), sa, sa ) 23.18/23.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), w, w ) 23.18/23.18 ( int, skv_13, x, x ) 23.18/23.18 ( int, skv_19, skv_14, skv_14 ) 23.18/23.18 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi, pi ) 23.18/23.18 ( complex, ii, ii, ii ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((Na $$unsorted) (P_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (zero_zero nat)))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 N_1))) (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_1)))) )) (hBOOL (hAPP nat bool P_1 Na))) ) 23.18/23.18 ( (zero_zero nat), (even_odd_even nat) ) 23.18/23.18 ( (zero_zero nat), prime ) 23.18/23.18 ( (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)) ) 23.18/23.18 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 23.18/23.18 ( (one_one nat), (even_odd_even nat) ) 23.18/23.18 ( (hAPP nat nat suc (zero_zero nat)), prime ) 23.18/23.18 ( n, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 23.18/23.18 ( tn, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150278 $$unsorted)) (or (not (real_normed_vector X_a)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_150278)) (zero_zero real))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_150278)))) ) 23.18/23.18 ( int, pls ) 23.18/23.18 ( int, min ) 23.18/23.18 ( int, s ) 23.18/23.18 ( int, s1 ) 23.18/23.18 ( int, m ) 23.18/23.18 ( int, t ) 23.18/23.18 ( int, v ) 23.18/23.18 ( int, w ) 23.18/23.18 ( int, y ) 23.18/23.18 ( int, sa ) 23.18/23.18 ( int, x ) 23.18/23.18 ( int, r ) 23.18/23.18 ( int, m1 ) 23.18/23.18 ( int, skv_14 ) 23.18/23.18 ( int, skv_20 ) 23.18/23.18 ( (fun int int), bit1 ) 23.18/23.18 ( (fun int int), bit0 ) 23.18/23.18 ( (fun int int), succ ) 23.18/23.18 ( (fun int int), pred ) 23.18/23.18 ( (fun int int), (fact_fact int) ) 23.18/23.18 ( (fun int int), zfact ) 23.18/23.18 ( nat, n ) 23.18/23.18 ( nat, tn ) 23.18/23.18 ( bool, fTrue ) 23.18/23.18 ( bool, fFalse ) 23.18/23.18 ( real, pi ) 23.18/23.18 ( (fun nat real), (real_1 nat) ) 23.18/23.18 ( (fun nat real), cos_coeff ) 23.18/23.18 ( (fun nat real), sin_coeff ) 23.18/23.18 ( (fun real real), sin ) 23.18/23.18 ( (fun real real), cos ) 23.18/23.18 ( (fun real real), sqrt ) 23.18/23.18 ( (fun real real), tan ) 23.18/23.18 ( (fun real real), ln ) 23.18/23.18 ( (fun real real), arctan ) 23.18/23.18 ( (fun real real), arcsin ) 23.18/23.18 ( (fun real real), arccos ) 23.18/23.18 ( (fun nat nat), suc ) 23.18/23.18 ( (fun nat nat), (fact_fact nat) ) 23.18/23.18 ( (fun nat nat), nat_size ) 23.18/23.18 ( (fun nat nat), (size_size nat) ) 23.18/23.18 ( (fun nat nat), fact ) 23.18/23.18 ( (filter nat), sequentially ) 23.18/23.18 ( (fun int (fun int rat)), fract ) 23.18/23.18 ( complex, ii ) 23.18/23.18 ( (fun int bool), zOdd ) 23.18/23.18 ( (fun int bool), zprime ) 23.18/23.18 ( (fun int bool), zEven ) 23.18/23.18 ( (fun int bool), nat_neg ) 23.18/23.18 ( (fun int bool), nat_is_nat ) 23.18/23.18 ( (fun int bool), (even_odd_even int) ) 23.18/23.18 ( (fun int bool), twoSqu1091635170sum2sq ) 23.18/23.18 ( (fun int (fun int int)), legacy_zgcd ) 23.18/23.18 ( (fun int (fun int int)), (gcd_gcd int) ) 23.18/23.18 ( (fun int (fun int int)), inv ) 23.18/23.18 ( (fun int (fun int int)), multInv ) 23.18/23.18 ( (fun int (fun int int)), legendre ) 23.18/23.18 ( (fun int (fun int int)), standardRes ) 23.18/23.18 ( (fun int (fun int int)), nat_tsub ) 23.18/23.18 ( (fun int (fun int int)), z3div ) 23.18/23.18 ( (fun int (fun int int)), z3mod ) 23.18/23.18 ( (fun int (fun int int)), int_lcm ) 23.18/23.18 ( (fun int (fun int int)), int_gcd ) 23.18/23.18 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.18/23.18 ( (fun bool bool), fNot ) 23.18/23.18 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.18/23.18 ( (fun bool (fun bool bool)), fconj ) 23.18/23.18 ( (fun bool (fun bool bool)), fdisj ) 23.18/23.18 ( (fun bool (fun bool bool)), fimplies ) 23.18/23.18 ( (fun int (fun int bool)), quadRes ) 23.18/23.18 ( (fun int (fun int bool)), d22set ) 23.18/23.18 ( (fun int (fun int bool)), norRRset ) 23.18/23.18 ( (fun int (fun int bool)), sRStar ) 23.18/23.18 ( (fun int (fun int bool)), sr ) 23.18/23.18 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.18/23.18 ( (fun nat bool), (even_odd_even nat) ) 23.18/23.18 ( (fun nat bool), prime ) 23.18/23.18 ( (fun real complex), cis ) 23.18/23.18 ( (fun nat (fun nat bool)), coprime ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.18/23.18 ( (fun (product_prod int int) bool), frac_1 ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.18/23.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.18/23.18 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.18/23.18 ( (fun (fun int bool) bool), nat_nat_set ) 23.18/23.18 ( (fun nat (fun real real)), root ) 23.18/23.18 ( (fun real (fun real real)), log ) 23.18/23.18 ( (fun real (fun real real)), powr ) 23.18/23.18 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.18/23.18 ( (fun complex complex), cnj ) 23.18/23.18 ( (fun complex complex), expi ) 23.18/23.18 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.18/23.18 ( (fun nat (fun nat nat)), nat_gcd ) 23.18/23.18 ( (fun nat (fun nat nat)), nat_lcm ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.18/23.18 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.18/23.18 ( (fun int (fun (fun int bool) bool)), resSet ) 23.18/23.18 ( (fun int nat), nat_1 ) 23.18/23.18 ( (fun int nat), phi ) 23.18/23.18 ( (fun complex real), re ) 23.18/23.18 ( (fun complex real), im ) 23.18/23.18 ( (fun complex real), arg ) 23.18/23.18 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.18/23.18 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.18/23.18 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.18/23.18 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.18/23.18 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.18/23.18 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.18/23.18 ( (fun (product_prod nat nat) bool), pred_nat ) 23.18/23.18 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.18/23.18 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.18/23.18 ( (fun (fun int bool) int), (the int) ) 23.18/23.18 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.18/23.18 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.18/23.18 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.18/23.18 ( (fun real (fun real complex)), rcis ) 23.18/23.18 ( (fun real (fun real complex)), complex_1 ) 23.18/23.18 ( (fun int (fun int (fun int bool))), zcong ) 23.18/23.18 ( (fun int (fun int (fun int bool))), wset ) 23.18/23.18 ( (fun int (fun int (fun int bool))), noXRRset ) 23.18/23.18 ( (fun int (fun int (fun int bool))), bnorRset ) 23.18/23.18 ( (fun int (fun int (fun int bool))), zcongm ) 23.18/23.18 ( (fun real nat), natceiling ) 23.18/23.18 ( (fun real nat), natfloor ) 23.18/23.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.18/23.18 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.18/23.18 ( (fun int real), (real_1 int) ) 23.18/23.18 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.18/23.18 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.18/23.18 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.18/23.18 ( (fun complex nat), (size_size complex) ) 23.18/23.18 ( (fun complex nat), complex_size ) 23.18/23.18 ( (fun (fun nat rat) bool), vanishes ) 23.18/23.18 ( (fun (product_prod int int) rat), frct ) 23.18/23.18 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.18/23.18 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.18/23.18 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.18/23.18 ( (fun rat real), ratreal ) 23.18/23.18 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.18/23.18 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.18/23.18 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.18/23.18 ( (fun rat (product_prod int int)), quotient_of ) 23.18/23.18 ( (fun int (fun nat nat)), nat_aux ) 23.18/23.18 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.18/23.18 ( (fun int (list int)), quickc666637781d_zero ) 23.18/23.18 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.18/23.18 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.18/23.18 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.18/23.18 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.18/23.18 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.18/23.18 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.18/23.18 ( (fun code_code_numeral int), code_int_of ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((U $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (zero_zero int))) (let ((_let_2 (fun nat bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) _let_1) U))) (= (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastLessThan int) _let_1) U) (hAPP _let_2 _let_0 (hAPP (fun nat int) (fun _let_2 _let_0) (image nat int) (semiring_1_of_nat int)) (hAPP nat _let_2 (ord_lessThan nat) (hAPP int nat nat_1 U)))))))) ) 23.18/23.18 ( pls ) 23.18/23.18 ( (one_one int) ) 23.18/23.18 ( min ) 23.18/23.18 ( (zero_zero int) ) 23.18/23.18 ( s ) 23.18/23.18 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.18 ( t ) 23.18/23.18 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.18 ( skv_4 ) 23.18/23.18 ( skv_5 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((M $$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)))) ) 23.18/23.18 ( (one_one int) ) 23.18/23.18 ( min ) 23.18/23.18 ( (zero_zero int) ) 23.18/23.18 ( s ) 23.18/23.18 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( t ) 23.18/23.18 ( m1 ) 23.18/23.18 ( skv_4 ) 23.18/23.18 ( skv_5 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150331 $$unsorted) (BOUND_VARIABLE_150332 $$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_150331) BOUND_VARIABLE_150332) (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_150331) BOUND_VARIABLE_150332)) BOUND_VARIABLE_150332))))) ) 23.18/23.18 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.18 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.18 ( 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)))), (one_one int) ) 23.18/23.18 ( 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), (one_one int) ) 23.18/23.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.18/23.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.18 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.18 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.18/23.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( nat, (one_one nat), (one_one nat) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150394 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (or (not (ordere142940540dd_abs X_a)) (= (hAPP X_a X_a _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_150394)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_150394)))) ) 23.18/23.18 ( int, pls ) 23.18/23.18 ( int, (one_one int) ) 23.18/23.18 ( int, min ) 23.18/23.18 ( int, v ) 23.18/23.18 ( int, w ) 23.18/23.18 ( int, skv_14 ) 23.18/23.18 ( int, skv_20 ) 23.18/23.18 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( real, (one_one real) ) 23.18/23.18 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.18/23.18 ( complex, ii ) 23.18/23.18 ( complex, (one_one complex) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150432 $$unsorted) (BOUND_VARIABLE_150433 $$unsorted) (BOUND_VARIABLE_150434 $$unsorted) (BOUND_VARIABLE_150435 $$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 (times_times X_a))) (let ((_let_4 (zero_zero X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150434) BOUND_VARIABLE_150435))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150432) BOUND_VARIABLE_150433))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_4) BOUND_VARIABLE_150435))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) _let_4) BOUND_VARIABLE_150432))) (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_150434) BOUND_VARIABLE_150432)) (hAPP X_a X_a (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_150435) BOUND_VARIABLE_150433))))))))) ) 23.18/23.18 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150495 $$unsorted) (BOUND_VARIABLE_150496 $$unsorted) (BOUND_VARIABLE_150497 $$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_150496))) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_150497))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_150497) BOUND_VARIABLE_150495))) (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_150495)))))) ) 23.18/23.18 ( int, min, min, min ) 23.18/23.18 ( int, (zero_zero int), (zero_zero int), min ) 23.18/23.18 ( 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))), (one_one int), t ) 23.18/23.18 ( 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))), min, (zero_zero int) ) 23.18/23.18 ( 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))), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int), pls ) 23.18/23.18 ( int, t, (zero_zero int), (one_one int) ) 23.18/23.18 ( 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) ) 23.18/23.18 ( 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)))) ) 23.18/23.18 ( real, (hAPP real real (hAPP 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, (zero_zero real) ) 23.18/23.18 ( 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 ) 23.18/23.18 ( 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) ) 23.18/23.18 ( 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 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) X) (zero_zero real)))) (= (zero_zero nat) (hAPP real nat natceiling X))) ) 23.18/23.18 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.18 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( (one_one real) ) 23.18/23.18 ( (zero_zero real) ) 23.18/23.18 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( skv_10 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((P_1 $$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 int) A_4) B_4))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) B_4) (zero_zero int)))) (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))))) ) 23.18/23.18 ( (ord_less int), (one_one int), t ) 23.18/23.18 ( (ord_less int), min, min ) 23.18/23.18 ( (ord_less int), min, (zero_zero int) ) 23.18/23.18 ( (ord_less int), (zero_zero int), pls ) 23.18/23.18 ( (ord_less int), (zero_zero int), (one_one int) ) 23.18/23.18 ( (ord_less int), (zero_zero int), min ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ( (ord_less_eq int), (one_one int), t ) 23.18/23.18 ( (ord_less_eq int), min, pls ) 23.18/23.18 ( (ord_less_eq int), min, min ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), pls ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), min ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), s ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), skv_4 ) 23.18/23.18 ( (ord_less_eq int), (zero_zero int), skv_5 ) 23.18/23.18 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ( 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) ) 23.18/23.18 ( (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) (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)) ) 23.18/23.18 ( (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (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))) ) 23.18/23.18 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real ln Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) (one_one real)))))))) ) 23.18/23.18 ( pi ) 23.18/23.18 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( (one_one real) ) 23.18/23.18 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( skv_2 ) 23.18/23.18 ( skv_9 ) 23.18/23.18 ( skv_12 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((A_1 $$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)))) ) 23.18/23.18 ( pi ) 23.18/23.18 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.18 ( (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)))) ) 23.18/23.18 ( (zero_zero real) ) 23.18/23.18 ( (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 bit0 (hAPP int int bit1 pls))))) ) 23.18/23.18 ( (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) ) 23.18/23.18 ( (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 (hAPP int int bit1 pls))))) ) 23.18/23.18 ( (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)))) ) 23.18/23.18 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.18/23.18 ( skv_10 ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((B_2 $$unsorted) (A_3 $$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_3) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 B_2) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (plus_plus int) A_3) B_2)) zEven)))))) ) 23.18/23.18 ( (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)))) ) 23.18/23.18 ( (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) ) 23.18/23.18 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.18/23.18 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.18/23.18 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.18 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.18 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.18/23.18 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.18 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.18 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.18 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.18 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.18/23.18 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150770 $$unsorted) (BOUND_VARIABLE_150776 $$unsorted)) (let ((_let_0 (even_odd_even nat))) (let ((_let_1 (one_one X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) (hAPP X_a X_a (uminus_uminus X_a) _let_1)))) (or (not (comm_ring_1 X_a)) (and (or (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_150770)) (= (hAPP X_a X_a (uminus_uminus X_a) _let_1) (hAPP nat X_a _let_2 BOUND_VARIABLE_150770))) (or (not (hBOOL (hAPP nat bool _let_0 BOUND_VARIABLE_150776))) (= _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_150776)))))))) ) 23.18/23.18 ( int, (one_one nat), (one_one nat) ) 23.18/23.18 ( complex, (zero_zero nat), (zero_zero nat) ) 23.18/23.18 ) 23.18/23.18 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150790 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_150790))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) BOUND_VARIABLE_150790)))) ) 23.18/23.18 ( int, t ) 23.18/23.18 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150803 $$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 BOUND_VARIABLE_150803) _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_150803) BOUND_VARIABLE_150803)) _let_2))))))) ) 23.18/23.19 ( int, (one_one int) ) 23.18/23.19 ( int, min ) 23.18/23.19 ( int, (zero_zero int) ) 23.18/23.19 ( 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)))) ) 23.18/23.19 ( 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) ) 23.18/23.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.19 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.18/23.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( nat, (one_one nat) ) 23.18/23.19 ( real, pi ) 23.18/23.19 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( 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))))) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (abs_Frac X_a))) (= _let_0 (ti (fun (product_prod int int) X_a) _let_0))) ) 23.18/23.19 ( rat ) 23.18/23.19 ( int ) 23.18/23.19 ( (fun int int) ) 23.18/23.19 ( bool ) 23.18/23.19 ( (fun int bool) ) 23.18/23.19 ( (product_prod int int) ) 23.18/23.19 ( (fun (product_prod int int) int) ) 23.18/23.19 ( (fun bool bool) ) 23.18/23.19 ( (fun (product_prod int int) bool) ) 23.18/23.19 ( (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 23.18/23.19 ( (fun (product_prod int int) (fun int bool)) ) 23.18/23.19 ( (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 23.18/23.19 ( (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((R_3 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (product_prod int int))) (or (not (= (hAPP rat _let_0 quotient_of R_3) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) P_5) Q_3))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) Q_3)))) ) 23.18/23.19 ( (one_one rat), (one_one int), (one_one int) ) 23.18/23.19 ( (zero_zero rat), (zero_zero int), (one_one int) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((A_1 $$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 (ord_less_eq int))) (let ((_let_4 (fun int _let_2))) (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_3 B) _let_1))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_3 _let_1) _let_5)))) (= (hAPP int _let_2 (hAPP int _let_4 (product_Pair int int) (hAPP int int (number_number_of int) min)) _let_5) (hAPP int _let_2 (hAPP int _let_4 negDivAlg A_1) B))))))))) ) 23.18/23.19 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.19 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.19 ( (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)))), (one_one int) ) 23.18/23.19 ( (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), (one_one int) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.19 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.19 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (product_prod int int))) (let ((_let_4 (ord_less_eq int))) (let ((_let_5 (hAPP int (fun int _let_3) negDivAlg A_1))) (or (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 B) _let_2)) (hBOOL (hAPP int bool (hAPP int _let_1 _let_4 _let_2) (hAPP int int (hAPP int _let_0 (plus_plus int) A_1) B))) (= (hAPP int _let_3 _let_5 B) (hAPP _let_3 _let_3 (hAPP int (fun _let_3 _let_3) adjust B) (hAPP int _let_3 _let_5 (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)))) B))))))))))) ) 23.18/23.19 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.19 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.19 ( (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)))), (one_one int) ) 23.18/23.19 ( (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), (one_one int) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.19 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.19 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150899 $$unsorted) (BOUND_VARIABLE_150900 $$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_150899) BOUND_VARIABLE_150900) sequentially)) (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((No $$unsorted)) (or (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) (hAPP nat X_a BOUND_VARIABLE_150899 N_1)) BOUND_VARIABLE_150900)) R_1))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) No)))) ))) )))) ) 23.18/23.19 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_150935 $$unsorted) (BOUND_VARIABLE_150936 $$unsorted)) (or (not (ab_group_add X_a)) (= (= (ti X_a BOUND_VARIABLE_150935) (ti X_a BOUND_VARIABLE_150936)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) BOUND_VARIABLE_150935) BOUND_VARIABLE_150936)))) ) 23.18/23.19 ( 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) ) 23.18/23.19 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.19 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.19 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.19 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.18/23.19 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.18/23.19 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((D_3 $$unsorted) (I_1 $$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_3) I_1))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (hAPP int int _let_1 D_3)) (hAPP int int _let_1 I_1)))))) ) 23.18/23.19 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 23.18/23.19 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.19 ) 23.18/23.19 (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 X_b bool))) (let ((_let_4 (fun X_a _let_3))) (let ((_let_5 (fun _let_0 X_b))) (let ((_let_6 (fun _let_0 _let_3))) (let ((_let_7 (fun _let_0 X_a))) (= (hAPP _let_1 _let_0 _let_2 (hAPP _let_5 _let_1 (hAPP _let_6 (fun _let_5 _let_1) (combs _let_0 X_b bool) (hAPP _let_7 _let_6 (hAPP _let_4 (fun _let_7 _let_6) (combb X_a _let_3 _let_0) P_1) (product_fst X_a X_b))) (product_snd X_a X_b))) (hAPP _let_1 _let_0 _let_2 (hAPP _let_4 _let_1 (product_prod_case X_a X_b bool) P_1))))))))))) ) 23.18/23.19 ( int, int, (fequal int) ) 23.18/23.19 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun int _let_1))) (let ((_let_7 (fun _let_0 _let_6))) (let ((_let_8 (fun int _let_6))) (let ((_let_9 (fun _let_6 _let_6))) (hAPP _let_6 _let_6 (hAPP _let_5 _let_9 (combb _let_1 _let_1 int) (hAPP _let_4 _let_5 (combs int bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_3) (fun _let_1 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_1 (ord_less int) (zero_zero int))))) (hAPP int _let_6 (hAPP _let_8 _let_8 (combc int int _let_1) (hAPP _let_8 _let_8 (hAPP _let_9 (fun _let_8 _let_8) (combb _let_6 _let_6 int) (combc int int bool)) (hAPP _let_2 _let_8 (hAPP _let_7 (fun _let_2 _let_8) (combb _let_0 _let_6 int) (hAPP _let_6 _let_7 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 23.18/23.19 ( 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))) ) 23.18/23.19 ( (product_prod int int), (product_prod int int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (fun _let_2 _let_4))) (let ((_let_11 (fun _let_2 _let_1))) (let ((_let_12 (fun _let_3 _let_11))) (let ((_let_13 (hAPP (fun int _let_1) _let_12 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_10 (hAPP (fun bool _let_4) (fun (fun _let_2 bool) _let_10) (combb bool _let_4 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_4 _let_7 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_11 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_3 _let_11 _let_13 _let_5)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_3))) (let ((_let_16 (fun _let_3 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_11))) (let ((_let_19 (fun _let_3 _let_3))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_3 _let_15))) (let ((_let_22 (fun _let_2 _let_0))) (let ((_let_23 (hAPP _let_3 _let_22 (hAPP (fun int _let_0) (fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb _let_3 _let_11 _let_2) _let_13) (hAPP _let_3 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_3 _let_3) (hAPP _let_22 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_22 _let_20) (combb _let_0 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_5)))) (hAPP _let_3 _let_15 (hAPP _let_24 _let_21 (combb int _let_3 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_5))))))))))))))))))))))))))))) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151016 $$unsorted) (BOUND_VARIABLE_151017 $$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_151016) BOUND_VARIABLE_151017))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_151016)) BOUND_VARIABLE_151017))))) ) 23.18/23.19 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.19 ) 23.18/23.19 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151038 $$unsorted) (BOUND_VARIABLE_151039 $$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_151039))) (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_151038) _let_3)) _let_2)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151038) _let_2)) (not (hBOOL (hAPP nat bool (even_odd_even nat) _let_3)))))))))) ) 23.18/23.19 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.19 ) 23.18/23.20 (instantiation (forall ((A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) A_3) Ma))) (= (one_one int) (hAPP int int (hAPP int _let_0 legacy_zgcd (hAPP _let_1 int (hAPP _let_0 (fun _let_1 int) (big_co302546470etprod int int) (combi int)) (hAPP int _let_1 (hAPP int (fun int _let_1) bnorRset A_3) Ma))) Ma))))) ) 23.18/23.20 ( (one_one int), t ) 23.18/23.20 ( min, min ) 23.18/23.20 ( min, (zero_zero int) ) 23.18/23.20 ( (zero_zero int), pls ) 23.18/23.20 ( (zero_zero int), (one_one int) ) 23.18/23.20 ( (zero_zero int), min ) 23.18/23.20 ( (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))) ) 23.18/23.20 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( 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))) ) 23.18/23.20 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.20 ( 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))) ) 23.18/23.20 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( 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))) ) 23.18/23.20 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((Z $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (ti int Z))) (= (or (= (hAPP int int (number_number_of int) min) _let_1) (= _let_0 _let_1)) (= _let_0 (hAPP int int (abs_abs int) Z))))) ) 23.18/23.20 ( pls ) 23.18/23.20 ( min ) 23.18/23.20 ( s ) 23.18/23.20 ( s1 ) 23.18/23.20 ( m ) 23.18/23.20 ( t ) 23.18/23.20 ( v ) 23.18/23.20 ( w ) 23.18/23.20 ( y ) 23.18/23.20 ( sa ) 23.18/23.20 ( x ) 23.18/23.20 ( r ) 23.18/23.20 ( m1 ) 23.18/23.20 ( skv_14 ) 23.18/23.20 ( skv_20 ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151091 $$unsorted) (BOUND_VARIABLE_151092 $$unsorted) (BOUND_VARIABLE_151093 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (inverse_divide X_a))) (or (not (field X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_151093)) (= (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_151091) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_151093) BOUND_VARIABLE_151092))) BOUND_VARIABLE_151093) (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_151091) BOUND_VARIABLE_151093)) BOUND_VARIABLE_151092)))))) ) 23.18/23.20 ( int, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), w, y ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), w, sa ) 23.18/23.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int (fun _let_0 bool) (member int) Xa))) (or (not (hBOOL (hAPP _let_0 bool _let_1 zEven))) (not (hBOOL (hAPP _let_0 bool _let_1 zOdd)))))) ) 23.18/23.20 ( (one_one int) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151131 $$unsorted) (BOUND_VARIABLE_151132 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (or (not (semiring_div X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_151132)) (= (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_151131) BOUND_VARIABLE_151132)) BOUND_VARIABLE_151132) (ti X_a BOUND_VARIABLE_151131)))) ) 23.18/23.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.18/23.20 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( 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))), t ) 23.18/23.20 ( 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))), m1 ) 23.18/23.20 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.18/23.20 ( 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))), skv_21 ) 23.18/23.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.18/23.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.18/23.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.18/23.20 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.18/23.20 ( int, y, v ) 23.18/23.20 ( int, y, w ) 23.18/23.20 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( int, sa, v ) 23.18/23.20 ( int, sa, w ) 23.18/23.20 ( int, x, v ) 23.18/23.20 ( int, x, w ) 23.18/23.20 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.20 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( int, r, v ) 23.18/23.20 ( int, r, w ) 23.18/23.20 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.18/23.20 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.18/23.20 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.18/23.20 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.18/23.20 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.20 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.18/23.20 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.18/23.20 ( 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)))))) ) 23.18/23.20 ( 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))))), pi ) 23.18/23.20 ( complex, ii, ii ) 23.18/23.20 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.18/23.20 ( 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)), ii ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151164 $$unsorted) (BOUND_VARIABLE_151165 $$unsorted) (BOUND_VARIABLE_151166 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151164))) (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_151165)) BOUND_VARIABLE_151166) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_151166)) BOUND_VARIABLE_151165)))))) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), m1 ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), m1, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.20 ) 23.18/23.20 (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)))))) ) 23.18/23.20 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ( 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))))) ) 23.18/23.20 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ( (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)))) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 X) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP real real (hAPP real _let_0 (minus_minus real) X) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real real ln (hAPP real real (hAPP real _let_0 (plus_plus real) _let_1) X))))))))) ) 23.18/23.20 ( (hAPP int real (number_number_of real) min) ) 23.18/23.20 ( pi ) 23.18/23.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.18/23.20 ( skv_10 ) 23.18/23.20 ( skv_11 ) 23.18/23.20 ( skv_15 ) 23.18/23.20 ( skv_18 ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_4 $$unsorted) (N_5 $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N_5))) (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) _let_0) X_4))) (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less_eq real) _let_0) (hAPP real real (hAPP nat (fun real real) root N_5) X_4)))))) ) 23.18/23.20 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$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))) ) 23.18/23.20 ( int, int, rat ) 23.18/23.20 ( int, int, int ) 23.18/23.20 ( int, int, (fun int int) ) 23.18/23.20 ( int, int, bool ) 23.18/23.20 ( int, int, (fun int bool) ) 23.18/23.20 ( int, int, (product_prod int int) ) 23.18/23.20 ( int, int, (fun (product_prod int int) int) ) 23.18/23.20 ( int, int, (fun bool bool) ) 23.18/23.20 ( int, int, (fun (product_prod int int) bool) ) 23.18/23.20 ( int, int, (let ((_let_0 (fun (product_prod int int) bool))) (fun _let_0 _let_0)) ) 23.18/23.20 ( int, int, (fun (product_prod int int) (fun int bool)) ) 23.18/23.20 ( int, int, (let ((_let_0 (product_prod int int))) (fun (fun _let_0 int) (fun _let_0 bool))) ) 23.18/23.20 ( int, int, (let ((_let_0 (fun (product_prod int int) int))) (fun _let_0 _let_0)) ) 23.18/23.20 ( nat, nat, bool ) 23.18/23.20 ( nat, nat, (fun (product_prod nat nat) bool) ) 23.18/23.20 ( real, real, bool ) 23.18/23.20 ( (product_prod int int), (product_prod int int), bool ) 23.18/23.20 ( (product_prod nat nat), (product_prod nat nat), bool ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_151223 $$unsorted) (BOUND_VARIABLE_151224 $$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_151223)) (zero_zero real)) BOUND_VARIABLE_151224)) (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_151223) (zero_zero X_b)) BOUND_VARIABLE_151224))))))) ) 23.18/23.20 ( nat, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 23.18/23.20 ( 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))))) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151247 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_151247))) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) (hAPP int int bit1 BOUND_VARIABLE_151247)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (one_one X_a)) _let_2)) _let_2)))))) ) 23.18/23.20 ( int, pls ) 23.18/23.20 ( int, (hAPP int int bit1 pls) ) 23.18/23.20 ( int, min ) 23.18/23.20 ( nat, pls ) 23.18/23.20 ( nat, (hAPP int int bit1 pls) ) 23.18/23.20 ( real, (hAPP int int bit1 pls) ) 23.18/23.20 ( real, min ) 23.18/23.20 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.20 ( 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))))))) ) 23.18/23.20 ( complex, min ) 23.18/23.20 ( quickcheck_code_int, pls ) 23.18/23.20 ( code_code_numeral, pls ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151270 $$unsorted) (BOUND_VARIABLE_151271 $$unsorted) (BOUND_VARIABLE_151272 $$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_151272) BOUND_VARIABLE_151271) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151270) BOUND_VARIABLE_151271))) (= (ti X_a BOUND_VARIABLE_151272) (ti X_a BOUND_VARIABLE_151270))))) ) 23.18/23.20 ( int, (one_one 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) ) 23.18/23.20 ( 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)))), m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.20 ( 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), (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) ) 23.18/23.20 ( 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 nat int (semiring_1_of_nat int) n), (one_one int) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) y) (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) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.20 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.18/23.20 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.18/23.20 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.18/23.20 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 23.18/23.20 ) 23.18/23.20 (instantiation (forall ((A_1 $$unsorted)) (= (hAPP complex complex (inverse_inverse complex) (hAPP real complex cis A_1)) (hAPP real complex cis (hAPP real real (uminus_uminus real) A_1))) ) 23.18/23.20 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.20 ( (one_one real) ) 23.18/23.20 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.18/23.20 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151300 $$unsorted) (BOUND_VARIABLE_151301 $$unsorted) (BOUND_VARIABLE_151302 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_151300))) (or (not (comple44059174attice X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_151301) BOUND_VARIABLE_151302))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_151301))) (hBOOL (hAPP X_a bool _let_1 (hAPP _let_0 X_a (complete_Sup_Sup X_a) BOUND_VARIABLE_151302)))))) ) 23.18/23.21 ( int, (zero_zero int), (one_one int), zEven ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151380 $$unsorted) (BOUND_VARIABLE_151381 $$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_151380) BOUND_VARIABLE_151381))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_151381)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_151380))))))) ) 23.18/23.21 ( int, pls, pls ) 23.18/23.21 ( int, pls, (one_one int) ) 23.18/23.21 ( int, (one_one int), pls ) 23.18/23.21 ( int, (one_one int), (one_one int) ) 23.18/23.21 ( int, (one_one int), t ) 23.18/23.21 ( int, min, pls ) 23.18/23.21 ( int, min, min ) 23.18/23.21 ( int, (zero_zero int), pls ) 23.18/23.21 ( int, (zero_zero int), (one_one int) ) 23.18/23.21 ( int, (zero_zero int), min ) 23.18/23.21 ( int, (zero_zero int), s ) 23.18/23.21 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.21 ( int, (zero_zero int), skv_4 ) 23.18/23.21 ( int, (zero_zero int), skv_5 ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.18/23.21 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( real, (zero_zero real), pi ) 23.18/23.21 ( 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)))) ) 23.18/23.21 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( real, (zero_zero real), skv_10 ) 23.18/23.21 ( real, (zero_zero real), skv_11 ) 23.18/23.21 ( real, (zero_zero real), skv_15 ) 23.18/23.21 ( real, (zero_zero real), skv_18 ) 23.18/23.21 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.18/23.21 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (or (not (sgn_if X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 23.18/23.21 ( rat ) 23.18/23.21 ( int ) 23.18/23.21 ( (fun int int) ) 23.18/23.21 ( nat ) 23.18/23.21 ( bool ) 23.18/23.21 ( real ) 23.18/23.21 ( (fun nat real) ) 23.18/23.21 ( (fun real real) ) 23.18/23.21 ( complex ) 23.18/23.21 ( (fun int bool) ) 23.18/23.21 ( (product_prod int int) ) 23.18/23.21 ( (fun (product_prod int int) int) ) 23.18/23.21 ( (fun int (fun int bool)) ) 23.18/23.21 ( (fun nat bool) ) 23.18/23.21 ( (fun (product_prod int int) bool) ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.18/23.21 ( (fun real bool) ) 23.18/23.21 ( code_code_numeral ) 23.18/23.21 ( (fun int (fun int (fun int bool))) ) 23.18/23.21 ( (fun int real) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (= _let_0 Xa) (= _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Xa))))) ) 23.18/23.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (let ((_let_5 (minus_minus int))) (= (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_5 (hAPP nat int (hAPP int _let_3 _let_4 A_1) _let_1)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) A_1)) B))) (hAPP nat int (hAPP int _let_3 _let_4 B) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 _let_5 A_1) B)) _let_1)))))))) ) 23.18/23.21 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.21 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151529 $$unsorted) (BOUND_VARIABLE_151530 $$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_151529)) BOUND_VARIABLE_151530))))) )) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_151529) BOUND_VARIABLE_151530))) ) 23.18/23.21 ( int, (one_one int), t ) 23.18/23.21 ( int, min, pls ) 23.18/23.21 ( int, min, min ) 23.18/23.21 ( int, (zero_zero int), pls ) 23.18/23.21 ( int, (zero_zero int), (one_one int) ) 23.18/23.21 ( int, (zero_zero int), min ) 23.18/23.21 ( int, (zero_zero int), s ) 23.18/23.21 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.21 ( int, (zero_zero int), skv_4 ) 23.18/23.21 ( int, (zero_zero int), skv_5 ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.18/23.21 ( 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 int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( real, (zero_zero real), pi ) 23.18/23.21 ( 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)))) ) 23.18/23.21 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( real, (zero_zero real), skv_10 ) 23.18/23.21 ( real, (zero_zero real), skv_11 ) 23.18/23.21 ( real, (zero_zero real), skv_15 ) 23.18/23.21 ( real, (zero_zero real), skv_18 ) 23.18/23.21 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.18/23.21 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X)) (not (hBOOL (hAPP int bool _let_0 Y))) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y)))))) ) 23.18/23.21 ( (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)))) ) 23.18/23.21 ( (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) ) 23.18/23.21 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.18/23.21 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.18/23.21 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.18/23.21 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.21 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.21 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.21 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.18/23.21 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc N)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) N) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.18/23.21 ( (zero_zero nat) ) 23.18/23.21 ( (one_one nat) ) 23.18/23.21 ( (hAPP nat nat suc (zero_zero nat)) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151572 $$unsorted)) (or (not (real_n2089651433ebra_1 X_a)) (= (hAPP real real (abs_abs real) BOUND_VARIABLE_151572) (hAPP X_a real (norm_norm X_a) (hAPP real X_a (of_real X_a) BOUND_VARIABLE_151572)))) ) 23.18/23.21 ( complex, (hAPP int real (number_number_of real) min) ) 23.18/23.21 ( complex, pi ) 23.18/23.21 ( complex, (hAPP real real (uminus_uminus real) (one_one real)) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real (hAPP real _let_0 (times_times real) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real ln (hAPP real real (exp real) (one_one real)))) (hAPP real real ln _let_1))) (hAPP real real ln X)) (hAPP real real (hAPP real _let_0 log _let_1) X))))) ) 23.18/23.21 ( pi ) 23.18/23.21 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (one_one real) ) 23.18/23.21 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( skv_2 ) 23.18/23.21 ( skv_9 ) 23.18/23.21 ( skv_12 ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$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)))) ) 23.18/23.21 ( rat ) 23.18/23.21 ( int ) 23.18/23.21 ( nat ) 23.18/23.21 ( real ) 23.18/23.21 ( complex ) 23.18/23.21 ( quickcheck_code_int ) 23.18/23.21 ( code_code_numeral ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151697 $$unsorted) (BOUND_VARIABLE_151698 $$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_151698))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151698) (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_151698) (hAPP nat nat suc BOUND_VARIABLE_151697))) BOUND_VARIABLE_151698))))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), v ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), w ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), y ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), x ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), skv_6 ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), skv_7 ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), skv_16 ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), skv_23 ) 23.18/23.21 ( int, (hAPP nat nat suc (zero_zero nat)), skv_24 ) 23.18/23.21 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151754 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_151754) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_151754) (hAPP int X_a (number_number_of X_a) pls)))) ) 23.18/23.21 ( int, pls ) 23.18/23.21 ( int, (one_one int) ) 23.18/23.21 ( int, min ) 23.18/23.21 ( int, s ) 23.18/23.21 ( 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)))) ) 23.18/23.21 ( int, s1 ) 23.18/23.21 ( int, m ) 23.18/23.21 ( 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) ) 23.18/23.21 ( int, t ) 23.18/23.21 ( int, v ) 23.18/23.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( int, w ) 23.18/23.21 ( int, y ) 23.18/23.21 ( int, sa ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( int, x ) 23.18/23.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.21 ( int, r ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.18/23.21 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.21 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.18/23.21 ( int, m1 ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.21 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.18/23.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( int, skv_14 ) 23.18/23.21 ( int, skv_20 ) 23.18/23.21 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (fun int int), bit1 ) 23.18/23.21 ( (fun int int), bit0 ) 23.18/23.21 ( (fun int int), succ ) 23.18/23.21 ( (fun int int), pred ) 23.18/23.21 ( (fun int int), (fact_fact int) ) 23.18/23.21 ( (fun int int), zfact ) 23.18/23.21 ( nat, (one_one nat) ) 23.18/23.21 ( nat, n ) 23.18/23.21 ( nat, tn ) 23.18/23.21 ( bool, fTrue ) 23.18/23.21 ( bool, fFalse ) 23.18/23.21 ( real, pi ) 23.18/23.21 ( (fun nat real), (real_1 nat) ) 23.18/23.21 ( (fun nat real), cos_coeff ) 23.18/23.21 ( (fun nat real), sin_coeff ) 23.18/23.21 ( (fun real real), sin ) 23.18/23.21 ( (fun real real), cos ) 23.18/23.21 ( (fun real real), sqrt ) 23.18/23.21 ( (fun real real), tan ) 23.18/23.21 ( (fun real real), ln ) 23.18/23.21 ( (fun real real), arctan ) 23.18/23.21 ( (fun real real), arcsin ) 23.18/23.21 ( (fun real real), arccos ) 23.18/23.21 ( (fun nat nat), suc ) 23.18/23.21 ( (fun nat nat), (fact_fact nat) ) 23.18/23.21 ( (fun nat nat), nat_size ) 23.18/23.21 ( (fun nat nat), (size_size nat) ) 23.18/23.21 ( (fun nat nat), fact ) 23.18/23.21 ( (filter nat), sequentially ) 23.18/23.21 ( (fun int (fun int rat)), fract ) 23.18/23.21 ( complex, ii ) 23.18/23.21 ( (fun int bool), zOdd ) 23.18/23.21 ( (fun int bool), zprime ) 23.18/23.21 ( (fun int bool), zEven ) 23.18/23.21 ( (fun int bool), nat_neg ) 23.18/23.21 ( (fun int bool), nat_is_nat ) 23.18/23.21 ( (fun int bool), (even_odd_even int) ) 23.18/23.21 ( (fun int bool), twoSqu1091635170sum2sq ) 23.18/23.21 ( (fun int (fun int int)), legacy_zgcd ) 23.18/23.21 ( (fun int (fun int int)), (gcd_gcd int) ) 23.18/23.21 ( (fun int (fun int int)), inv ) 23.18/23.21 ( (fun int (fun int int)), multInv ) 23.18/23.21 ( (fun int (fun int int)), legendre ) 23.18/23.21 ( (fun int (fun int int)), standardRes ) 23.18/23.21 ( (fun int (fun int int)), nat_tsub ) 23.18/23.21 ( (fun int (fun int int)), z3div ) 23.18/23.21 ( (fun int (fun int int)), z3mod ) 23.18/23.21 ( (fun int (fun int int)), int_lcm ) 23.18/23.21 ( (fun int (fun int int)), int_gcd ) 23.18/23.21 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.18/23.21 ( (fun bool bool), fNot ) 23.18/23.21 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.18/23.21 ( (fun bool (fun bool bool)), fconj ) 23.18/23.21 ( (fun bool (fun bool bool)), fdisj ) 23.18/23.21 ( (fun bool (fun bool bool)), fimplies ) 23.18/23.21 ( (fun int (fun int bool)), quadRes ) 23.18/23.21 ( (fun int (fun int bool)), d22set ) 23.18/23.21 ( (fun int (fun int bool)), norRRset ) 23.18/23.21 ( (fun int (fun int bool)), sRStar ) 23.18/23.21 ( (fun int (fun int bool)), sr ) 23.18/23.21 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.18/23.21 ( (fun nat bool), (even_odd_even nat) ) 23.18/23.21 ( (fun nat bool), prime ) 23.18/23.21 ( (fun real complex), cis ) 23.18/23.21 ( (fun nat (fun nat bool)), coprime ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.18/23.21 ( (fun (product_prod int int) bool), frac_1 ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.18/23.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.18/23.21 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.18/23.21 ( (fun (fun int bool) bool), nat_nat_set ) 23.18/23.21 ( (fun nat (fun real real)), root ) 23.18/23.21 ( (fun real (fun real real)), log ) 23.18/23.21 ( (fun real (fun real real)), powr ) 23.18/23.21 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.18/23.21 ( (fun complex complex), cnj ) 23.18/23.21 ( (fun complex complex), expi ) 23.18/23.21 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.18/23.21 ( (fun nat (fun nat nat)), nat_gcd ) 23.18/23.21 ( (fun nat (fun nat nat)), nat_lcm ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.18/23.21 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.18/23.21 ( (fun int (fun (fun int bool) bool)), resSet ) 23.18/23.21 ( (fun int nat), nat_1 ) 23.18/23.21 ( (fun int nat), phi ) 23.18/23.21 ( (fun complex real), re ) 23.18/23.21 ( (fun complex real), im ) 23.18/23.21 ( (fun complex real), arg ) 23.18/23.21 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.18/23.21 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.18/23.21 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.18/23.21 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.18/23.21 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.18/23.21 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.18/23.21 ( (fun (product_prod nat nat) bool), pred_nat ) 23.18/23.21 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.18/23.21 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.18/23.21 ( (fun (fun int bool) int), (the int) ) 23.18/23.21 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.18/23.21 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.18/23.21 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.18/23.21 ( (fun real (fun real complex)), rcis ) 23.18/23.21 ( (fun real (fun real complex)), complex_1 ) 23.18/23.21 ( (fun int (fun int (fun int bool))), zcong ) 23.18/23.21 ( (fun int (fun int (fun int bool))), wset ) 23.18/23.21 ( (fun int (fun int (fun int bool))), noXRRset ) 23.18/23.21 ( (fun int (fun int (fun int bool))), bnorRset ) 23.18/23.21 ( (fun int (fun int (fun int bool))), zcongm ) 23.18/23.21 ( (fun real nat), natceiling ) 23.18/23.21 ( (fun real nat), natfloor ) 23.18/23.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.18/23.21 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.18/23.21 ( (fun int real), (real_1 int) ) 23.18/23.21 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.18/23.21 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.18/23.21 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.18/23.21 ( (fun complex nat), (size_size complex) ) 23.18/23.21 ( (fun complex nat), complex_size ) 23.18/23.21 ( (fun (fun nat rat) bool), vanishes ) 23.18/23.21 ( (fun (product_prod int int) rat), frct ) 23.18/23.21 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.18/23.21 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.18/23.21 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.18/23.21 ( (fun rat real), ratreal ) 23.18/23.21 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.18/23.21 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.18/23.21 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.18/23.21 ( (fun rat (product_prod int int)), quotient_of ) 23.18/23.21 ( (fun int (fun nat nat)), nat_aux ) 23.18/23.21 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.18/23.21 ( (fun int (list int)), quickc666637781d_zero ) 23.18/23.21 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.18/23.21 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.18/23.21 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.18/23.21 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.18/23.21 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.18/23.21 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.18/23.21 ( (fun code_code_numeral int), code_int_of ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) B_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_3) B_2))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) B_2) A_3))))) ) 23.18/23.21 ( pls, min ) 23.18/23.21 ( pls, (zero_zero int) ) 23.18/23.21 ( (one_one int), (one_one int) ) 23.18/23.21 ( (one_one int), (zero_zero int) ) 23.18/23.21 ( min, min ) 23.18/23.21 ( min, (zero_zero int) ) 23.18/23.21 ( (zero_zero int), (one_one int) ) 23.18/23.21 ( s, (zero_zero int) ) 23.18/23.21 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.18/23.21 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.18/23.21 ( t, (one_one int) ) 23.18/23.21 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.18/23.21 ( skv_4, (zero_zero int) ) 23.18/23.21 ( skv_5, (zero_zero int) ) 23.18/23.21 ) 23.18/23.21 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP int real (number_number_of real) min)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 X) _let_0))) (= (hAPP real real sin (hAPP real real arccos X)) (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) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))))) ) 23.18/23.21 ( (hAPP int real (number_number_of real) min) ) 23.18/23.21 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.21 ( (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)))) ) 23.18/23.21 ( (zero_zero real) ) 23.18/23.21 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.21 ( (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)))) ) 23.18/23.21 ( skv_10 ) 23.18/23.21 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151813 $$unsorted) (BOUND_VARIABLE_151814 $$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_151813)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_151814)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_151813))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_151814) BOUND_VARIABLE_151813)))))) ) 23.18/23.22 ( int, pls, min ) 23.18/23.22 ( int, pls, (zero_zero int) ) 23.18/23.22 ( int, (one_one int), (zero_zero int) ) 23.18/23.22 ( int, min, min ) 23.18/23.22 ( int, min, (zero_zero int) ) 23.18/23.22 ( int, s, (zero_zero int) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.18/23.22 ( int, t, (one_one int) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.18/23.22 ( int, skv_4, (zero_zero int) ) 23.18/23.22 ( int, skv_5, (zero_zero int) ) 23.18/23.22 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( real, pi, (zero_zero real) ) 23.18/23.22 ( 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)))) ) 23.18/23.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.18/23.22 ( 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)))), (zero_zero real) ) 23.18/23.22 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.18/23.22 ( real, skv_10, (zero_zero real) ) 23.18/23.22 ( real, skv_11, (zero_zero real) ) 23.18/23.22 ( real, skv_15, (zero_zero real) ) 23.18/23.22 ( real, skv_18, (zero_zero real) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_151889 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) pls) BOUND_VARIABLE_151889))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (one_one X_a)) (hAPP int X_a _let_0 BOUND_VARIABLE_151889)) (hAPP int X_a _let_0 (hAPP int int succ BOUND_VARIABLE_151889))))) ) 23.18/23.22 ( int, pls ) 23.18/23.22 ( int, min ) 23.18/23.22 ( nat, pls ) 23.18/23.22 ( nat, (hAPP int int bit1 pls) ) 23.18/23.22 ( nat, min ) 23.18/23.22 ( quickcheck_code_int, pls ) 23.18/23.22 ( quickcheck_code_int, min ) 23.18/23.22 ( code_code_numeral, pls ) 23.18/23.22 ( code_code_numeral, min ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_0 (fun nat nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N) M))) (= M (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) N) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N))))) ) 23.18/23.22 ( (one_one nat), (hAPP int nat nat_1 t) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((L $$unsorted) (U $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (= (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (minus_minus int) U) L)) (one_one int))) (hAPP _let_1 nat (finite_card int) (hAPP int _let_1 (hAPP int (fun int _let_1) (ord_atLeastAtMost int) L) U))))) ) 23.18/23.22 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.18/23.22 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.18/23.22 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.22 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex cnj Z_1) (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)))) ) 23.18/23.22 ( (zero_zero complex) ) 23.18/23.22 ( ii ) 23.18/23.22 ( (one_one complex) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) (zero_zero real)) Xa))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (deriv real) ln) Xa) (hAPP real real (hAPP real _let_0 (inverse_divide real) (one_one real)) Xa)))))) ) 23.18/23.22 ( pi ) 23.18/23.22 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.22 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))) ) 23.18/23.22 ( skv_2 ) 23.18/23.22 ( skv_9 ) 23.18/23.22 ( skv_12 ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152031 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (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_0 _let_4 (hAPP (fun real _let_3) (fun _let_0 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_152031)))))))))) ) 23.18/23.22 ( int, s ) 23.18/23.22 ( int, s1 ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( int, v ) 23.18/23.22 ( int, w ) 23.18/23.22 ( int, y ) 23.18/23.22 ( int, x ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.22 ( int, skv_6 ) 23.18/23.22 ( int, skv_7 ) 23.18/23.22 ( int, skv_16 ) 23.18/23.22 ( int, skv_23 ) 23.18/23.22 ( int, skv_24 ) 23.18/23.22 ( real, (hAPP int real (number_number_of real) min) ) 23.18/23.22 ( 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)))) ) 23.18/23.22 ( complex, ii ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152046 $$unsorted) (BOUND_VARIABLE_152047 $$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_152046))) (or (not (real_normed_algebra X_a)) (= (hAPP X_a X_a _let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_152047)) (hAPP X_a X_a _let_0 (hAPP X_a X_a _let_1 BOUND_VARIABLE_152047)))))) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.18/23.22 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( 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 ) 23.18/23.22 ( 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))), m1 ) 23.18/23.22 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.18/23.22 ( 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_21 ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.18/23.22 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.18/23.22 ( int, y, v ) 23.18/23.22 ( int, y, w ) 23.18/23.22 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( int, sa, v ) 23.18/23.22 ( int, sa, w ) 23.18/23.22 ( int, x, v ) 23.18/23.22 ( int, x, w ) 23.18/23.22 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.22 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( int, r, v ) 23.18/23.22 ( int, r, w ) 23.18/23.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.18/23.22 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.18/23.22 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.18/23.22 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.18/23.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.18/23.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.22 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.18/23.22 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.18/23.22 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.18/23.22 ( 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)))))) ) 23.18/23.22 ( 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 ) 23.18/23.22 ( complex, ii, ii ) 23.18/23.22 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.18/23.22 ( 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 ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152084 $$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) _let_0) BOUND_VARIABLE_152084)))) ) 23.18/23.22 ( 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))) m1))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc N)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) N)) ) 23.18/23.22 ( (zero_zero nat) ) 23.18/23.22 ( (hAPP nat nat suc (zero_zero nat)) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((Xa $$unsorted) (K $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (or (not (= (ti int Xa) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) K)) (one_one int)))) (hBOOL (hAPP _let_1 bool (hAPP int (fun _let_1 bool) (member int) Xa) zOdd))))) ) 23.18/23.22 ( s1, (hAPP int int (abs_abs int) w) ) 23.18/23.22 ( m, (hAPP int int (abs_abs int) skv_20) ) 23.18/23.22 ( v, (hAPP int int (abs_abs int) v) ) 23.18/23.22 ( r, (hAPP int int (abs_abs int) skv_14) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152107 $$unsorted) (BOUND_VARIABLE_152108 $$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_152107)) BOUND_VARIABLE_152108) (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_152108)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152107) BOUND_VARIABLE_152108))))))) ) 23.18/23.22 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((P_5 $$unsorted)) (or (not (hBOOL (hAPP nat bool prime P_5))) (not (hBOOL (hAPP nat bool (even_odd_even nat) P_5))) (= (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) P_5)) ) 23.18/23.22 ( (zero_zero nat) ) 23.18/23.22 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.22 ( (one_one nat) ) 23.18/23.22 ( (hAPP nat nat suc (zero_zero nat)) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (hAPP int (fun nat int) (power_power int) Z_1))) (let ((_let_2 (hAPP nat int _let_1 (hAPP int nat _let_0 W)))) (= (hAPP int int (hAPP int (fun int int) (times_times int) _let_2) _let_2) (hAPP nat int _let_1 (hAPP int nat _let_0 (hAPP int int bit0 W))))))) ) 23.18/23.22 ( s, (hAPP int int bit1 pls) ) 23.18/23.22 ( s1, (hAPP int int bit1 pls) ) 23.18/23.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit1 pls) ) 23.18/23.22 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.22 ( v, (hAPP int int bit1 pls) ) 23.18/23.22 ( w, (hAPP int int bit1 pls) ) 23.18/23.22 ( y, (hAPP int int bit1 pls) ) 23.18/23.22 ( x, (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit1 pls) ) 23.18/23.22 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit1 pls) ) 23.18/23.22 ( skv_6, (hAPP int int bit1 pls) ) 23.18/23.22 ( skv_7, (hAPP int int bit1 pls) ) 23.18/23.22 ( skv_16, (hAPP int int bit1 pls) ) 23.18/23.22 ( skv_23, (hAPP int int bit1 pls) ) 23.18/23.22 ( skv_24, (hAPP int int bit1 pls) ) 23.18/23.22 ) 23.18/23.22 (instantiation (forall ((N $$unsorted) (D_3 $$unsorted)) (let ((_let_0 (real_1 int))) (or (= (zero_zero int) (ti int D_3)) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) D_3) N))) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP int real _let_0 N)) (hAPP int real _let_0 D_3)) (hAPP int real _let_0 (hAPP int int (hAPP int (fun int int) (div_div int) N) D_3))))) ) 23.18/23.22 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.22 ( (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.22 ) 23.18/23.23 (instantiation (forall ((L $$unsorted) (F $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real F N_1)) (hAPP nat real F (hAPP nat nat suc N_1)))) )) (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real F N_1)) L)) )) (not (forall ((E $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) E))) (not (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) L) (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real F N_1)) E)))) ))) )) (hBOOL (hAPP (filter nat) bool (hAPP real _let_0 (hAPP (fun nat real) (fun real _let_0) (tendsto nat real) F) L) sequentially)))) ) 23.18/23.23 ( (zero_zero real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152297 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (plus_plus X_a))) (or (not (ring_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_152297) (ring_1_Ints X_a)))) (not (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (one_one X_a)) BOUND_VARIABLE_152297)) BOUND_VARIABLE_152297))))))) ) 23.18/23.23 ( int, (one_one int) ) 23.18/23.23 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.23 ( int, (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.23 ( nat, (one_one nat) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152321 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (zero_zero X_a))) (or (not (linordered_idom X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) BOUND_VARIABLE_152321) (ring_1_Ints X_a)))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (hAPP X_a X_a (hAPP X_a _let_2 _let_3 (one_one X_a)) BOUND_VARIABLE_152321)) BOUND_VARIABLE_152321)) _let_4)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152321) _let_4))))))))) ) 23.18/23.23 ( int, (one_one int) ) 23.18/23.23 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.23 ( int, (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.23 ( nat, (one_one nat) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152350 $$unsorted) (BOUND_VARIABLE_152351 $$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_152351) BOUND_VARIABLE_152350))) (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_152351))) (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_152351) _let_2))))))) ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.18/23.23 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.18/23.23 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.18/23.23 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.18/23.23 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.18/23.23 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.18/23.23 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.18/23.23 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.18/23.23 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.18/23.23 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.18/23.23 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152371 $$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_152371) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (zero_zero X_a))))) ) 23.18/23.23 ( int, s ) 23.18/23.23 ( int, s1 ) 23.18/23.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.23 ( int, v ) 23.18/23.23 ( int, w ) 23.18/23.23 ( int, y ) 23.18/23.23 ( int, x ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.23 ( int, skv_6 ) 23.18/23.23 ( int, skv_7 ) 23.18/23.23 ( int, skv_16 ) 23.18/23.23 ( int, skv_23 ) 23.18/23.23 ( int, skv_24 ) 23.18/23.23 ( real, (hAPP int real (number_number_of real) min) ) 23.18/23.23 ( 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)))) ) 23.18/23.23 ( complex, ii ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((Xa $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool nat_nat_set A_2))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) A_2))) (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) (zero_zero int)) Xa)))) ) 23.18/23.23 ( (one_one int), zEven ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((M $$unsorted) (N $$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)) (hAPP nat nat _let_1 N)))) ) 23.18/23.23 ( (one_one nat), (one_one nat) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((N $$unsorted)) (= (hAPP nat nat suc (hAPP nat nat suc (hAPP nat nat suc N))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))) N)) ) 23.18/23.23 ( (zero_zero nat) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((Z_1 $$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)))) ) 23.18/23.23 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.23 ( pi, (zero_zero real) ) 23.18/23.23 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.18/23.23 ( (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)))) ) 23.18/23.23 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.18/23.23 ( (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 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.23 ( (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 pls)))), (zero_zero real) ) 23.18/23.23 ( (zero_zero real), pi ) 23.18/23.23 ( (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)))) ) 23.18/23.23 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ( (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ( (zero_zero real), skv_10 ) 23.18/23.23 ( (zero_zero real), skv_11 ) 23.18/23.23 ( (zero_zero real), skv_15 ) 23.18/23.23 ( (zero_zero real), skv_18 ) 23.18/23.23 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.18/23.23 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.18/23.23 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.23 ( skv_10, (zero_zero real) ) 23.18/23.23 ( skv_11, (zero_zero real) ) 23.18/23.23 ( skv_15, (zero_zero real) ) 23.18/23.23 ( skv_18, (zero_zero real) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 _let_2) B_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_3) _let_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_3) B_2)) (zero_zero rat)))))))) ) 23.18/23.23 ( (one_one int), (one_one int) ) 23.18/23.23 ( (zero_zero int), (one_one int) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$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)))) ) 23.18/23.23 ( rat ) 23.18/23.23 ( int ) 23.18/23.23 ( nat ) 23.18/23.23 ( bool ) 23.18/23.23 ( real ) 23.18/23.23 ( (filter nat) ) 23.18/23.23 ( (fun int bool) ) 23.18/23.23 ( (product_prod int int) ) 23.18/23.23 ( (fun nat bool) ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.18/23.23 ( quickcheck_code_int ) 23.18/23.23 ( code_code_numeral ) 23.18/23.23 ( (product_prod real real) ) 23.18/23.23 ( (filter real) ) 23.18/23.23 ( (product_prod nat nat) ) 23.18/23.23 ( (fun nat rat) ) 23.18/23.23 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152526 $$unsorted)) (or (not (monoid_add X_a)) (= (ti X_a BOUND_VARIABLE_152526) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_152526))) ) 23.18/23.23 ( int, pls ) 23.18/23.23 ( int, min ) 23.18/23.23 ( int, s ) 23.18/23.23 ( int, s1 ) 23.18/23.23 ( int, m ) 23.18/23.23 ( int, t ) 23.18/23.23 ( int, v ) 23.18/23.23 ( int, w ) 23.18/23.23 ( int, y ) 23.18/23.23 ( int, sa ) 23.18/23.23 ( int, x ) 23.18/23.23 ( int, r ) 23.18/23.23 ( int, m1 ) 23.18/23.23 ( int, skv_14 ) 23.18/23.23 ( int, skv_20 ) 23.18/23.23 ( (fun int int), bit1 ) 23.18/23.23 ( (fun int int), bit0 ) 23.18/23.23 ( (fun int int), succ ) 23.18/23.23 ( (fun int int), pred ) 23.18/23.23 ( (fun int int), (fact_fact int) ) 23.18/23.23 ( (fun int int), zfact ) 23.18/23.23 ( nat, n ) 23.18/23.23 ( nat, tn ) 23.18/23.23 ( bool, fTrue ) 23.18/23.23 ( bool, fFalse ) 23.18/23.23 ( real, pi ) 23.18/23.23 ( (fun nat real), (real_1 nat) ) 23.18/23.23 ( (fun nat real), cos_coeff ) 23.18/23.23 ( (fun nat real), sin_coeff ) 23.18/23.23 ( (fun real real), sin ) 23.18/23.23 ( (fun real real), cos ) 23.18/23.23 ( (fun real real), sqrt ) 23.18/23.23 ( (fun real real), tan ) 23.18/23.23 ( (fun real real), ln ) 23.18/23.23 ( (fun real real), arctan ) 23.18/23.23 ( (fun real real), arcsin ) 23.18/23.23 ( (fun real real), arccos ) 23.18/23.23 ( (fun nat nat), suc ) 23.18/23.23 ( (fun nat nat), (fact_fact nat) ) 23.18/23.23 ( (fun nat nat), nat_size ) 23.18/23.23 ( (fun nat nat), (size_size nat) ) 23.18/23.23 ( (fun nat nat), fact ) 23.18/23.23 ( (filter nat), sequentially ) 23.18/23.23 ( (fun int (fun int rat)), fract ) 23.18/23.23 ( complex, ii ) 23.18/23.23 ( (fun int bool), zOdd ) 23.18/23.23 ( (fun int bool), zprime ) 23.18/23.23 ( (fun int bool), zEven ) 23.18/23.23 ( (fun int bool), nat_neg ) 23.18/23.23 ( (fun int bool), nat_is_nat ) 23.18/23.23 ( (fun int bool), (even_odd_even int) ) 23.18/23.23 ( (fun int bool), twoSqu1091635170sum2sq ) 23.18/23.23 ( (fun int (fun int int)), legacy_zgcd ) 23.18/23.23 ( (fun int (fun int int)), (gcd_gcd int) ) 23.18/23.23 ( (fun int (fun int int)), inv ) 23.18/23.23 ( (fun int (fun int int)), multInv ) 23.18/23.23 ( (fun int (fun int int)), legendre ) 23.18/23.23 ( (fun int (fun int int)), standardRes ) 23.18/23.23 ( (fun int (fun int int)), nat_tsub ) 23.18/23.23 ( (fun int (fun int int)), z3div ) 23.18/23.23 ( (fun int (fun int int)), z3mod ) 23.18/23.23 ( (fun int (fun int int)), int_lcm ) 23.18/23.23 ( (fun int (fun int int)), int_gcd ) 23.18/23.23 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.18/23.23 ( (fun bool bool), fNot ) 23.18/23.23 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.18/23.23 ( (fun bool (fun bool bool)), fconj ) 23.18/23.23 ( (fun bool (fun bool bool)), fdisj ) 23.18/23.23 ( (fun bool (fun bool bool)), fimplies ) 23.18/23.23 ( (fun int (fun int bool)), quadRes ) 23.18/23.23 ( (fun int (fun int bool)), d22set ) 23.18/23.23 ( (fun int (fun int bool)), norRRset ) 23.18/23.23 ( (fun int (fun int bool)), sRStar ) 23.18/23.23 ( (fun int (fun int bool)), sr ) 23.18/23.23 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.18/23.23 ( (fun nat bool), (even_odd_even nat) ) 23.18/23.23 ( (fun nat bool), prime ) 23.18/23.23 ( (fun real complex), cis ) 23.18/23.23 ( (fun nat (fun nat bool)), coprime ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.18/23.23 ( (fun (product_prod int int) bool), frac_1 ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.18/23.23 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.18/23.23 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.18/23.23 ( (fun (fun int bool) bool), nat_nat_set ) 23.18/23.23 ( (fun nat (fun real real)), root ) 23.18/23.23 ( (fun real (fun real real)), log ) 23.18/23.23 ( (fun real (fun real real)), powr ) 23.18/23.23 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.18/23.23 ( (fun complex complex), cnj ) 23.18/23.23 ( (fun complex complex), expi ) 23.18/23.23 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.18/23.23 ( (fun nat (fun nat nat)), nat_gcd ) 23.18/23.23 ( (fun nat (fun nat nat)), nat_lcm ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.18/23.23 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.18/23.23 ( (fun int (fun (fun int bool) bool)), resSet ) 23.18/23.23 ( (fun int nat), nat_1 ) 23.18/23.23 ( (fun int nat), phi ) 23.18/23.23 ( (fun complex real), re ) 23.18/23.23 ( (fun complex real), im ) 23.18/23.23 ( (fun complex real), arg ) 23.18/23.23 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.18/23.23 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.18/23.23 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.18/23.23 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.18/23.23 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.18/23.23 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.18/23.23 ( (fun (product_prod nat nat) bool), pred_nat ) 23.18/23.23 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.18/23.23 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.18/23.23 ( (fun (fun int bool) int), (the int) ) 23.18/23.23 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.18/23.23 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.18/23.23 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.18/23.23 ( (fun real (fun real complex)), rcis ) 23.18/23.23 ( (fun real (fun real complex)), complex_1 ) 23.18/23.23 ( (fun int (fun int (fun int bool))), zcong ) 23.18/23.23 ( (fun int (fun int (fun int bool))), wset ) 23.18/23.23 ( (fun int (fun int (fun int bool))), noXRRset ) 23.18/23.23 ( (fun int (fun int (fun int bool))), bnorRset ) 23.18/23.23 ( (fun int (fun int (fun int bool))), zcongm ) 23.18/23.23 ( (fun real nat), natceiling ) 23.18/23.23 ( (fun real nat), natfloor ) 23.18/23.23 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.18/23.23 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.18/23.23 ( (fun int real), (real_1 int) ) 23.18/23.23 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.18/23.23 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.18/23.23 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.18/23.23 ( (fun complex nat), (size_size complex) ) 23.18/23.23 ( (fun complex nat), complex_size ) 23.18/23.23 ( (fun (fun nat rat) bool), vanishes ) 23.18/23.23 ( (fun (product_prod int int) rat), frct ) 23.18/23.23 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.18/23.23 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.18/23.23 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.18/23.23 ( (fun rat real), ratreal ) 23.18/23.23 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.18/23.23 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.18/23.23 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.18/23.23 ( (fun rat (product_prod int int)), quotient_of ) 23.18/23.23 ( (fun int (fun nat nat)), nat_aux ) 23.18/23.23 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.18/23.23 ( (fun int (list int)), quickc666637781d_zero ) 23.18/23.23 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.18/23.23 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.18/23.23 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.18/23.23 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.18/23.23 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.18/23.23 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.18/23.23 ( (fun code_code_numeral int), code_int_of ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int real (number_number_of real) _let_1))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun real bool))) (let ((_let_5 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_4 _let_5 (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 (inverse_divide real) _let_3) _let_2))) X))) (not (hBOOL (hAPP real bool (hAPP real _let_4 _let_5 X) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_4 _let_5 (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real ln (hAPP real real (hAPP real _let_0 (plus_plus real) _let_3) X))) X))) (hAPP real real (hAPP real _let_0 (times_times real) _let_2) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) _let_1)))))))))))) ) 23.18/23.23 ( (hAPP int real (number_number_of real) min) ) 23.18/23.23 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152541 $$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_152541) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.23 ( int, s ) 23.18/23.23 ( int, s1 ) 23.18/23.23 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.23 ( int, v ) 23.18/23.23 ( int, w ) 23.18/23.23 ( int, y ) 23.18/23.23 ( int, x ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.18/23.23 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.23 ( int, skv_6 ) 23.18/23.23 ( int, skv_7 ) 23.18/23.23 ( int, skv_16 ) 23.18/23.23 ( int, skv_23 ) 23.18/23.23 ( int, skv_24 ) 23.18/23.23 ( real, (hAPP int real (number_number_of real) min) ) 23.18/23.23 ( 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)))) ) 23.18/23.23 ( complex, ii ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (one_one int))) (let ((_let_1 (fun int bool))) (or (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_1 (dvd_dvd int) P_5) X)) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_0)))) _let_0) P_5))))) ) 23.18/23.23 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.23 ( (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((Z $$unsorted) (Z_3 $$unsorted)) (let ((_let_0 (hAPP int nat nat_1 Z))) (or (not (hBOOL (hAPP int bool nat_neg Z_3))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_0) (hAPP int nat nat_1 Z_3))))) ) 23.18/23.23 ( t, (one_one int) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((Z $$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)))))) ) 23.18/23.23 ( (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) ) 23.18/23.23 ( t, (one_one int) ) 23.18/23.23 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.23 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.23 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.23 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.18/23.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.18/23.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.23 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.18/23.23 ( (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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya)) zOdd)))))) ) 23.18/23.23 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.18/23.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.18/23.23 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.23 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.18/23.23 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152725 $$unsorted) (BOUND_VARIABLE_152726 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_152725))) (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_152726))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_152726) _let_1))) (= (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_152726) (ti int BOUND_VARIABLE_152725))))) ) 23.18/23.23 ( real, (zero_zero int), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.23 ) 23.18/23.23 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_152807 $$unsorted) (BOUND_VARIABLE_152808 $$unsorted) (BOUND_VARIABLE_152809 $$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_152809)))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_152809) _let_2)))) (let ((_let_7 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_152807))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a _let_4 (times_times X_a) _let_7) BOUND_VARIABLE_152809))) (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_152808) _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_152808)))) (hBOOL (hAPP X_a bool _let_9 (hAPP X_a X_a (hAPP X_a _let_4 (inverse_divide X_a) BOUND_VARIABLE_152808) BOUND_VARIABLE_152809))))))))))))))) ) 23.18/23.23 ( int, pls, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.23 ( int, pls, (one_one int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, pls, skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.18/23.24 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w) ) 23.18/23.24 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v) ) 23.18/23.24 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14) ) 23.18/23.24 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20) ) 23.18/23.24 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.18/23.24 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), (zero_zero real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.18/23.24 ) 23.18/23.24 (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 (uminus_uminus int))) (let ((_let_3 (fun int 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) A_4) B_4)))) (and (hBOOL (hAPP int bool (hAPP int _let_3 (ord_less int) B_4) (zero_zero int))) (not (hBOOL (hAPP int bool (hAPP int _let_3 P_1 (hAPP int int _let_2 A_4)) (hAPP int int _let_2 B_4))))) (hBOOL (hAPP int bool (hAPP int _let_3 P_1 A_4) B_4))))) )) (hBOOL (hAPP int bool (hAPP int (fun int bool) P_1 A0) A1))))) ) 23.18/23.24 ( (ord_less int), (one_one int), t ) 23.18/23.24 ( (ord_less int), min, min ) 23.18/23.24 ( (ord_less int), min, (zero_zero int) ) 23.18/23.24 ( (ord_less int), (zero_zero int), pls ) 23.18/23.24 ( (ord_less int), (zero_zero int), (one_one int) ) 23.18/23.24 ( (ord_less int), (zero_zero int), min ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (ord_less int), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (ord_less int), m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (ord_less int), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( (ord_less_eq int), (one_one int), t ) 23.18/23.24 ( (ord_less_eq int), min, pls ) 23.18/23.24 ( (ord_less_eq int), min, min ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), pls ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), (one_one int) ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), min ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), s ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), skv_4 ) 23.18/23.24 ( (ord_less_eq int), (zero_zero int), skv_5 ) 23.18/23.24 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( 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) ) 23.18/23.24 ( (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) (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)) ) 23.18/23.24 ( (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (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))) ) 23.18/23.24 ( (hAPP int (fun int (fun int bool)) zcong s1), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( (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), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ) 23.18/23.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun int (fun int int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun real bool))) (let ((_let_5 (ring_1_of_int real))) (let ((_let_6 (fun int real))) (let ((_let_7 (fun int _let_4))) (= (hAPP _let_0 int (the int) (hAPP _let_0 _let_0 (hAPP _let_3 (fun _let_0 _let_0) (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 real _let_0 (hAPP _let_7 (fun real _let_0) (combc int real bool) (hAPP _let_6 _let_7 (hAPP (fun real _let_4) (fun _let_6 _let_7) (combb real _let_4 int) (ord_less_eq real)) _let_5)) Xa))) (hAPP _let_6 _let_0 (hAPP _let_4 (fun _let_6 _let_0) (combb real bool int) (hAPP real _let_4 (ord_less real) Xa)) (hAPP (fun int int) _let_6 (hAPP _let_6 (fun (fun int int) _let_6) (combb int real int) _let_5) (hAPP int (fun int int) (hAPP _let_1 _let_1 (combc int int int) (plus_plus int)) (one_one int)))))) (hAPP real int (archim2085082626_floor real) Xa)))))))))) ) 23.18/23.24 ( pi ) 23.18/23.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.24 ( (one_one real) ) 23.18/23.24 ( (zero_zero real) ) 23.18/23.24 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.24 ( (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))))) ) 23.18/23.24 ( (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)) ) 23.18/23.24 ) 23.18/23.24 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (uminus_uminus real))) (= (hAPP _let_0 real (suminf real) (hAPP _let_0 _let_0 (hAPP _let_1 _let_3 (combb real real nat) _let_4) (hAPP _let_0 _let_0 (hAPP _let_2 _let_3 (combs nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) sin_coeff)) (hAPP real _let_0 (power_power real) Xa)))) (hAPP real real _let_4 (hAPP real real sin Xa)))))))) ) 23.18/23.24 ( (hAPP int real (number_number_of real) min) ) 23.18/23.24 ( pi ) 23.18/23.24 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.24 ( (zero_zero real) ) 23.18/23.24 ( (hAPP real 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))))) ) 23.18/23.24 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.18/23.24 ( (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)))) ) 23.18/23.24 ( (hAPP real real (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))))) ) 23.18/23.24 ( (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)))) ) 23.18/23.24 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.18/23.24 ) 23.18/23.24 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (abs_abs real) (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y)) (hAPP real real (hAPP real _let_0 (dist_dist real) X) Y))) ) 23.18/23.24 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 23.18/23.24 ) 23.18/23.24 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_152951 $$unsorted) (BOUND_VARIABLE_152952 $$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_normed_vector X_b)) (not (hBOOL (hAPP X_a bool (hAPP _let_0 _let_1 _let_2 BOUND_VARIABLE_152951) BOUND_VARIABLE_152952))) (= (zero_zero X_b) (hAPP X_a X_b BOUND_VARIABLE_152951 BOUND_VARIABLE_152952)) (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_152951)) BOUND_VARIABLE_152952)))))) ) 23.18/23.24 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 23.18/23.24 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 23.18/23.24 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 23.18/23.24 ( 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))) ) 23.18/23.24 ( int, int, bit1, pls ) 23.18/23.24 ( int, int, bit1, (hAPP int int bit1 pls) ) 23.18/23.24 ( int, int, bit1, min ) 23.18/23.24 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.18/23.24 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.18/23.24 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.18/23.24 ( 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)))))) ) 23.18/23.24 ( 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))))))) ) 23.18/23.24 ( int, int, (uminus_uminus int), pls ) 23.18/23.24 ( int, int, (uminus_uminus int), (one_one int) ) 23.18/23.24 ( int, int, (uminus_uminus int), min ) 23.18/23.24 ( int, int, bit0, pls ) 23.18/23.24 ( int, int, bit0, (hAPP int int bit1 pls) ) 23.18/23.24 ( int, int, bit0, min ) 23.18/23.24 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.24 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.18/23.24 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.18/23.24 ( int, int, succ, pls ) 23.18/23.24 ( int, int, succ, min ) 23.18/23.24 ( int, int, (number_number_of int), pls ) 23.18/23.24 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 23.18/23.24 ( int, int, (number_number_of int), min ) 23.18/23.24 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.18/23.24 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.18/23.24 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.18/23.24 ( 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 ) 23.18/23.24 ( 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) ) 23.18/23.24 ( int, int, (abs_abs int), v ) 23.18/23.24 ( int, int, (abs_abs int), w ) 23.18/23.24 ( int, int, (abs_abs int), skv_14 ) 23.18/23.24 ( int, int, (abs_abs int), skv_20 ) 23.18/23.24 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.18/23.24 ( int, int, pred, pls ) 23.18/23.24 ( int, int, pred, min ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (abs_abs int) w) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (abs_abs int) v) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (abs_abs int) skv_14) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int int (abs_abs int) skv_20) ) 23.18/23.24 ( int, int, (fact_fact int), (one_one int) ) 23.18/23.24 ( int, int, (fact_fact int), (zero_zero int) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1 ) 23.18/23.24 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), skv_3 ) 23.18/23.24 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) sa), v ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) sa), w ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP nat int (hAPP int _let_2 _let_3 x) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 y) _let_1))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) x), v ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) x), w ) 23.32/23.30 ( 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) x) v))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) y), v ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) y), w ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 x) v)) (hAPP int int (hAPP int _let_0 _let_2 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) x) w))), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.32/23.30 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.30 ( 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 ) 23.32/23.30 ( 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))))), m1 ) 23.32/23.30 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.32/23.30 ( 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_21 ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) r), v ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) r), w ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), v ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), v ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), w ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), w ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), v ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), w ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_2 r) v)))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int 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bit1 pls))))) m)) (one_one int))) m1))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus 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))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.32/23.30 ( 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) r) v))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w)))))), m1 ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (let ((_let_4 (minus_minus int))) (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) r) w))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.30 ( 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) ) 23.32/23.30 ( 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) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.32/23.30 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) skv_13), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (times_times int) skv_19), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.30 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.30 ( 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))) ) 23.32/23.30 ( 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))) ) 23.32/23.30 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 23.32/23.30 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (semiring_1_of_nat int), (one_one nat) ) 23.32/23.30 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (semiring_1_of_nat int), n ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) v), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) w), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) x), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (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))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2))))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_6), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_7), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_16), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_23), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.30 ( int, nat, (hAPP int (fun nat int) (power_power int) skv_24), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( int, quickcheck_code_int, quickcheck_int_of, (zero_zero quickcheck_code_int) ) 23.32/23.31 ( int, code_code_numeral, code_int_of, (zero_zero code_code_numeral) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (one_one int) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (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) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.32/23.31 ( (fun int int), int, (plus_plus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.31 ( (fun int int), int, (plus_plus int), (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (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))) ) 23.32/23.31 ( (fun int int), int, (times_times int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( (fun int int), int, (times_times int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( (fun int int), int, (times_times int), y ) 23.32/23.31 ( (fun int int), int, (times_times int), sa ) 23.32/23.31 ( (fun int int), int, (times_times int), x ) 23.32/23.31 ( (fun int int), int, (times_times int), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.32/23.31 ( (fun int int), int, (times_times int), r ) 23.32/23.31 ( (fun int int), int, (times_times int), (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.32/23.31 ( (fun int int), int, (times_times int), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.32/23.31 ( (fun int int), int, (times_times int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.32/23.31 ( (fun int int), int, (times_times int), skv_13 ) 23.32/23.31 ( (fun int int), int, (times_times int), skv_19 ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (fun int int), int, (minus_minus int), y ) 23.32/23.31 ( (fun int int), int, (minus_minus int), x ) 23.32/23.31 ( (fun int int), int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.32/23.31 ( (fun int int), int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.32/23.31 ( (fun int int), int, (minus_minus int), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.32/23.31 ( (fun int int), int, (minus_minus 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.32/23.31 ( (fun int int), int, (minus_minus 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))) m1))) ) 23.32/23.31 ( (fun int int), int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.32/23.31 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min) ) 23.32/23.31 ( (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) ) 23.32/23.31 ( (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))) ) 23.32/23.31 ( nat, int, (number_number_of nat), pls ) 23.32/23.31 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 23.32/23.31 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.32/23.31 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.32/23.31 ( nat, int, nat_1, (one_one int) ) 23.32/23.31 ( nat, int, nat_1, (zero_zero int) ) 23.32/23.31 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( nat, int, nat_1, t ) 23.32/23.31 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.31 ( nat, nat, suc, (zero_zero nat) ) 23.32/23.31 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 23.32/23.31 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 23.32/23.31 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 23.32/23.31 ( nat, nat, (fact_fact nat), (one_one nat) ) 23.32/23.31 ( nat, nat, nat_size, (zero_zero nat) ) 23.32/23.31 ( nat, nat, (size_size nat), (zero_zero nat) ) 23.32/23.31 ( nat, nat, fact, (zero_zero nat) ) 23.32/23.31 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 23.32/23.31 ( nat, nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (one_one nat) ) 23.32/23.31 ( nat, real, natceiling, (one_one real) ) 23.32/23.31 ( nat, real, natceiling, (zero_zero real) ) 23.32/23.31 ( nat, real, natfloor, (one_one real) ) 23.32/23.31 ( nat, real, natfloor, (zero_zero real) ) 23.32/23.31 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 23.32/23.31 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 23.32/23.31 ( bool, int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), min ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 23.32/23.31 ( bool, int, nat_neg, (one_one int) ) 23.32/23.31 ( bool, int, nat_neg, (zero_zero int) ) 23.32/23.31 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min) ) 23.32/23.31 ( bool, int, nat_is_nat, (one_one int) ) 23.32/23.31 ( bool, int, nat_is_nat, (zero_zero int) ) 23.32/23.31 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 23.32/23.31 ( bool, int, (even_odd_even int), (one_one int) ) 23.32/23.31 ( bool, int, (even_odd_even int), (zero_zero int) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 23.32/23.31 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( 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) (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)) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.32/23.31 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 23.32/23.31 ( bool, nat, (even_odd_even nat), (one_one nat) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 23.32/23.31 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 23.32/23.31 ( bool, nat, prime, (zero_zero nat) ) 23.32/23.31 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( bool, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 23.32/23.31 ( 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 ) 23.32/23.31 ( 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 ) 23.32/23.31 ( 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) ) 23.32/23.31 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( bool, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 23.32/23.31 ( bool, (filter nat), (trivial_limit nat), sequentially ) 23.32/23.31 ( 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)) ) 23.32/23.31 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 23.32/23.31 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( real, rat, ratreal, (one_one rat) ) 23.32/23.31 ( real, rat, ratreal, (zero_zero rat) ) 23.32/23.31 ( real, int, (number_number_of real), min ) 23.32/23.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.32/23.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.32/23.31 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.31 ( 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)))))))) ) 23.32/23.31 ( real, int, (real_1 int), (one_one int) ) 23.32/23.31 ( real, int, (real_1 int), (zero_zero int) ) 23.32/23.31 ( real, nat, (real_1 nat), (zero_zero nat) ) 23.32/23.31 ( real, nat, (real_1 nat), (one_one nat) ) 23.32/23.31 ( real, real, sin, pi ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, sin, (zero_zero real) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.32/23.31 ( real, real, cos, pi ) 23.32/23.31 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, cos, (zero_zero real) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.32/23.31 ( real, real, cos, skv_10 ) 23.32/23.31 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( real, 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)))) ) 23.32/23.31 ( real, real, (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)))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, (uminus_uminus real), (one_one real) ) 23.32/23.31 ( 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) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( 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))))))))) ) 23.32/23.31 ( real, real, (sgn_sgn real), (zero_zero real) ) 23.32/23.31 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( real, real, sqrt, (one_one real) ) 23.32/23.31 ( real, real, sqrt, (zero_zero real) ) 23.32/23.31 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( real, real, tan, pi ) 23.32/23.31 ( real, real, tan, (zero_zero real) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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)))) ) 23.32/23.31 ( real, real, ln, (one_one real) ) 23.32/23.31 ( real, real, (inverse_inverse real), (zero_zero real) ) 23.32/23.31 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.32/23.31 ( real, real, (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.32/23.31 ( real, real, arctan, (one_one real) ) 23.32/23.31 ( real, real, arctan, (zero_zero real) ) 23.32/23.31 ( 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))))) ) 23.32/23.31 ( 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)))))))))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 23.32/23.31 ( 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)))))) ) 23.32/23.31 ( real, real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))), (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))))))))))) ) 23.32/23.31 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 23.32/23.31 ( real, complex, re, (zero_zero complex) ) 23.32/23.31 ( real, complex, re, ii ) 23.32/23.31 ( real, complex, re, (one_one complex) ) 23.32/23.31 ( real, complex, im, (zero_zero complex) ) 23.32/23.31 ( real, complex, im, ii ) 23.32/23.31 ( real, complex, im, (one_one complex) ) 23.32/23.31 ( real, (fun real bool), (the real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2)))))))))))))) ) 23.32/23.31 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (fun nat real), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), (one_one real) ) 23.32/23.31 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 23.32/23.31 ( (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))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 23.32/23.31 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (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)))))) ) 23.32/23.31 ( (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 ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (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 ) 23.32/23.31 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( (fun real real), real, (inverse_divide real), pi ) 23.32/23.31 ( (fun real real), real, (inverse_divide real), (one_one real) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (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))))) ) 23.32/23.31 ( (fun real real), real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.32/23.31 ( (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 ) 23.32/23.31 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 23.32/23.31 ( (fun nat nat), nat, (minus_minus nat), (hAPP int nat nat_1 t) ) 23.32/23.31 ( (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))) ) 23.32/23.31 ( (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) ) 23.32/23.31 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 23.32/23.31 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.32/23.31 ( (fun int rat), int, fract, (one_one int) ) 23.32/23.31 ( (fun int rat), int, fract, (zero_zero int) ) 23.32/23.31 ( complex, int, (number_number_of complex), min ) 23.32/23.31 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 23.32/23.31 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 23.32/23.31 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min) ) 23.32/23.31 ( complex, real, (of_real complex), pi ) 23.32/23.31 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 23.32/23.31 ( complex, real, cis, (zero_zero real) ) 23.32/23.31 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 23.32/23.31 ( complex, complex, cnj, (zero_zero complex) ) 23.32/23.31 ( complex, complex, cnj, ii ) 23.32/23.31 ( complex, complex, cnj, (one_one complex) ) 23.32/23.31 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 23.32/23.31 ( complex, complex, (uminus_uminus complex), ii ) 23.32/23.31 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 23.32/23.31 ( complex, complex, expi, (zero_zero complex) ) 23.32/23.31 ( 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))) ) 23.32/23.31 ( complex, complex, (inverse_inverse complex), ii ) 23.32/23.31 ( 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) ) 23.32/23.31 ( 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 ) 23.32/23.31 ( (fun int bool), int, (ord_less int), (one_one int) ) 23.32/23.31 ( (fun int bool), int, (ord_less int), min ) 23.32/23.31 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 23.32/23.31 ( (fun int bool), int, (ord_less int), s ) 23.32/23.31 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( (fun int bool), int, (ord_less int), t ) 23.32/23.31 ( (fun int bool), int, (ord_less int), m1 ) 23.32/23.31 ( (fun int bool), int, (ord_less int), skv_4 ) 23.32/23.31 ( (fun int bool), int, (ord_less int), skv_5 ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq int), min ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.32/23.31 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.32/23.31 ( (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)))) ) 23.32/23.31 ( (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) ) 23.32/23.31 ( (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) ) 23.32/23.31 ( (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))) ) 23.32/23.31 ( (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))) ) 23.32/23.31 ( (fun int bool), int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.32/23.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 23.32/23.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 23.32/23.31 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_5 ) 23.32/23.31 ( (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) ) 23.32/23.32 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min) ) 23.32/23.32 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_1))) (let ((_let_5 (fun int _let_4))) (hAPP _let_3 _let_1 (hAPP (fun _let_1 bool) (fun _let_3 _let_1) (combb _let_1 bool int) (fEx int)) (hAPP _let_0 _let_3 (hAPP _let_5 (fun _let_0 _let_3) (combc int _let_0 _let_1) (hAPP _let_3 _let_5 (hAPP (fun _let_1 _let_4) (fun _let_3 _let_5) (combb _let_1 _let_4 int) (combb int bool int)) (fequal int))) (hAPP int _let_0 (hAPP _let_2 _let_2 (combc int int int) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (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)))))))))) ) 23.32/23.32 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int int))) (let 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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)))) ) 23.32/23.32 ( (fun int (fun int bool)), (fun int (fun int bool)), (combc int int bool), (fequal int) ) 23.32/23.32 ( (fun int (fun int 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_0))) (let ((_let_4 (fun int _let_0))) (hAPP _let_3 (fun _let_4 _let_4) (combb _let_0 _let_0 int) (hAPP _let_2 _let_3 (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_3))) (let ((_let_5 (fun int _let_3))) (hAPP int _let_3 (hAPP _let_5 _let_5 (combc int int _let_1) (hAPP _let_5 _let_5 (hAPP (fun _let_3 _let_3) (fun _let_5 _let_5) (combb _let_3 _let_3 int) (combc int int bool)) (hAPP _let_2 _let_5 (hAPP _let_4 (fun _let_2 _let_5) (combb _let_0 _let_3 int) (hAPP _let_3 _let_4 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int)))))))) ) 23.32/23.32 ( (fun nat bool), nat, (ord_less nat), (zero_zero nat) ) 23.32/23.32 ( (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) ) 23.32/23.32 ( (fun nat bool), bool, (combk bool nat), fTrue ) 23.32/23.32 ( (fun nat bool), (fun nat bool), (collect nat), prime ) 23.32/23.32 ( (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))) ) 23.32/23.32 ( (fun real complex), real, complex_1, (one_one real) ) 23.32/23.32 ( (fun real complex), real, complex_1, (zero_zero real) ) 23.32/23.32 ( (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 ) 23.32/23.32 ( (fun nat (fun nat bool)), (fun nat (fun nat bool)), (combc nat nat bool), (fequal nat) ) 23.32/23.32 ( (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 int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_7))) (let ((_let_9 (fun _let_6 _let_6))) (let ((_let_10 (fun _let_2 _let_4))) (let ((_let_11 (fun _let_2 _let_1))) (let ((_let_12 (fun _let_3 _let_11))) (let ((_let_13 (hAPP (fun int _let_1) _let_12 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_14 (hAPP (fun _let_2 bool) _let_10 (hAPP (fun bool _let_4) (fun (fun _let_2 bool) _let_10) (combb bool _let_4 _let_2) fconj) (hAPP (fun _let_2 bool) (fun _let_2 bool) (hAPP _let_4 _let_7 (combb bool bool _let_2) fNot) (hAPP int (fun _let_2 bool) (hAPP _let_11 (fun int (fun _let_2 bool)) (combc _let_2 int bool) (hAPP _let_3 _let_11 _let_13 _let_5)) (zero_zero int)))))) (let ((_let_15 (fun _let_2 _let_3))) (let ((_let_16 (fun _let_3 (fun _let_2 bool)))) (let ((_let_17 (fun _let_2 _let_16))) (let ((_let_18 (fun _let_2 _let_11))) (let ((_let_19 (fun _let_3 _let_3))) (let ((_let_20 (fun _let_2 _let_19))) (let ((_let_21 (fun _let_3 _let_15))) (let ((_let_22 (fun _let_2 _let_0))) (let ((_let_23 (hAPP _let_3 _let_22 (hAPP (fun int _let_0) (fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 (fun (product_prod _let_2 _let_2) bool) (product_prod_case _let_2 _let_2 bool) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb 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(fun _let_3 _let_22) (combb int _let_0 _let_2) (times_times int)) (product_fst int int)))) (let ((_let_24 (fun int _let_3))) (hAPP _let_6 _let_6 (hAPP _let_8 _let_9 (combs _let_2 (fun _let_2 bool) (fun _let_2 bool)) (hAPP _let_10 _let_8 (hAPP (fun _let_4 _let_7) (fun _let_10 _let_8) (combb _let_4 _let_7 _let_2) (combb bool bool _let_2)) _let_14)) (hAPP _let_6 _let_6 (hAPP _let_7 _let_9 (combb (fun _let_2 bool) (fun _let_2 bool) _let_2) (hAPP _let_10 _let_7 (combs _let_2 bool bool) _let_14)) (hAPP _let_15 _let_6 (hAPP _let_17 (fun _let_15 _let_6) (combs _let_2 _let_3 (fun _let_2 bool)) (hAPP _let_18 _let_17 (hAPP (fun _let_11 _let_16) (fun _let_18 _let_17) (combb _let_11 _let_16 _let_2) (combs _let_2 int bool)) (hAPP _let_15 _let_18 (hAPP _let_12 (fun _let_15 _let_18) (combb _let_3 _let_11 _let_2) _let_13) (hAPP _let_3 _let_15 (hAPP _let_20 _let_21 (combc _let_2 _let_3 _let_3) (hAPP _let_22 _let_20 (hAPP (fun _let_0 _let_19) (fun _let_22 _let_20) (combb _let_0 _let_19 _let_2) (combb int int _let_2)) _let_23)) _let_5)))) (hAPP _let_3 _let_15 (hAPP _let_24 _let_21 (combb int _let_3 _let_2) (hAPP _let_22 _let_24 (combc _let_2 int int) _let_23)) _let_5))))))))))))))))))))))))))))) ) 23.32/23.32 ( (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 int))) (let ((_let_3 (fun _let_1 _let_0))) (hAPP _let_3 (fun int (fun _let_1 bool)) (combc _let_1 int bool) (hAPP _let_2 _let_3 (hAPP (fun int _let_0) (fun _let_2 _let_3) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))))))), (zero_zero int) ) 23.32/23.32 ( (fun (product_prod int int) bool), (fun int (fun int bool)), (product_prod_case int int bool), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun bool bool))) (let ((_let_4 (fun int _let_3))) (let ((_let_5 (fun _let_1 _let_1))) (let ((_let_6 (fun int _let_1))) (let ((_let_7 (fun _let_0 _let_6))) (let ((_let_8 (fun int _let_6))) (let ((_let_9 (fun _let_6 _let_6))) (hAPP _let_6 _let_6 (hAPP _let_5 _let_9 (combb _let_1 _let_1 int) (hAPP _let_4 _let_5 (combs int bool bool) (hAPP _let_1 _let_4 (hAPP (fun bool _let_3) (fun _let_1 _let_4) (combb bool _let_3 int) fconj) (hAPP int _let_1 (ord_less int) (zero_zero int))))) (hAPP int _let_6 (hAPP _let_8 _let_8 (combc int int _let_1) (hAPP _let_8 _let_8 (hAPP _let_9 (fun _let_8 _let_8) (combb _let_6 _let_6 int) (combc int int bool)) (hAPP _let_2 _let_8 (hAPP _let_7 (fun _let_2 _let_8) (combb _let_0 _let_6 int) (hAPP _let_6 _let_7 (combb int _let_1 int) (fequal int))) int_gcd))) (one_one int))))))))))))) ) 23.32/23.32 ( (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 int))) (let ((_let_3 (fun _let_1 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(hAPP (fun bool _let_3) (fun _let_4 _let_8) (combb bool _let_3 _let_1) fconj) (hAPP _let_4 _let_4 (hAPP _let_3 _let_6 _let_9 fNot) (hAPP int _let_4 (hAPP _let_10 (fun int _let_4) (combc _let_1 int bool) (hAPP _let_2 _let_10 (hAPP (fun int _let_0) (fun _let_2 _let_10) (combb int _let_0 _let_1) (fequal int)) (product_snd int int))) (zero_zero int))))))))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (product_prod int int))) (let ((_let_3 (fun _let_2 int))) (let ((_let_4 (fun bool bool))) (let ((_let_5 (product_snd int int))) (let ((_let_6 (fun _let_2 (fun _let_2 bool)))) (let ((_let_7 (fun (fun _let_2 bool) (fun _let_2 bool)))) (let ((_let_8 (fun _let_2 _let_4))) (let ((_let_9 (fun _let_2 _let_1))) (let ((_let_10 (fun _let_3 _let_9))) (let ((_let_11 (hAPP (fun int _let_1) _let_10 (combb int _let_1 _let_2) (fequal int)))) (let ((_let_12 (fun _let_2 _let_3))) (let ((_let_13 (fun _let_3 (fun _let_2 bool)))) (let ((_let_14 (fun _let_2 _let_13))) (let 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real)) _let_5))) _let_5))))))))))))))))))))))))))))))) ) 23.35/23.38 ( (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun (fun int bool) _let_2))) (let ((_let_4 (real_1 int))) (let ((_let_5 (fun real bool))) (let ((_let_6 (fun real _let_5))) (let ((_let_7 (fun int _let_2))) (let ((_let_8 (fun (fun int (fun int bool)) _let_7))) (let ((_let_9 (fun int real))) (let ((_let_10 (fun int _let_0))) (let ((_let_11 (fun _let_9 (fun int bool)))) (let ((_let_12 (fun real (fun int (fun int bool))))) (let ((_let_13 (fun real _let_7))) (let ((_let_14 (fun int _let_9))) (let ((_let_15 (fun _let_14 (fun int (fun int bool))))) (let ((_let_16 (fun real _let_15))) (let ((_let_17 (fun real _let_11))) (let ((_let_18 (fun _let_9 _let_9))) (let ((_let_19 (fun int _let_18))) (hAPP _let_12 _let_13 (hAPP _let_8 (fun _let_12 _let_13) (combb (fun int (fun int bool)) _let_7 real) (hAPP _let_3 _let_8 (combb (fun int bool) _let_2 int) (hAPP (fun bool _let_1) _let_3 (combb bool _let_1 int) fconj))) (hAPP _let_14 _let_12 (hAPP _let_16 (fun _let_14 _let_12) (combc real _let_14 (fun int (fun int bool))) (hAPP _let_17 _let_16 (hAPP (fun _let_11 _let_15) (fun _let_17 _let_16) (combb _let_11 _let_15 real) (combb _let_9 (fun int bool) int)) (hAPP _let_6 _let_17 (hAPP (fun _let_5 _let_11) (fun _let_6 _let_17) (combb _let_5 _let_11 real) (combb real bool int)) (fequal real)))) (hAPP _let_9 _let_14 (hAPP _let_19 (fun _let_9 _let_14) (combc int _let_9 _let_9) (hAPP _let_10 _let_19 (hAPP (fun _let_0 _let_18) (fun _let_10 _let_19) (combb _let_0 _let_18 int) (combb real real int)) (hAPP _let_9 _let_10 (hAPP (fun real _let_0) (fun _let_9 _let_10) (combb real _let_0 int) (inverse_divide real)) _let_4))) _let_4))))))))))))))))))))))) ) 23.35/23.38 ( (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)) ) 23.35/23.38 ( (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 bool bool))) (let ((_let_2 (fun int _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 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real real int) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (zero X_a)) (= _let_0 (ti X_a _let_0)))) ) 23.43/23.42 ( rat ) 23.43/23.42 ( int ) 23.43/23.42 ( nat ) 23.43/23.42 ( real ) 23.43/23.42 ( complex ) 23.43/23.42 ( quickcheck_code_int ) 23.43/23.42 ( code_code_numeral ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((N $$unsorted) (M $$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))) (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) M) (hAPP int int (fact_fact int) N)))))) ) 23.43/23.42 ( pls, min ) 23.43/23.42 ( pls, (zero_zero int) ) 23.43/23.42 ( (one_one int), (zero_zero int) ) 23.43/23.42 ( min, min ) 23.43/23.42 ( min, (zero_zero int) ) 23.43/23.42 ( s, (zero_zero int) ) 23.43/23.42 ( (hAPP int int (number_number_of int) (hAPP int int bit0 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(ti X_a BOUND_VARIABLE_153125)))) ) 23.43/23.42 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), pls ) 23.43/23.42 ( int, min, y, min ) 23.43/23.42 ( int, s, x, s ) 23.43/23.42 ( int, s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), s1 ) 23.43/23.42 ( int, m, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), m ) 23.43/23.42 ( int, t, r, t ) 23.43/23.42 ( int, v, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.43/23.42 ( int, w, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), w ) 23.43/23.42 ( int, y, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), y ) 23.43/23.42 ( int, sa, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), sa ) 23.43/23.42 ( int, x, skv_13, x ) 23.43/23.42 ( int, r, sa, r ) 23.43/23.42 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 23.43/23.42 ( int, skv_14, skv_19, skv_14 ) 23.43/23.42 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.42 ( complex, ii, ii, ii ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X)) (hBOOL (hAPP int bool _let_0 Y)) (not (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y)))))) ) 23.43/23.42 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.43/23.42 ( 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))) ) 23.43/23.42 ( v, y ) 23.43/23.42 ( v, sa ) 23.43/23.42 ( v, x ) 23.43/23.42 ( v, r ) 23.43/23.42 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.42 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.42 ( w, y ) 23.43/23.42 ( w, sa ) 23.43/23.42 ( w, x ) 23.43/23.42 ( w, r ) 23.43/23.42 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.42 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.42 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.43/23.42 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.42 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.43/23.42 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( skv_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))) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153214 $$unsorted) (BOUND_VARIABLE_153215 $$unsorted) (BOUND_VARIABLE_153216 $$unsorted) (BOUND_VARIABLE_153217 $$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_153216))) (let ((_let_3 (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153214) BOUND_VARIABLE_153215)))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_153217)) (hAPP X_a X_a _let_3 (hAPP X_a X_a _let_2 BOUND_VARIABLE_153217)))))))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153326 $$unsorted) (BOUND_VARIABLE_153327 $$unsorted) (BOUND_VARIABLE_153328 $$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_153326))) (let ((_let_4 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_2) BOUND_VARIABLE_153328)))) (let ((_let_5 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_153326) BOUND_VARIABLE_153328))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_153328) _let_2)))) (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_153327) BOUND_VARIABLE_153328))) (and (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_5) BOUND_VARIABLE_153327))) (or _let_4 (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_153327) _let_5))))))))))))))) ) 23.43/23.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) w) ) 23.43/23.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) v) ) 23.43/23.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.42 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 bit1 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_4, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_5, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.42 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.42 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.42 ( real, (zero_zero real), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))))) (let ((_let_2 (div_div nat))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat suc X)) _let_1) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 X) _let_1))))))) ) 23.43/23.42 ( (zero_zero nat) ) 23.43/23.42 ( (one_one nat) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((Z_1 $$unsorted)) (= (hAPP complex complex (hAPP complex (fun complex complex) (plus_plus complex) Z_1) (hAPP complex complex cnj Z_1)) (hAPP real complex (of_real complex) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP complex real re Z_1)))) ) 23.43/23.42 ( (zero_zero complex) ) 23.43/23.42 ( ii ) 23.43/23.42 ( (one_one complex) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153406 $$unsorted) (BOUND_VARIABLE_153407 $$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_153406) BOUND_VARIABLE_153407)) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP X_a real _let_0 BOUND_VARIABLE_153406)) BOUND_VARIABLE_153407)))) ) 23.43/23.42 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153515 $$unsorted) (BOUND_VARIABLE_153516 $$unsorted) (BOUND_VARIABLE_153517 $$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_153517) (ti X_a BOUND_VARIABLE_153516))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153517) BOUND_VARIABLE_153515))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_153516) BOUND_VARIABLE_153515))))) ) 23.43/23.42 ( int, pls, pls, (zero_zero int) ) 23.43/23.42 ( int, (one_one int), r, (zero_zero int) ) 23.43/23.42 ( int, min, min, min ) 23.43/23.42 ( int, min, w, (zero_zero int) ) 23.43/23.42 ( int, (zero_zero int), s, min ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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, (zero_zero int) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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, t ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), y, s ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), x, skv_4 ) 23.43/23.42 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_14, skv_5 ) 23.43/23.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v, (zero_zero int) ) 23.43/23.42 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, m1 ) 23.43/23.42 ( int, t, m1, (one_one int) ) 23.43/23.42 ( nat, n, n, (zero_zero nat) ) 23.43/23.42 ( nat, tn, tn, (zero_zero nat) ) 23.43/23.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi, pi ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Ya) Xa))) (= Xa (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_gr676655987ssThan real) Ya) Xa))))) ) 23.43/23.42 ( pi, (zero_zero real) ) 23.43/23.42 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (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))) ) 23.43/23.42 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (zero_zero real), pi ) 23.43/23.42 ( (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)))) ) 23.43/23.42 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.42 ( (zero_zero real), skv_2 ) 23.43/23.42 ( (zero_zero real), skv_9 ) 23.43/23.42 ( (zero_zero real), skv_12 ) 23.43/23.42 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.43/23.42 ( (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))))), (zero_zero real) ) 23.43/23.42 ( (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)), pi ) 23.43/23.42 ) 23.43/23.42 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153613 $$unsorted) (BOUND_VARIABLE_153614 $$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_153613)) (hAPP X_a X_a (hAPP X_a _let_2 _let_4 BOUND_VARIABLE_153614) BOUND_VARIABLE_153613)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_153614))))))))) ) 23.43/23.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.42 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 23.43/23.43 ( 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)))) ) 23.43/23.43 ( 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))) ) 23.43/23.43 ( 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)))) ) 23.43/23.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.43/23.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 23.43/23.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 23.43/23.43 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 23.43/23.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 23.43/23.43 ( 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) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X $$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))) (not (= _let_0 (hAPP real real sin X))) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (= X (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_1)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))))) )))) ) 23.43/23.43 ( pi ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (zero_zero real) ) 23.43/23.43 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (inverse_divide real) (hAPP int real _let_1 (hAPP int int bit1 _let_0))) (hAPP int real _let_1 (hAPP int int bit0 _let_0)))) pi)))) ) 23.43/23.43 ( skv_10 ) 23.43/23.43 ( skv_11 ) 23.43/23.43 ( skv_15 ) 23.43/23.43 ( skv_18 ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153646 $$unsorted) (BOUND_VARIABLE_153647 $$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_153646) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_153646) BOUND_VARIABLE_153647)))) ) 23.43/23.43 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 23.43/23.43 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.43 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.43 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.43 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.43 ( int, y, v ) 23.43/23.43 ( int, y, w ) 23.43/23.43 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, sa, v ) 23.43/23.43 ( int, sa, w ) 23.43/23.43 ( int, x, v ) 23.43/23.43 ( int, x, w ) 23.43/23.43 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.43 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, r, v ) 23.43/23.43 ( int, r, w ) 23.43/23.43 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.43 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.43 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.43 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.43 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.43 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.43 ( 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)))))) ) 23.43/23.43 ( 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 ) 23.43/23.43 ( complex, ii, ii ) 23.43/23.43 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.43 ( 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 ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153722 $$unsorted) (BOUND_VARIABLE_153723 $$unsorted) (BOUND_VARIABLE_153724 $$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_153722) BOUND_VARIABLE_153723) (hAPP real _let_0 (at real) BOUND_VARIABLE_153724))) (forall ((S_2 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (let ((_let_2 (fun nat X_a))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (tendsto nat real) S_2) BOUND_VARIABLE_153724) sequentially))) (not (forall ((N_1 $$unsorted)) (not (= (hAPP nat real S_2 N_1) BOUND_VARIABLE_153724)) )) (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_153722) S_2)) BOUND_VARIABLE_153723) sequentially)))))) ))))) ) 23.43/23.43 ( 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)))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (the X_a))) (or (not (comm_monoid_add X_a)) (not (topological_space X_a)) (= _let_0 (ti (fun (fun X_a bool) X_a) _let_0)))) ) 23.43/23.43 ( rat ) 23.43/23.43 ( int ) 23.43/23.43 ( nat ) 23.43/23.43 ( bool ) 23.43/23.43 ( real ) 23.43/23.43 ( (filter nat) ) 23.43/23.43 ( complex ) 23.43/23.43 ( (fun int bool) ) 23.43/23.43 ( (product_prod int int) ) 23.43/23.43 ( (fun nat bool) ) 23.43/23.43 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.43/23.43 ( quickcheck_code_int ) 23.43/23.43 ( code_code_numeral ) 23.43/23.43 ( (product_prod real real) ) 23.43/23.43 ( (filter real) ) 23.43/23.43 ( (product_prod nat nat) ) 23.43/23.43 ( (fun nat rat) ) 23.43/23.43 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_153808 $$unsorted) (BOUND_VARIABLE_153809 $$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) (hAPP nat X_a _let_0 BOUND_VARIABLE_153808)) (hAPP nat X_a _let_0 BOUND_VARIABLE_153809)) (hAPP nat X_a _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) BOUND_VARIABLE_153808) BOUND_VARIABLE_153809))))) ) 23.43/23.43 ( int, (one_one nat), (zero_zero nat) ) 23.43/23.43 ( int, (one_one nat), (one_one nat) ) 23.43/23.43 ( int, (one_one nat), n ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_153868 $$unsorted) (BOUND_VARIABLE_153869 $$unsorted) (BOUND_VARIABLE_153870 $$unsorted) (BOUND_VARIABLE_153871 $$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_a))) (let ((_let_5 (fun nat X_b))) (or (not (metric_space X_a)) (not (metric_space X_b)) (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_153868) BOUND_VARIABLE_153869) (hAPP X_a _let_1 (at X_a) BOUND_VARIABLE_153870)))) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_4 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_153871) BOUND_VARIABLE_153870) sequentially))) (not (forall ((N_1 $$unsorted)) (not (= (ti X_a BOUND_VARIABLE_153870) (hAPP nat X_a BOUND_VARIABLE_153871 N_1))) )) (hBOOL (hAPP (filter nat) bool (hAPP X_b _let_0 (hAPP _let_5 (fun X_b _let_0) (tendsto nat X_b) (hAPP _let_4 _let_5 (hAPP _let_3 (fun _let_4 _let_5) (combb X_a X_b nat) BOUND_VARIABLE_153868) BOUND_VARIABLE_153871)) BOUND_VARIABLE_153869) sequentially))))))))) ) 23.43/23.43 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP nat nat suc (zero_zero nat)))) (or (hBOOL (hAPP nat bool (even_odd_even nat) X)) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X) (hAPP nat nat suc _let_0))))) ) 23.43/23.43 ( (zero_zero nat) ) 23.43/23.43 ( (one_one nat) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((N $$unsorted)) (= (hAPP int nat (number_number_of nat) N) (hAPP real nat natfloor (hAPP int real (number_number_of real) N))) ) 23.43/23.43 ( pls ) 23.43/23.43 ( (hAPP int int bit1 pls) ) 23.43/23.43 ( min ) 23.43/23.43 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.43 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.43 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.43 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154027 $$unsorted) (BOUND_VARIABLE_154028 $$unsorted) (BOUND_VARIABLE_154029 $$unsorted) (BOUND_VARIABLE_154030 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (inverse_divide X_a))) (let ((_let_3 (plus_plus X_a))) (let ((_let_4 (times_times X_a))) (or (not (field X_a)) (= _let_0 (ti X_a BOUND_VARIABLE_154030)) (= _let_0 (ti X_a BOUND_VARIABLE_154029)) (= (hAPP X_a X_a (hAPP X_a _let_1 _let_3 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_154027) BOUND_VARIABLE_154030)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_154028) BOUND_VARIABLE_154029)) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (hAPP X_a _let_1 _let_3 (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_154027) BOUND_VARIABLE_154029)) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_154028) BOUND_VARIABLE_154030))) (hAPP X_a X_a (hAPP X_a _let_1 _let_4 BOUND_VARIABLE_154030) BOUND_VARIABLE_154029))))))))) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.43 ( int, x, y, v, w ) 23.43/23.43 ( int, r, sa, v, w ) 23.43/23.43 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v, w ) 23.43/23.43 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (one_one real)) X))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) (hAPP real real ln X)))))) ) 23.43/23.43 ( (one_one real) ) 23.43/23.43 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (abs_abs real) X) (hAPP real real sqrt (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.43 ( (hAPP int real (number_number_of real) min) ) 23.43/23.43 ( (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)))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154088 $$unsorted) (BOUND_VARIABLE_154089 $$unsorted) (BOUND_VARIABLE_154090 $$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_154089))) (let ((_let_3 (ti X_a BOUND_VARIABLE_154090))) (let ((_let_4 (= _let_1 _let_2))) (or (not (number X_a)) (not (field_inverse_zero X_a)) (= (= (hAPP X_a X_a (hAPP X_a _let_0 (inverse_divide X_a) BOUND_VARIABLE_154088) _let_2) _let_3) (and (or (not _let_4) (= _let_1 _let_3)) (or _let_4 (= (ti X_a BOUND_VARIABLE_154088) (hAPP X_a X_a (hAPP X_a _let_0 (times_times X_a) BOUND_VARIABLE_154090) _let_2))))))))))) ) 23.43/23.43 ( real, (hAPP real real sqrt (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)), pi ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154141 $$unsorted) (BOUND_VARIABLE_154142 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (or (not (metric_space X_a)) (not (forall ((R_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1))) (not (forall ((No $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) No) N_1))) (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_154141 N_1)) BOUND_VARIABLE_154142)) R_1))) )) ))) )) (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_154141) BOUND_VARIABLE_154142) sequentially)))) ) 23.43/23.43 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (zero_zero int) (hAPP X_a int (archimedean_ceiling X_a) (zero_zero X_a)))) ) 23.43/23.43 ( rat ) 23.43/23.43 ( int ) 23.43/23.43 ( nat ) 23.43/23.43 ( real ) 23.43/23.43 ( complex ) 23.43/23.43 ( quickcheck_code_int ) 23.43/23.43 ( code_code_numeral ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154199 $$unsorted) (BOUND_VARIABLE_154200 $$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_154200))) (= (hAPP X_a X_a (hAPP X_a _let_2 _let_4 (hAPP _let_0 X_a _let_1 BOUND_VARIABLE_154200)) BOUND_VARIABLE_154199) (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_154200)) BOUND_VARIABLE_154199))))))))) ) 23.43/23.43 ( real, (one_one real), (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) ) 23.43/23.43 ) 23.43/23.43 (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 int nat nat_1 (hAPP int int (hAPP int (fun int int) (minus_minus int) P_5) _let_1)) (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)))))) ) 23.43/23.43 ( (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)))) ) 23.43/23.43 ( t ) 23.43/23.43 ( y ) 23.43/23.43 ( x ) 23.43/23.43 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.43/23.43 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.43/23.43 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.43 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.43/23.43 ( (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))) m1))) ) 23.43/23.43 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154338 $$unsorted) (BOUND_VARIABLE_154339 $$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_154339)) BOUND_VARIABLE_154338)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_154338)) BOUND_VARIABLE_154339))))))) ) 23.43/23.43 ( int, pls, pls ) 23.43/23.43 ( int, pls, (one_one int) ) 23.43/23.43 ( int, pls, min ) 23.43/23.43 ( 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))) ) 23.43/23.43 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (one_one int), pls ) 23.43/23.43 ( int, (one_one int), min ) 23.43/23.43 ( int, (one_one int), (zero_zero int) ) 23.43/23.43 ( int, min, pls ) 23.43/23.43 ( int, min, (one_one int) ) 23.43/23.43 ( int, (zero_zero int), (one_one int) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), pls ) 23.43/23.43 ( 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) ) 23.43/23.43 ( real, (hAPP real real (hAPP 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) ) 23.43/23.43 ( 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)))) ) 23.43/23.43 ( 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 ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (zero_zero real)) X))) (not (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 X) _let_1))) (hBOOL (hAPP real bool (hAPP real _let_2 _let_3 (hAPP real real (exp real) (hAPP real real (hAPP real _let_0 (minus_minus real) X) (hAPP nat real (hAPP real (fun nat real) (power_power real) X) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP real real (hAPP real _let_0 (plus_plus real) _let_1) X)))))))) ) 23.43/23.43 ( (hAPP int real (number_number_of real) min) ) 23.43/23.43 ( pi ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.43/23.43 ( skv_10 ) 23.43/23.43 ( skv_11 ) 23.43/23.43 ( skv_15 ) 23.43/23.43 ( skv_18 ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 B_2))) (= (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) (hAPP int rat (hAPP int (fun int rat) fract A_3) B_2))) (hBOOL (hAPP int bool _let_0 A_3))))) ) 23.43/23.43 ( (one_one int), (one_one int) ) 23.43/23.43 ( (zero_zero int), (one_one int) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((Ma $$unsorted) (Va $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) Va))) (= (= (hAPP nat int (semiring_1_of_nat int) Ma) _let_0) (and (= Ma (hAPP int nat nat_1 _let_0)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) _let_0))))) ) 23.43/23.43 ( (zero_zero nat), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.43 ( (one_one nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.43 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit1 pls) ) 23.43/23.43 ( n, min ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154546 $$unsorted) (BOUND_VARIABLE_154547 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (inverse_inverse X_a))) (let ((_let_3 (zero_zero X_a))) (or (not (division_ring X_a)) (= _let_3 (ti X_a BOUND_VARIABLE_154547)) (= _let_3 (ti X_a BOUND_VARIABLE_154546)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154547) BOUND_VARIABLE_154546)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_154546)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_154547)))))))) ) 23.43/23.43 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.43/23.43 ( 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))) ) 23.43/23.43 ( int, v, y ) 23.43/23.43 ( int, v, sa ) 23.43/23.43 ( int, v, x ) 23.43/23.43 ( int, v, r ) 23.43/23.43 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.43 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.43 ( int, w, y ) 23.43/23.43 ( int, w, sa ) 23.43/23.43 ( int, w, x ) 23.43/23.43 ( int, w, r ) 23.43/23.43 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.43 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.43 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.43/23.43 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.43 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.43/23.43 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.43 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( int, skv_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))) ) 23.43/23.43 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( 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))))) ) 23.43/23.43 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ( 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)))) ) 23.43/23.43 ( complex, ii, ii ) 23.43/23.43 ( 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)) ) 23.43/23.43 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.43 ) 23.43/23.43 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 X))) (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y))))) ) 23.43/23.43 ( (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)))) ) 23.43/23.43 ( (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) ) 23.43/23.43 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.43/23.43 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.43/23.43 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.43 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.43 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.43/23.43 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.43 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.43/23.43 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.43 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.43/23.43 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.43/23.43 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.43 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.43/23.44 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.43/23.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154614 $$unsorted) (BOUND_VARIABLE_154615 $$unsorted) (BOUND_VARIABLE_154616 $$unsorted) (BOUND_VARIABLE_154617 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun X_a X_a))) (let ((_let_2 (fun X_a _let_0))) (let ((_let_3 (deriv X_a))) (let ((_let_4 (fun nat X_a))) (let ((_let_5 (fun X_a _let_4))) (let ((_let_6 (power_power X_a))) (let ((_let_7 (times_times X_a))) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_154615) BOUND_VARIABLE_154616) BOUND_VARIABLE_154617))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 (hAPP nat _let_1 (hAPP _let_5 (fun nat _let_1) (combc X_a nat X_a) (hAPP _let_1 _let_5 (hAPP _let_5 (fun _let_1 _let_5) (combb X_a _let_4 X_a) _let_6) BOUND_VARIABLE_154615)) (hAPP nat nat suc BOUND_VARIABLE_154614))) BOUND_VARIABLE_154616) (hAPP X_a X_a (hAPP X_a _let_1 _let_7 (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) (one_one X_a)) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_154614))) (hAPP X_a X_a (hAPP X_a _let_1 _let_7 BOUND_VARIABLE_154617) (hAPP nat X_a (hAPP X_a _let_4 _let_6 (hAPP X_a X_a BOUND_VARIABLE_154615 BOUND_VARIABLE_154616)) BOUND_VARIABLE_154614)))))))))))))) ) 23.43/23.44 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w)))))), m1, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) r) w))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (number_of_frac X_a))) (= _let_0 (ti (fun int X_a) _let_0))) ) 23.43/23.44 ( rat ) 23.43/23.44 ( int ) 23.43/23.44 ( (fun int int) ) 23.43/23.44 ( nat ) 23.43/23.44 ( bool ) 23.43/23.44 ( real ) 23.43/23.44 ( (fun nat real) ) 23.43/23.44 ( (fun real real) ) 23.43/23.44 ( (fun nat nat) ) 23.43/23.44 ( (fun int rat) ) 23.43/23.44 ( (fun int bool) ) 23.43/23.44 ( (product_prod int int) ) 23.43/23.44 ( (fun (product_prod int int) int) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 23.43/23.44 ( (fun nat int) ) 23.43/23.44 ( (fun bool bool) ) 23.43/23.44 ( (fun int (fun bool bool)) ) 23.43/23.44 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 23.43/23.44 ( (fun int (fun int bool)) ) 23.43/23.44 ( (fun nat bool) ) 23.43/23.44 ( (fun (product_prod int int) bool) ) 23.43/23.44 ( (fun int (fun (product_prod int int) bool)) ) 23.43/23.44 ( quickcheck_code_int ) 23.43/23.44 ( (fun (fun int bool) bool) ) 23.43/23.44 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 23.43/23.44 ( (product_prod int (product_prod int int)) ) 23.43/23.44 ( (fun int (product_prod int (product_prod int int))) ) 23.43/23.44 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 23.43/23.44 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 23.43/23.44 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 23.43/23.44 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 23.43/23.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 23.43/23.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 23.43/23.44 ( (fun nat (fun bool bool)) ) 23.43/23.44 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 23.43/23.44 ( (fun int (product_prod int int)) ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 23.43/23.44 ( (fun int (fun (fun int bool) bool)) ) 23.43/23.44 ( (fun (fun int int) (fun int bool)) ) 23.43/23.44 ( (list int) ) 23.43/23.44 ( (fun int (fun int (fun int bool))) ) 23.43/23.44 ( (fun int real) ) 23.43/23.44 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154655 $$unsorted) (BOUND_VARIABLE_154656 $$unsorted) (BOUND_VARIABLE_154657 $$unsorted)) (let ((_let_0 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_154655))) (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_154656) BOUND_VARIABLE_154657)) (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_154656)) (hAPP nat X_a _let_0 BOUND_VARIABLE_154657))))) ) 23.43/23.44 ( int, s, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, s1, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, v, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, w, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, y, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, x, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (one_one nat), (one_one nat) ) 23.43/23.44 ( int, skv_6, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, skv_7, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, skv_16, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, skv_23, (one_one nat), (one_one nat) ) 23.43/23.44 ( int, skv_24, (one_one nat), (one_one nat) ) 23.43/23.44 ( complex, ii, (one_one nat), (one_one nat) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154673 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) BOUND_VARIABLE_154673)) (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_154673))))) ) 23.43/23.44 ( int, pls ) 23.43/23.44 ( int, (one_one int) ) 23.43/23.44 ( int, min ) 23.43/23.44 ( int, s ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.44 ( int, skv_4 ) 23.43/23.44 ( int, skv_5 ) 23.43/23.44 ( real, pi ) 23.43/23.44 ( 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)))) ) 23.43/23.44 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( real, skv_10 ) 23.43/23.44 ( real, skv_11 ) 23.43/23.44 ( real, skv_15 ) 23.43/23.44 ( real, skv_18 ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) W))) (= (hAPP int nat (number_number_of nat) (hAPP int int bit0 W)) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_0) _let_0))) ) 23.43/23.44 ( pls ) 23.43/23.44 ( (hAPP int int bit1 pls) ) 23.43/23.44 ( min ) 23.43/23.44 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.44 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_0 (fun int int))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Y) X))) (= (hAPP int int (hAPP int _let_0 (minus_minus int) X) Y) (hAPP int int (hAPP int _let_0 nat_tsub X) Y)))) ) 23.43/23.44 ( (one_one int), t ) 23.43/23.44 ( min, pls ) 23.43/23.44 ( min, min ) 23.43/23.44 ( (zero_zero int), pls ) 23.43/23.44 ( (zero_zero int), (one_one int) ) 23.43/23.44 ( (zero_zero int), min ) 23.43/23.44 ( (zero_zero int), s ) 23.43/23.44 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.44 ( (zero_zero int), skv_4 ) 23.43/23.44 ( (zero_zero int), skv_5 ) 23.43/23.44 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.43/23.44 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.44 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.43/23.44 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.43/23.44 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (times_times int) Xa) Ya)) zEven)))))) ) 23.43/23.44 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.43/23.44 ( 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))) ) 23.43/23.44 ( v, y ) 23.43/23.44 ( v, sa ) 23.43/23.44 ( v, x ) 23.43/23.44 ( v, r ) 23.43/23.44 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.44 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.44 ( w, y ) 23.43/23.44 ( w, sa ) 23.43/23.44 ( w, x ) 23.43/23.44 ( w, r ) 23.43/23.44 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.44 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.44 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.43/23.44 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.44 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.43/23.44 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( skv_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))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_b $$unsorted) (BOUND_VARIABLE_154866 $$unsorted) (BOUND_VARIABLE_154867 $$unsorted) (BOUND_VARIABLE_154878 $$unsorted) (BOUND_VARIABLE_154879 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (fun X_b X_b))) (let ((_let_3 (times_times X_b))) (let ((_let_4 (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_154878)) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_154879)))) (or (not (number X_b)) (not (monoid_mult X_b)) (and (or (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_154867))) (= (one_one X_b) (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_154866)) (hAPP int nat (number_number_of nat) (hAPP int int bit1 BOUND_VARIABLE_154867))))) (or (not (hBOOL (hAPP int bool _let_0 (hAPP int int _let_1 BOUND_VARIABLE_154879)))) (= (hAPP nat X_b (hAPP X_b (fun nat X_b) (power_power X_b) (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_154878)) (hAPP int nat (number_number_of nat) (hAPP int int bit1 BOUND_VARIABLE_154879))) (hAPP X_b X_b (hAPP X_b _let_2 _let_3 (hAPP X_b X_b (hAPP X_b _let_2 _let_3 (hAPP int X_b (number_number_of X_b) BOUND_VARIABLE_154878)) _let_4)) _let_4)))))))))) ) 23.43/23.44 ( int, min, (hAPP int int bit1 (hAPP int int bit1 pls)), min, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.44 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), min, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), min ) 23.43/23.44 ( nat, (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)), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.44 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)), pls, (hAPP int int bit0 (hAPP int int bit1 pls)), pls ) 23.43/23.44 ( quickcheck_code_int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)), pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.44 ( code_code_numeral, pls, (hAPP int int bit1 pls), pls, (hAPP int int bit1 pls) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154950 $$unsorted) (BOUND_VARIABLE_154951 $$unsorted) (BOUND_VARIABLE_154952 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_154952))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_154952) (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_154950)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_154951))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_154951) BOUND_VARIABLE_154950))))))) ) 23.43/23.44 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_154989 $$unsorted) (BOUND_VARIABLE_154990 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (let ((_let_2 (fun X_a _let_0))) (let ((_let_3 (tendsto nat X_a))) (let ((_let_4 (inverse_inverse X_a))) (or (not (real_n1866405975lgebra X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_154989) BOUND_VARIABLE_154990) sequentially))) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_154990)) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 _let_2 _let_3 (hAPP _let_1 _let_1 (hAPP (fun X_a X_a) (fun _let_1 _let_1) (combb X_a X_a nat) _let_4) BOUND_VARIABLE_154989)) (hAPP X_a X_a _let_4 BOUND_VARIABLE_154990)) sequentially)))))))) ) 23.43/23.44 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))), (zero_zero real) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (fun real real))) (let ((_let_3 (one_one real))) (let ((_let_4 (fun nat _let_2))) (let ((_let_5 (fun _let_0 _let_0))) (let ((_let_6 (combs nat real real))) (let ((_let_7 (hAPP (fun real _let_2) (fun _let_0 _let_4) (combb real _let_2 nat) (times_times real)))) (let ((_let_8 (fun (fun nat nat) _let_0))) (let ((_let_9 (combb nat real nat))) (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) Xa)) _let_3))) (hBOOL (hAPP _let_0 bool (summable real) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 _let_7 (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)))) (hAPP _let_0 _let_0 (hAPP _let_4 _let_5 _let_6 (hAPP _let_0 _let_4 _let_7 (hAPP _let_0 _let_0 (hAPP _let_2 _let_5 (combb real real nat) (hAPP real _let_2 (inverse_divide real) _let_3)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_8 _let_9 (real_1 nat)) _let_11)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_8 _let_9 (hAPP real _let_0 _let_1 Xa)) _let_11)))))))))))))))))) ) 23.43/23.44 ( (hAPP int real (number_number_of real) min) ) 23.43/23.44 ( (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)))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155130 $$unsorted)) (let ((_let_0 (zero_zero X_a))) (or (not (real_normed_vector X_a)) (= (= _let_0 (ti X_a BOUND_VARIABLE_155130)) (= _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_155130))))) ) 23.43/23.44 ( rat, (zero_zero rat) ) 23.43/23.44 ( int, pls ) 23.43/23.44 ( int, min ) 23.43/23.44 ( int, s ) 23.43/23.44 ( int, s1 ) 23.43/23.44 ( int, m ) 23.43/23.44 ( int, t ) 23.43/23.44 ( int, v ) 23.43/23.44 ( int, w ) 23.43/23.44 ( int, y ) 23.43/23.44 ( int, sa ) 23.43/23.44 ( int, x ) 23.43/23.44 ( int, r ) 23.43/23.44 ( int, m1 ) 23.43/23.44 ( int, skv_14 ) 23.43/23.44 ( int, skv_20 ) 23.43/23.44 ( (fun int int), bit1 ) 23.43/23.44 ( (fun int int), bit0 ) 23.43/23.44 ( (fun int int), succ ) 23.43/23.44 ( (fun int int), pred ) 23.43/23.44 ( (fun int int), (fact_fact int) ) 23.43/23.44 ( (fun int int), zfact ) 23.43/23.44 ( nat, n ) 23.43/23.44 ( nat, tn ) 23.43/23.44 ( bool, fTrue ) 23.43/23.44 ( bool, fFalse ) 23.43/23.44 ( real, pi ) 23.43/23.44 ( real, (zero_zero real) ) 23.43/23.44 ( (fun nat real), (real_1 nat) ) 23.43/23.44 ( (fun nat real), cos_coeff ) 23.43/23.44 ( (fun nat real), sin_coeff ) 23.43/23.44 ( (fun real real), sin ) 23.43/23.44 ( (fun real real), cos ) 23.43/23.44 ( (fun real real), sqrt ) 23.43/23.44 ( (fun real real), tan ) 23.43/23.44 ( (fun real real), ln ) 23.43/23.44 ( (fun real real), arctan ) 23.43/23.44 ( (fun real real), arcsin ) 23.43/23.44 ( (fun real real), arccos ) 23.43/23.44 ( (fun nat nat), suc ) 23.43/23.44 ( (fun nat nat), (fact_fact nat) ) 23.43/23.44 ( (fun nat nat), nat_size ) 23.43/23.44 ( (fun nat nat), (size_size nat) ) 23.43/23.44 ( (fun nat nat), fact ) 23.43/23.44 ( (filter nat), sequentially ) 23.43/23.44 ( (fun int (fun int rat)), fract ) 23.43/23.44 ( complex, ii ) 23.43/23.44 ( (fun int bool), zOdd ) 23.43/23.44 ( (fun int bool), zprime ) 23.43/23.44 ( (fun int bool), zEven ) 23.43/23.44 ( (fun int bool), nat_neg ) 23.43/23.44 ( (fun int bool), nat_is_nat ) 23.43/23.44 ( (fun int bool), (even_odd_even int) ) 23.43/23.44 ( (fun int bool), twoSqu1091635170sum2sq ) 23.43/23.44 ( (fun int (fun int int)), legacy_zgcd ) 23.43/23.44 ( (fun int (fun int int)), (gcd_gcd int) ) 23.43/23.44 ( (fun int (fun int int)), inv ) 23.43/23.44 ( (fun int (fun int int)), multInv ) 23.43/23.44 ( (fun int (fun int int)), legendre ) 23.43/23.44 ( (fun int (fun int int)), standardRes ) 23.43/23.44 ( (fun int (fun int int)), nat_tsub ) 23.43/23.44 ( (fun int (fun int int)), z3div ) 23.43/23.44 ( (fun int (fun int int)), z3mod ) 23.43/23.44 ( (fun int (fun int int)), int_lcm ) 23.43/23.44 ( (fun int (fun int int)), int_gcd ) 23.43/23.44 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.43/23.44 ( (fun bool bool), fNot ) 23.43/23.44 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.43/23.44 ( (fun bool (fun bool bool)), fconj ) 23.43/23.44 ( (fun bool (fun bool bool)), fdisj ) 23.43/23.44 ( (fun bool (fun bool bool)), fimplies ) 23.43/23.44 ( (fun int (fun int bool)), quadRes ) 23.43/23.44 ( (fun int (fun int bool)), d22set ) 23.43/23.44 ( (fun int (fun int bool)), norRRset ) 23.43/23.44 ( (fun int (fun int bool)), sRStar ) 23.43/23.44 ( (fun int (fun int bool)), sr ) 23.43/23.44 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.43/23.44 ( (fun nat bool), (even_odd_even nat) ) 23.43/23.44 ( (fun nat bool), prime ) 23.43/23.44 ( (fun real complex), cis ) 23.43/23.44 ( (fun nat (fun nat bool)), coprime ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.43/23.44 ( (fun (product_prod int int) bool), frac_1 ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.43/23.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.43/23.44 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.43/23.44 ( (fun (fun int bool) bool), nat_nat_set ) 23.43/23.44 ( (fun nat (fun real real)), root ) 23.43/23.44 ( (fun real (fun real real)), log ) 23.43/23.44 ( (fun real (fun real real)), powr ) 23.43/23.44 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.43/23.44 ( (fun complex complex), cnj ) 23.43/23.44 ( (fun complex complex), expi ) 23.43/23.44 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.43/23.44 ( (fun nat (fun nat nat)), nat_gcd ) 23.43/23.44 ( (fun nat (fun nat nat)), nat_lcm ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.43/23.44 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.43/23.44 ( (fun int (fun (fun int bool) bool)), resSet ) 23.43/23.44 ( (fun int nat), nat_1 ) 23.43/23.44 ( (fun int nat), phi ) 23.43/23.44 ( (fun complex real), re ) 23.43/23.44 ( (fun complex real), im ) 23.43/23.44 ( (fun complex real), arg ) 23.43/23.44 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.43/23.44 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.43/23.44 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.43/23.44 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.43/23.44 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.43/23.44 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.43/23.44 ( (fun (product_prod nat nat) bool), pred_nat ) 23.43/23.44 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.43/23.44 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.43/23.44 ( (fun (fun int bool) int), (the int) ) 23.43/23.44 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.43/23.44 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.43/23.44 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.43/23.44 ( (fun real (fun real complex)), rcis ) 23.43/23.44 ( (fun real (fun real complex)), complex_1 ) 23.43/23.44 ( (fun int (fun int (fun int bool))), zcong ) 23.43/23.44 ( (fun int (fun int (fun int bool))), wset ) 23.43/23.44 ( (fun int (fun int (fun int bool))), noXRRset ) 23.43/23.44 ( (fun int (fun int (fun int bool))), bnorRset ) 23.43/23.44 ( (fun int (fun int (fun int bool))), zcongm ) 23.43/23.44 ( (fun real nat), natceiling ) 23.43/23.44 ( (fun real nat), natfloor ) 23.43/23.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.43/23.44 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.43/23.44 ( (fun int real), (real_1 int) ) 23.43/23.44 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.43/23.44 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.43/23.44 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.43/23.44 ( (fun complex nat), (size_size complex) ) 23.43/23.44 ( (fun complex nat), complex_size ) 23.43/23.44 ( (fun (fun nat rat) bool), vanishes ) 23.43/23.44 ( (fun (product_prod int int) rat), frct ) 23.43/23.44 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.43/23.44 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.43/23.44 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.43/23.44 ( (fun rat real), ratreal ) 23.43/23.44 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.43/23.44 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.43/23.44 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.43/23.44 ( (fun rat (product_prod int int)), quotient_of ) 23.43/23.44 ( (fun int (fun nat nat)), nat_aux ) 23.43/23.44 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.43/23.44 ( (fun int (list int)), quickc666637781d_zero ) 23.43/23.44 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.43/23.44 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.43/23.44 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.43/23.44 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.43/23.44 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.43/23.44 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.43/23.44 ( (fun code_code_numeral int), code_int_of ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155142 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_155142) (zero_zero X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_155142)) (zero_zero int))))) ) 23.43/23.44 ( int, (one_one int) ) 23.43/23.44 ( int, min ) 23.43/23.44 ( int, (zero_zero int) ) 23.43/23.44 ( int, s ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( int, t ) 23.43/23.44 ( int, m1 ) 23.43/23.44 ( int, skv_4 ) 23.43/23.44 ( int, skv_5 ) 23.43/23.44 ( nat, (zero_zero nat) ) 23.43/23.44 ( real, pi ) 23.43/23.44 ( 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)))) ) 23.43/23.44 ( real, (one_one real) ) 23.43/23.44 ( real, (zero_zero real) ) 23.43/23.44 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.44 ( 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))))) ) 23.43/23.44 ( 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)) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int int bit1 (hAPP int int pred K_4)) (hAPP int int pred (hAPP int int bit0 K_4))) ) 23.43/23.44 ( pls ) 23.43/23.44 ( (hAPP int int bit1 pls) ) 23.43/23.44 ( min ) 23.43/23.44 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.44 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.44 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.44 ) 23.43/23.44 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155159 $$unsorted) (BOUND_VARIABLE_155160 $$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_155160) _let_2)) (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_155159))) (and (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_155160)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155159) _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_155159) BOUND_VARIABLE_155160)) _let_2)))))))) ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.44 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( 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))), t ) 23.43/23.44 ( 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))), m1 ) 23.43/23.44 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.44 ( 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))), skv_21 ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.44 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.44 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.44 ( int, y, v ) 23.43/23.44 ( int, y, w ) 23.43/23.44 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( int, sa, v ) 23.43/23.44 ( int, sa, w ) 23.43/23.44 ( int, x, v ) 23.43/23.44 ( int, x, w ) 23.43/23.44 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.44 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.44 ( int, r, v ) 23.43/23.44 ( int, r, w ) 23.43/23.44 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.44 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.44 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.44 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.44 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.45 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.45 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.45 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.45 ( 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)))))) ) 23.43/23.45 ( 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 ) 23.43/23.45 ( complex, ii, ii ) 23.43/23.45 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.45 ( 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 ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155190 $$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_155190) (ti X_a BOUND_VARIABLE_155190))) ) 23.43/23.45 ( int, pls ) 23.43/23.45 ( int, min ) 23.43/23.45 ( int, s ) 23.43/23.45 ( int, s1 ) 23.43/23.45 ( int, m ) 23.43/23.45 ( int, t ) 23.43/23.45 ( int, v ) 23.43/23.45 ( int, w ) 23.43/23.45 ( int, y ) 23.43/23.45 ( int, sa ) 23.43/23.45 ( int, x ) 23.43/23.45 ( int, r ) 23.43/23.45 ( int, m1 ) 23.43/23.45 ( int, skv_14 ) 23.43/23.45 ( int, skv_20 ) 23.43/23.45 ( (fun int int), bit1 ) 23.43/23.45 ( (fun int int), bit0 ) 23.43/23.45 ( (fun int int), succ ) 23.43/23.45 ( (fun int int), pred ) 23.43/23.45 ( (fun int int), (fact_fact int) ) 23.43/23.45 ( (fun int int), zfact ) 23.43/23.45 ( nat, n ) 23.43/23.45 ( nat, tn ) 23.43/23.45 ( bool, fTrue ) 23.43/23.45 ( bool, fFalse ) 23.43/23.45 ( real, pi ) 23.43/23.45 ( (fun nat real), (real_1 nat) ) 23.43/23.45 ( (fun nat real), cos_coeff ) 23.43/23.45 ( (fun nat real), sin_coeff ) 23.43/23.45 ( (fun real real), sin ) 23.43/23.45 ( (fun real real), cos ) 23.43/23.45 ( (fun real real), sqrt ) 23.43/23.45 ( (fun real real), tan ) 23.43/23.45 ( (fun real real), ln ) 23.43/23.45 ( (fun real real), arctan ) 23.43/23.45 ( (fun real real), arcsin ) 23.43/23.45 ( (fun real real), arccos ) 23.43/23.45 ( (fun nat nat), suc ) 23.43/23.45 ( (fun nat nat), (fact_fact nat) ) 23.43/23.45 ( (fun nat nat), nat_size ) 23.43/23.45 ( (fun nat nat), (size_size nat) ) 23.43/23.45 ( (fun nat nat), fact ) 23.43/23.45 ( (filter nat), sequentially ) 23.43/23.45 ( (fun int (fun int rat)), fract ) 23.43/23.45 ( complex, ii ) 23.43/23.45 ( (fun int bool), zOdd ) 23.43/23.45 ( (fun int bool), zprime ) 23.43/23.45 ( (fun int bool), zEven ) 23.43/23.45 ( (fun int bool), nat_neg ) 23.43/23.45 ( (fun int bool), nat_is_nat ) 23.43/23.45 ( (fun int bool), (even_odd_even int) ) 23.43/23.45 ( (fun int bool), twoSqu1091635170sum2sq ) 23.43/23.45 ( (fun int (fun int int)), legacy_zgcd ) 23.43/23.45 ( (fun int (fun int int)), (gcd_gcd int) ) 23.43/23.45 ( (fun int (fun int int)), inv ) 23.43/23.45 ( (fun int (fun int int)), multInv ) 23.43/23.45 ( (fun int (fun int int)), legendre ) 23.43/23.45 ( (fun int (fun int int)), standardRes ) 23.43/23.45 ( (fun int (fun int int)), nat_tsub ) 23.43/23.45 ( (fun int (fun int int)), z3div ) 23.43/23.45 ( (fun int (fun int int)), z3mod ) 23.43/23.45 ( (fun int (fun int int)), int_lcm ) 23.43/23.45 ( (fun int (fun int int)), int_gcd ) 23.43/23.45 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.43/23.45 ( (fun bool bool), fNot ) 23.43/23.45 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.43/23.45 ( (fun bool (fun bool bool)), fconj ) 23.43/23.45 ( (fun bool (fun bool bool)), fdisj ) 23.43/23.45 ( (fun bool (fun bool bool)), fimplies ) 23.43/23.45 ( (fun int (fun int bool)), quadRes ) 23.43/23.45 ( (fun int (fun int bool)), d22set ) 23.43/23.45 ( (fun int (fun int bool)), norRRset ) 23.43/23.45 ( (fun int (fun int bool)), sRStar ) 23.43/23.45 ( (fun int (fun int bool)), sr ) 23.43/23.45 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.43/23.45 ( (fun nat bool), (even_odd_even nat) ) 23.43/23.45 ( (fun nat bool), prime ) 23.43/23.45 ( (fun real complex), cis ) 23.43/23.45 ( (fun nat (fun nat bool)), coprime ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.43/23.45 ( (fun (product_prod int int) bool), frac_1 ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.43/23.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.43/23.45 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.43/23.45 ( (fun (fun int bool) bool), nat_nat_set ) 23.43/23.45 ( (fun nat (fun real real)), root ) 23.43/23.45 ( (fun real (fun real real)), log ) 23.43/23.45 ( (fun real (fun real real)), powr ) 23.43/23.45 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.43/23.45 ( (fun complex complex), cnj ) 23.43/23.45 ( (fun complex complex), expi ) 23.43/23.45 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.43/23.45 ( (fun nat (fun nat nat)), nat_gcd ) 23.43/23.45 ( (fun nat (fun nat nat)), nat_lcm ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.43/23.45 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.43/23.45 ( (fun int (fun (fun int bool) bool)), resSet ) 23.43/23.45 ( (fun int nat), nat_1 ) 23.43/23.45 ( (fun int nat), phi ) 23.43/23.45 ( (fun complex real), re ) 23.43/23.45 ( (fun complex real), im ) 23.43/23.45 ( (fun complex real), arg ) 23.43/23.45 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.43/23.45 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.43/23.45 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.43/23.45 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.43/23.45 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.43/23.45 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.43/23.45 ( (fun (product_prod nat nat) bool), pred_nat ) 23.43/23.45 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.43/23.45 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.43/23.45 ( (fun (fun int bool) int), (the int) ) 23.43/23.45 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.43/23.45 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.43/23.45 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.43/23.45 ( (fun real (fun real complex)), rcis ) 23.43/23.45 ( (fun real (fun real complex)), complex_1 ) 23.43/23.45 ( (fun int (fun int (fun int bool))), zcong ) 23.43/23.45 ( (fun int (fun int (fun int bool))), wset ) 23.43/23.45 ( (fun int (fun int (fun int bool))), noXRRset ) 23.43/23.45 ( (fun int (fun int (fun int bool))), bnorRset ) 23.43/23.45 ( (fun int (fun int (fun int bool))), zcongm ) 23.43/23.45 ( (fun real nat), natceiling ) 23.43/23.45 ( (fun real nat), natfloor ) 23.43/23.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.43/23.45 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.43/23.45 ( (fun int real), (real_1 int) ) 23.43/23.45 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.43/23.45 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.43/23.45 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.43/23.45 ( (fun complex nat), (size_size complex) ) 23.43/23.45 ( (fun complex nat), complex_size ) 23.43/23.45 ( (fun (fun nat rat) bool), vanishes ) 23.43/23.45 ( (fun (product_prod int int) rat), frct ) 23.43/23.45 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.43/23.45 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.43/23.45 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.43/23.45 ( (fun rat real), ratreal ) 23.43/23.45 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.43/23.45 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.43/23.45 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.43/23.45 ( (fun rat (product_prod int int)), quotient_of ) 23.43/23.45 ( (fun int (fun nat nat)), nat_aux ) 23.43/23.45 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.43/23.45 ( (fun int (list int)), quickc666637781d_zero ) 23.43/23.45 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.43/23.45 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.43/23.45 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.43/23.45 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.43/23.45 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.43/23.45 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.43/23.45 ( (fun code_code_numeral int), code_int_of ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155388 $$unsorted) (BOUND_VARIABLE_155389 $$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_155389) _let_3))) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_155388) _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_155389) BOUND_VARIABLE_155388)) _let_3))))))) ) 23.43/23.45 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.43/23.45 ( 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))) ) 23.43/23.45 ( int, v, y ) 23.43/23.45 ( int, v, sa ) 23.43/23.45 ( int, v, x ) 23.43/23.45 ( int, v, r ) 23.43/23.45 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.45 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.45 ( int, w, y ) 23.43/23.45 ( int, w, sa ) 23.43/23.45 ( int, w, x ) 23.43/23.45 ( int, w, r ) 23.43/23.45 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.45 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.45 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.43/23.45 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.45 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.43/23.45 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, skv_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))) ) 23.43/23.45 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( 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))))) ) 23.43/23.45 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( 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)))) ) 23.43/23.45 ( complex, ii, ii ) 23.43/23.45 ( 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)) ) 23.43/23.45 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) Ya) Xa))) (= Xa (hAPP _let_0 real (complete_Sup_Sup real) (hAPP real _let_0 (hAPP real (fun real _let_0) (ord_atLeastLessThan real) Ya) Xa))))) ) 23.43/23.45 ( pi, (zero_zero real) ) 23.43/23.45 ( pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (zero_zero real), pi ) 23.43/23.45 ( (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (zero_zero real), skv_2 ) 23.43/23.45 ( (zero_zero real), skv_9 ) 23.43/23.45 ( (zero_zero real), skv_12 ) 23.43/23.45 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.43/23.45 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero real) ) 23.43/23.45 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)), pi ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155424 $$unsorted) (BOUND_VARIABLE_155425 $$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_155425))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155425) _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_155425) (hAPP nat nat suc BOUND_VARIABLE_155424))) _let_2)))))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), s ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), s1 ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), v ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), w ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), y ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), x ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), skv_6 ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), skv_7 ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), skv_16 ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), skv_23 ) 23.43/23.45 ( int, (hAPP nat nat suc (zero_zero nat)), skv_24 ) 23.43/23.45 ( complex, (hAPP nat nat suc (zero_zero nat)), ii ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((N $$unsorted) (V $$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))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP int nat _let_1 V)) N)) (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP int nat _let_1 (hAPP int int succ V))) N)))))) ) 23.43/23.45 ( (one_one nat), pls ) 23.43/23.45 ( (one_one nat), (hAPP int int bit1 pls) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((N $$unsorted) (V $$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)))) (= (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) V)) N)) (hAPP nat nat (hAPP nat _let_0 _let_1 (one_one nat)) N))))) ) 23.43/23.45 ( (one_one nat), (hAPP int int bit1 pls) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int _let_0 (gcd_gcd int) M))) (= (hAPP int int _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) M) N)) (hAPP int int _let_1 N)))) ) 23.43/23.45 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.43/23.45 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.43/23.45 ( (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) ) 23.43/23.45 ( (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) ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.43/23.45 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.45 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X $$unsorted)) (= (hAPP real real ln X) (hAPP real real (hAPP real (fun real real) log (hAPP real real (exp real) (one_one real))) X)) ) 23.43/23.45 ( (one_one real) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155510 $$unsorted) (BOUND_VARIABLE_155511 $$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_155510) (hAPP X_a _let_0 (ord_atMost X_a) BOUND_VARIABLE_155511))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) BOUND_VARIABLE_155510) BOUND_VARIABLE_155511))))) ) 23.43/23.45 ( int, (one_one int), t ) 23.43/23.45 ( int, min, pls ) 23.43/23.45 ( int, min, min ) 23.43/23.45 ( int, (zero_zero int), pls ) 23.43/23.45 ( int, (zero_zero int), (one_one int) ) 23.43/23.45 ( int, (zero_zero int), min ) 23.43/23.45 ( int, (zero_zero int), s ) 23.43/23.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.45 ( int, (zero_zero int), skv_4 ) 23.43/23.45 ( int, (zero_zero int), skv_5 ) 23.43/23.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.45 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( real, (zero_zero real), pi ) 23.43/23.45 ( 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)))) ) 23.43/23.45 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( real, (zero_zero real), skv_10 ) 23.43/23.45 ( real, (zero_zero real), skv_11 ) 23.43/23.45 ( real, (zero_zero real), skv_15 ) 23.43/23.45 ( real, (zero_zero real), skv_18 ) 23.43/23.45 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.43/23.45 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155529 $$unsorted) (BOUND_VARIABLE_155530 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (dvd_dvd X_a))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_155529) BOUND_VARIABLE_155530)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_155529)) BOUND_VARIABLE_155530)))))) ) 23.43/23.45 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)) ) 23.43/23.45 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155606 $$unsorted)) (or (not (sgn_div_norm X_a)) (= (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_155606) (hAPP X_a X_a (hAPP real (fun X_a X_a) (scaleR_scaleR X_a) (hAPP real real (inverse_inverse real) (hAPP X_a real (norm_norm X_a) BOUND_VARIABLE_155606))) BOUND_VARIABLE_155606))) ) 23.43/23.45 ( rat, (zero_zero rat) ) 23.43/23.45 ( real, (zero_zero real) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (= (hAPP real real _let_1 (hAPP real real _let_0 X)) (hAPP real real _let_0 (hAPP real real _let_1 X)))))) ) 23.43/23.45 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((Ya $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (hAPP int _let_0 (ord_less_eq int) (zero_zero int)))) (let ((_let_2 (fun _let_0 bool))) (let ((_let_3 (member int))) (let ((_let_4 (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min)))) (or (not (hBOOL (hAPP int bool _let_1 Xa))) (not (hBOOL (hAPP int bool _let_1 Ya))) (= (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Xa) zEven))) (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_3 Ya) zEven))) (= (hAPP nat int _let_4 (hAPP int nat nat_1 Ya)) (hAPP nat int _let_4 (hAPP int nat nat_1 Xa))))))))) ) 23.43/23.45 ( pls, (one_one int) ) 23.43/23.45 ( (one_one int), pls ) 23.43/23.45 ( (one_one int), (one_one int) ) 23.43/23.45 ( min, min ) 23.43/23.45 ( min, s ) 23.43/23.45 ( s, min ) 23.43/23.45 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.45 ( skv_4, skv_4 ) 23.43/23.45 ( skv_4, skv_5 ) 23.43/23.45 ( skv_5, skv_4 ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (not (= (hAPP int int bit0 K_4) (hAPP int int bit1 L_4))) ) 23.43/23.45 ( pls, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.43/23.45 ( (hAPP int int bit1 pls), pls ) 23.43/23.45 ( min, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit1 pls) ) 23.43/23.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)), min ) 23.43/23.45 ( (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 A_3) B_2)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_3) B_2)) (one_one rat))))))) ) 23.43/23.45 ( (one_one int), (one_one int) ) 23.43/23.45 ( (one_one int), t ) 23.43/23.45 ( min, min ) 23.43/23.45 ( min, (zero_zero int) ) 23.43/23.45 ( (zero_zero int), pls ) 23.43/23.45 ( (zero_zero int), (one_one int) ) 23.43/23.45 ( (zero_zero int), min ) 23.43/23.45 ( (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))) ) 23.43/23.45 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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))) ) 23.43/23.45 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.45 ( 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))) ) 23.43/23.45 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.45 ( 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))) ) 23.43/23.45 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155648 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) BOUND_VARIABLE_155648)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_155648))))) ) 23.43/23.45 ( real, (one_one int) ) 23.43/23.45 ( real, (zero_zero int) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted)) (or (not (ring_1 X_a)) (= (one_one X_a) (hAPP int X_a (ring_1_of_int X_a) (one_one int)))) ) 23.43/23.45 ( rat ) 23.43/23.45 ( int ) 23.43/23.45 ( nat ) 23.43/23.45 ( real ) 23.43/23.45 ( complex ) 23.43/23.45 ( quickcheck_code_int ) 23.43/23.45 ( code_code_numeral ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155717 $$unsorted) (BOUND_VARIABLE_155718 $$unsorted) (BOUND_VARIABLE_155719 $$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_155719))) (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_155718) _let_0) _let_6))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_155719)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) (hAPP X_a real BOUND_VARIABLE_155717 X_1)))) )) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_155719)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real BOUND_VARIABLE_155717 X_1)) (hAPP X_a real BOUND_VARIABLE_155718 X_1)))) )) (hBOOL (hAPP _let_1 bool (hAPP real _let_2 (hAPP _let_3 _let_4 _let_5 BOUND_VARIABLE_155717) _let_0) _let_6)))))))))) ) 23.43/23.45 ( 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)))) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (hAPP int (fun int rat) fract (one_one int)) (hAPP int int (number_number_of int) K_4)) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4))) ) 23.43/23.45 ( pls ) 23.43/23.45 ( (hAPP int int bit1 pls) ) 23.43/23.45 ( min ) 23.43/23.45 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.45 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.45 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.45 ) 23.43/23.45 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (div_div 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 (even_odd_even int) X))) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) X) (one_one int))) _let_2) (hAPP int int (hAPP int _let_0 _let_1 X) _let_2)))))) ) 23.43/23.45 ( (one_one int) ) 23.43/23.45 ( (zero_zero int) ) 23.43/23.45 ( (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)))) ) 23.43/23.45 ( (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) ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.45 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.45 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.46 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.46 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.43/23.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((I_1 $$unsorted)) (= (hAPP int nat nat_1 (hAPP quickcheck_code_int int quickcheck_int_of I_1)) (hAPP quickcheck_code_int nat quickcheck_nat_of I_1)) ) 23.43/23.46 ( (zero_zero quickcheck_code_int) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (plus_plus nat))) (= (hAPP nat nat (hAPP nat _let_0 _let_1 M) N) (hAPP nat nat (hAPP nat _let_0 _let_1 N) M)))) ) 23.43/23.46 ( (one_one nat), (one_one nat) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((X_a $$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))))) ) 23.43/23.46 ( rat ) 23.43/23.46 ( int ) 23.43/23.46 ( (fun int int) ) 23.43/23.46 ( nat ) 23.43/23.46 ( bool ) 23.43/23.46 ( real ) 23.43/23.46 ( (fun nat real) ) 23.43/23.46 ( (fun real real) ) 23.43/23.46 ( (fun nat nat) ) 23.43/23.46 ( complex ) 23.43/23.46 ( (fun int bool) ) 23.43/23.46 ( (product_prod int int) ) 23.43/23.46 ( (fun (product_prod int int) int) ) 23.43/23.46 ( (fun bool bool) ) 23.43/23.46 ( (fun int (fun int bool)) ) 23.43/23.46 ( (fun nat bool) ) 23.43/23.46 ( (fun nat (fun nat bool)) ) 23.43/23.46 ( (fun (product_prod int int) bool) ) 23.43/23.46 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.43/23.46 ( (fun real bool) ) 23.43/23.46 ( quickcheck_code_int ) 23.43/23.46 ( code_code_numeral ) 23.43/23.46 ( (fun nat (product_prod int int)) ) 23.43/23.46 ( (product_prod real real) ) 23.43/23.46 ( (product_prod nat nat) ) 23.43/23.46 ( (fun (product_prod nat nat) bool) ) 23.43/23.46 ( (fun nat (fun (product_prod nat nat) bool)) ) 23.43/23.46 ( (fun nat (product_prod nat nat)) ) 23.43/23.46 ( (fun int (fun int (fun int bool))) ) 23.43/23.46 ( (fun int real) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (times_times int) Z_1) (one_one int))) ) 23.43/23.46 ( pls ) 23.43/23.46 ( min ) 23.43/23.46 ( s ) 23.43/23.46 ( s1 ) 23.43/23.46 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.46 ( m ) 23.43/23.46 ( (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))) ) 23.43/23.46 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.46 ( t ) 23.43/23.46 ( v ) 23.43/23.46 ( w ) 23.43/23.46 ( y ) 23.43/23.46 ( sa ) 23.43/23.46 ( x ) 23.43/23.46 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.43/23.46 ( r ) 23.43/23.46 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.43/23.46 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.43/23.46 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.46 ( m1 ) 23.43/23.46 ( skv_13 ) 23.43/23.46 ( skv_14 ) 23.43/23.46 ( skv_19 ) 23.43/23.46 ( skv_20 ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_155878 $$unsorted) (BOUND_VARIABLE_155879 $$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_155878)) BOUND_VARIABLE_155879) (hAPP X_a X_a _let_0 (hAPP nat X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_155878) BOUND_VARIABLE_155879))))))) ) 23.43/23.46 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V) pls))) (= (zero_zero nat) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat (number_number_of nat) V)) (one_one nat)))) ) 23.43/23.46 ( pls ) 23.43/23.46 ( (hAPP int int bit1 pls) ) 23.43/23.46 ( (one_one int) ) 23.43/23.46 ( min ) 23.43/23.46 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.46 ( (zero_zero int) ) 23.43/23.46 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.43/23.46 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) V) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat _let_0 V)) (one_one nat)) (hAPP int nat _let_0 (hAPP int int pred V))))) ) 23.43/23.46 ( pls ) 23.43/23.46 ( (one_one int) ) 23.43/23.46 ( min ) 23.43/23.46 ( (zero_zero int) ) 23.43/23.46 ( (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)))) (hAPP int int (abs_abs int) w)) ) 23.43/23.46 ( (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)))) (hAPP int int (abs_abs int) v)) ) 23.43/23.46 ( (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.43/23.46 ( (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (or (not (hBOOL (hAPP int bool _let_0 X))) (hBOOL (hAPP int bool _let_0 (hAPP int int (fact_fact int) X))))) ) 23.43/23.46 ( (one_one int) ) 23.43/23.46 ( (zero_zero int) ) 23.43/23.46 ) 23.43/23.46 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156073 $$unsorted) (BOUND_VARIABLE_156074 $$unsorted) (BOUND_VARIABLE_156075 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_156073))) (or (not (cancel_semigroup_add X_a)) (= (= (ti X_a BOUND_VARIABLE_156074) (ti X_a BOUND_VARIABLE_156075)) (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_156075) (hAPP X_a X_a _let_0 BOUND_VARIABLE_156074))))) ) 23.43/23.46 ( int, (one_one int), s1, s1 ) 23.43/23.46 ( int, (one_one int), v, s1 ) 23.43/23.46 ( 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)))), pls, pls ) 23.43/23.46 ( 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)))), min, min ) 23.43/23.46 ( 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)))), s1, s1 ) 23.43/23.46 ( 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)))), t, t ) 23.43/23.46 ( 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)))), x, x ) 23.43/23.46 ( 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)))), r, r ) 23.43/23.46 ( 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)))), m1, m1 ) 23.43/23.46 ( 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)))), skv_20, skv_20 ) 23.43/23.46 ( 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), s1, s1 ) 23.43/23.46 ( 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), s1, v ) 23.43/23.46 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s1 ) 23.43/23.46 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), r, m ) 23.43/23.46 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 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(hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), s, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), sa, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), t, y ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), y, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))), m1, m1 ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), pls, pls ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), min, min ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), s1, s1 ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), t, t ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), x, x ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), r, r ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), m1, m1 ) 23.43/23.46 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), skv_14, x ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), pls, pls ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), pls, w ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), min, min ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), s1, s1 ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), t, t ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), r, r ) 23.43/23.46 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), pls, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), w, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), pls, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), x, x ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), x, skv_14 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), pls, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), x, x ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), skv_20, skv_20 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), pls, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), x, x ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))), skv_20, skv_20 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), pls, pls ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), min, min ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), s1, s1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), t, t ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), x, x ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), r, r ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), m1, m1 ) 23.43/23.46 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), skv_20, skv_20 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, pls ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, min ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s1 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), t, t ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), x, x ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), r, r ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), m1, m1 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_20, skv_20 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), pls, pls ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), min, min ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), s1, s1 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), t, t ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), x, x ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), r, r ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), m1, m1 ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), skv_20, skv_20 ) 23.43/23.47 ( nat, (one_one nat), n, n ) 23.43/23.47 ( nat, (one_one nat), n, tn ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156123 $$unsorted)) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) BOUND_VARIABLE_156123)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (zero_zero X_a)) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_156123))))) ) 23.43/23.47 ( real, (one_one int) ) 23.43/23.47 ( real, (zero_zero int) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool _let_0 Na))) (= (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_2 (fun (fun int bool) (fun int bool)) (combs int bool bool) (hAPP (fun int bool) _let_2 (hAPP (fun bool _let_1) (fun (fun int bool) _let_2) (combb bool _let_1 int) fconj) _let_0)) (hAPP int (fun int bool) (hAPP _let_3 _let_3 (combc int int bool) (ord_less int)) Na)))) (hAPP int nat nat_1 Na))))))) ) 23.43/23.47 ( pls ) 23.43/23.47 ( (one_one int) ) 23.43/23.47 ( min ) 23.43/23.47 ( (zero_zero int) ) 23.43/23.47 ( s ) 23.43/23.47 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.47 ( t ) 23.43/23.47 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.47 ( skv_4 ) 23.43/23.47 ( skv_5 ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156146 $$unsorted) (BOUND_VARIABLE_156147 $$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_156146)) BOUND_VARIABLE_156147) (hAPP X_a X_a _let_0 (hAPP X_a X_a (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_156146) BOUND_VARIABLE_156147))))))) ) 23.43/23.47 ( int, pls, (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))) m1))) ) 23.43/23.47 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.47 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.47 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.47 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( 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))), m1 ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.47 ( 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_21 ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.47 ( int, y, v ) 23.43/23.47 ( int, y, w ) 23.43/23.47 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, sa, v ) 23.43/23.47 ( int, sa, w ) 23.43/23.47 ( int, x, v ) 23.43/23.47 ( int, x, w ) 23.43/23.47 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.47 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, r, v ) 23.43/23.47 ( int, r, w ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.47 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.47 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.47 ( 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)))))) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( complex, ii, ii ) 23.43/23.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.47 ( 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 ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (BOUND_VARIABLE_156190 $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) A_3) B_2))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) F) X_1))) )) (not (forall ((X_1 $$unsorted)) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X_1) B_2))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) X_1))) (hBOOL (hAPP real bool (hAPP real _let_0 (hAPP (fun real real) (fun real _let_0) (deriv real) F) X_1) (zero_zero real))))) )) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 A_3) BOUND_VARIABLE_156190))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 BOUND_VARIABLE_156190) B_2))) (= (hAPP real real F A_3) (hAPP real real F BOUND_VARIABLE_156190))))) ) 23.43/23.47 ( sin, (zero_zero real), pi, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.47 ( cos, (zero_zero real), skv_2, skv_10 ) 23.43/23.47 ( sqrt, (zero_zero real), skv_9, skv_11 ) 23.43/23.47 ( tan, (zero_zero real), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.47 ( (inverse_inverse real), (zero_zero real), skv_12, skv_15 ) 23.43/23.47 ( (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.47 ( arctan, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((W $$unsorted)) (let ((_let_0 (uminus_uminus int))) (let ((_let_1 (one_one int))) (let ((_let_2 (product_prod int 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_1) _let_3) (hAPP _let_2 int (product_fst int int) (hAPP _let_2 _let_2 negateSnd (hAPP int _let_2 (hAPP int (fun int _let_2) negDivAlg (hAPP int int _let_0 _let_1)) (hAPP int int _let_0 _let_3)))))))))) ) 23.43/23.47 ( pls ) 23.43/23.47 ( (hAPP int int bit1 pls) ) 23.43/23.47 ( min ) 23.43/23.47 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.47 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.47 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP int rat (ring_1_of_int rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract K_4) (one_one int))) ) 23.43/23.47 ( (one_one int) ) 23.43/23.47 ( (zero_zero int) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156223 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (let ((_let_2 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_156223))) (or (not (linordered_idom X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 _let_2) _let_2) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156223) BOUND_VARIABLE_156223)))))) ) 23.43/23.47 ( int, v ) 23.43/23.47 ( int, w ) 23.43/23.47 ( int, skv_14 ) 23.43/23.47 ( int, skv_20 ) 23.43/23.47 ( complex, ii ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP rat real ratreal X)) (hAPP rat real ratreal (hAPP rat rat (uminus_uminus rat) X))) ) 23.43/23.47 ( (one_one rat) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((Z_1 $$unsorted)) (= Z_1 (hAPP complex complex cnj (hAPP complex complex cnj Z_1))) ) 23.43/23.47 ( (zero_zero complex) ) 23.43/23.47 ( (one_one complex) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156264 $$unsorted) (BOUND_VARIABLE_156265 $$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_156264) BOUND_VARIABLE_156265)) BOUND_VARIABLE_156265) (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_156264) (one_one X_a))) BOUND_VARIABLE_156265)))))) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.47 ( 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 (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( 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), m1 ) 23.43/23.47 ( 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 (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.47 ( 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_21 ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( 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))), m1 ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.47 ( 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_21 ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.47 ( int, y, v ) 23.43/23.47 ( int, y, w ) 23.43/23.47 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, sa, v ) 23.43/23.47 ( int, sa, w ) 23.43/23.47 ( int, x, v ) 23.43/23.47 ( int, x, w ) 23.43/23.47 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.47 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, r, v ) 23.43/23.47 ( int, r, w ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.47 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.47 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.47 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.47 ( 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)))))) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( complex, ii, ii ) 23.43/23.47 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.47 ( 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 ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156294 $$unsorted) (BOUND_VARIABLE_156295 $$unsorted) (BOUND_VARIABLE_156296 $$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_156295))) (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_156296) _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_156294) _let_3)) BOUND_VARIABLE_156296)) (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_156294))) (or _let_5 (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_156296))))) (or (not _let_4) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156294) _let_6))))))))))))) ) 23.43/23.47 ( 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))) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156378 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (times_times X_a))) (or (not (monoid_mult 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_1 BOUND_VARIABLE_156378) BOUND_VARIABLE_156378)) BOUND_VARIABLE_156378) (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_156378) (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 23.43/23.47 ( int, s ) 23.43/23.47 ( int, s1 ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, v ) 23.43/23.47 ( int, w ) 23.43/23.47 ( int, y ) 23.43/23.47 ( int, x ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.43/23.47 ( int, skv_6 ) 23.43/23.47 ( int, skv_7 ) 23.43/23.47 ( int, skv_16 ) 23.43/23.47 ( int, skv_23 ) 23.43/23.47 ( int, skv_24 ) 23.43/23.47 ( real, (hAPP int real (number_number_of real) min) ) 23.43/23.47 ( 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)))) ) 23.43/23.47 ( complex, ii ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156399 $$unsorted) (BOUND_VARIABLE_156400 $$unsorted) (BOUND_VARIABLE_156401 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_156401))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (one_one X_a)) BOUND_VARIABLE_156401))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP nat X_a _let_1 BOUND_VARIABLE_156399)) (hAPP nat X_a _let_1 BOUND_VARIABLE_156400)))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_156399) BOUND_VARIABLE_156400))))) ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156424 $$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_156424))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_156424))))) ) 23.43/23.47 ( real, (zero_zero real) ) 23.43/23.47 ( complex, ii ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156537 $$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_156537)) (one_one int))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_156537) (one_one X_a))))) ) 23.43/23.47 ( int, (one_one int) ) 23.43/23.47 ( int, min ) 23.43/23.47 ( int, (zero_zero int) ) 23.43/23.47 ( int, s ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, t ) 23.43/23.47 ( int, m1 ) 23.43/23.47 ( int, skv_4 ) 23.43/23.47 ( int, skv_5 ) 23.43/23.47 ( nat, (zero_zero nat) ) 23.43/23.47 ( real, pi ) 23.43/23.47 ( 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)))) ) 23.43/23.47 ( real, (one_one real) ) 23.43/23.47 ( real, (zero_zero real) ) 23.43/23.47 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.47 ( 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))))) ) 23.43/23.47 ( 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)) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156562 $$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_156562))) (not (forall ((N_1 $$unsorted)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (inverse_inverse X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (hAPP nat nat suc N_1)))) BOUND_VARIABLE_156562))) ))) ) 23.43/23.47 ( int, pls ) 23.43/23.47 ( int, (one_one int) ) 23.43/23.47 ( int, min ) 23.43/23.47 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.47 ( nat, n ) 23.43/23.47 ( nat, tn ) 23.43/23.47 ( real, pi ) 23.43/23.47 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.47 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.47 ( real, skv_2 ) 23.43/23.47 ( real, skv_9 ) 23.43/23.47 ( real, skv_12 ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156597 $$unsorted) (BOUND_VARIABLE_156598 $$unsorted) (BOUND_VARIABLE_156599 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (dvd_dvd nat))) (let ((_let_2 (fun nat X_a))) (or (not (order X_a)) (not (hBOOL (hAPP _let_2 bool (hAPP (fun nat _let_0) (fun _let_2 bool) (mono nat X_a) _let_1) BOUND_VARIABLE_156599))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 BOUND_VARIABLE_156597) BOUND_VARIABLE_156598))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (hAPP nat X_a BOUND_VARIABLE_156599 BOUND_VARIABLE_156597)) (hAPP nat X_a BOUND_VARIABLE_156599 BOUND_VARIABLE_156598))))))) ) 23.43/23.47 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 23.43/23.47 ( int, (zero_zero nat), (one_one nat), (semiring_1_of_nat int) ) 23.43/23.47 ( int, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))), (semiring_1_of_nat int) ) 23.43/23.47 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((Z_1 $$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)))))) ) 23.43/23.47 ( pls ) 23.43/23.47 ( (one_one int) ) 23.43/23.47 ( min ) 23.43/23.47 ( s ) 23.43/23.47 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.47 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.43/23.47 ( (hAPP nat int (semiring_1_of_nat int) n) ) 23.43/23.47 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.47 ( skv_4 ) 23.43/23.47 ( skv_5 ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat nat))) (= (hAPP nat nat (hAPP nat _let_0 (plus_plus nat) Z_1) Z_1) (hAPP nat nat (hAPP nat _let_0 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) Z_1))) ) 23.43/23.47 ( (one_one nat) ) 23.43/23.47 ) 23.43/23.47 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156754 $$unsorted) (BOUND_VARIABLE_156755 $$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_156754) BOUND_VARIABLE_156755)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_156754)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_156755))))))) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( 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 ) 23.43/23.47 ( 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))), m1 ) 23.43/23.47 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.47 ( 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_21 ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.47 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.47 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.47 ( int, y, v ) 23.43/23.47 ( int, y, w ) 23.43/23.47 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, sa, v ) 23.43/23.47 ( int, sa, w ) 23.43/23.47 ( int, x, v ) 23.43/23.47 ( int, x, w ) 23.43/23.47 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.47 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.47 ( int, r, v ) 23.43/23.47 ( int, r, w ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.47 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.47 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.48 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.48 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.48 ( 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)))))) ) 23.43/23.48 ( 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 ) 23.43/23.48 ( complex, ii, ii ) 23.43/23.48 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.48 ( 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 ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156772 $$unsorted) (BOUND_VARIABLE_156773 $$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 (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_156773)))) (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_156772) BOUND_VARIABLE_156773))) (or (= (zero_zero nat) BOUND_VARIABLE_156773) (and (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_156772)) (not _let_2)) (and _let_2 (not (= _let_0 (ti X_a BOUND_VARIABLE_156772)))))))))) ) 23.43/23.48 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_0 (hAPP int (fun nat int) (power_power int) X))) (= (hAPP nat int _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) Y) Z_1)) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP nat int _let_0 Y)) (hAPP nat int _let_0 Z_1)))) ) 23.43/23.48 ( s, (one_one nat), (one_one nat) ) 23.43/23.48 ( s1, (one_one nat), (one_one nat) ) 23.43/23.48 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (one_one nat), (one_one nat) ) 23.43/23.48 ( v, (one_one nat), (one_one nat) ) 23.43/23.48 ( w, (one_one nat), (one_one nat) ) 23.43/23.48 ( y, (one_one nat), (one_one nat) ) 23.43/23.48 ( x, (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (one_one nat), (one_one nat) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (one_one nat), (one_one nat) ) 23.43/23.48 ( skv_6, (one_one nat), (one_one nat) ) 23.43/23.48 ( skv_7, (one_one nat), (one_one nat) ) 23.43/23.48 ( skv_16, (one_one nat), (one_one nat) ) 23.43/23.48 ( skv_23, (one_one nat), (one_one nat) ) 23.43/23.48 ( skv_24, (one_one nat), (one_one nat) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zEven))) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) (div_mod int) Xa) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.48 ( (one_one int) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$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)))))) ) 23.43/23.48 ( rat ) 23.43/23.48 ( int ) 23.43/23.48 ( (fun int int) ) 23.43/23.48 ( nat ) 23.43/23.48 ( bool ) 23.43/23.48 ( real ) 23.43/23.48 ( (fun real real) ) 23.43/23.48 ( (fun nat nat) ) 23.43/23.48 ( complex ) 23.43/23.48 ( (product_prod int int) ) 23.43/23.48 ( (fun bool bool) ) 23.43/23.48 ( (fun nat bool) ) 23.43/23.48 ( (fun nat (fun nat bool)) ) 23.43/23.48 ( quickcheck_code_int ) 23.43/23.48 ( code_code_numeral ) 23.43/23.48 ( (fun nat (product_prod int int)) ) 23.43/23.48 ( (product_prod real real) ) 23.43/23.48 ( (product_prod nat nat) ) 23.43/23.48 ( (fun (product_prod nat nat) bool) ) 23.43/23.48 ( (fun nat (fun (product_prod nat nat) bool)) ) 23.43/23.48 ( (fun nat (product_prod nat nat)) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((Xa $$unsorted) (Na $$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) Na))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (hAPP int real (number_number_of real) Na))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP real nat natceiling Xa)) (hAPP int nat (number_number_of nat) Na))))))) ) 23.43/23.48 ( (hAPP real real (hAPP 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)) ) 23.43/23.48 ( skv_10, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156864 $$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_156864)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_156864)) _let_2))))))) ) 23.43/23.48 ( int, pls ) 23.43/23.48 ( int, (one_one int) ) 23.43/23.48 ( int, min ) 23.43/23.48 ( int, s ) 23.43/23.48 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, skv_4 ) 23.43/23.48 ( int, skv_5 ) 23.43/23.48 ( real, pi ) 23.43/23.48 ( 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)))) ) 23.43/23.48 ( real, (one_one real) ) 23.43/23.48 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( 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) ) 23.43/23.48 ( real, skv_10 ) 23.43/23.48 ( real, skv_11 ) 23.43/23.48 ( real, skv_15 ) 23.43/23.48 ( real, skv_18 ) 23.43/23.48 ( complex, ii ) 23.43/23.48 ( complex, (one_one complex) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_156977 $$unsorted) (BOUND_VARIABLE_156978 $$unsorted) (BOUND_VARIABLE_156979 $$unsorted) (BOUND_VARIABLE_156980 $$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 (ord_less X_a))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_156979) BOUND_VARIABLE_156980))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 BOUND_VARIABLE_156977) BOUND_VARIABLE_156978))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 _let_2) BOUND_VARIABLE_156979))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_2) BOUND_VARIABLE_156977))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_3 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_156979) BOUND_VARIABLE_156977)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_156980) BOUND_VARIABLE_156978)))))))))) ) 23.43/23.48 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (Xa $$unsorted) (Ya $$unsorted)) (let ((_let_0 (product_prod X_a X_b))) (let ((_let_1 (product_prod X_a X_c))) (= (hAPP _let_1 _let_0 (hAPP (fun X_c X_b) (fun _let_1 _let_0) (product_apsnd X_c X_b X_a) F) (hAPP X_c _let_1 (hAPP X_a (fun X_c _let_1) (product_Pair X_a X_c) Xa) Ya)) (hAPP X_b _let_0 (hAPP X_a (fun X_b _let_0) (product_Pair X_a X_b) Xa) (hAPP X_c X_b F Ya))))) ) 23.43/23.48 ( int, int, int, (fact_fact int), (one_one int), (zero_zero int) ) 23.43/23.48 ( int, int, int, (fact_fact int), (zero_zero int), (zero_zero int) ) 23.43/23.48 ( int, int, int, (fact_fact int), s, (zero_zero int) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$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)))) ) 23.43/23.48 ( rat ) 23.43/23.48 ( int ) 23.43/23.48 ( nat ) 23.43/23.48 ( bool ) 23.43/23.48 ( real ) 23.43/23.48 ( (filter nat) ) 23.43/23.48 ( (fun int bool) ) 23.43/23.48 ( (product_prod int int) ) 23.43/23.48 ( (fun nat bool) ) 23.43/23.48 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.43/23.48 ( (product_prod real real) ) 23.43/23.48 ( (filter real) ) 23.43/23.48 ( (product_prod nat nat) ) 23.43/23.48 ( (fun nat rat) ) 23.43/23.48 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157069 $$unsorted) (BOUND_VARIABLE_157070 $$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_157070))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_157070) BOUND_VARIABLE_157069))))) ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.43/23.48 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.43/23.48 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.43/23.48 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.43/23.48 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.43/23.48 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.43/23.48 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.43/23.48 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.43/23.48 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.43/23.48 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((A_3 $$unsorted) (C $$unsorted) (D_1 $$unsorted) (B_2 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int rat))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (times_times int))) (or (= _let_2 (ti int B_2)) (= _let_2 (ti int D_1)) (= (= (hAPP int rat (hAPP int _let_1 fract C) D_1) (hAPP int rat (hAPP int _let_1 fract A_3) B_2)) (= (hAPP int int (hAPP int _let_0 _let_3 C) B_2) (hAPP int int (hAPP int _let_0 _let_3 A_3) D_1)))))))) ) 23.43/23.48 ( (one_one int), (zero_zero int), s1, s1 ) 23.43/23.48 ( (zero_zero int), (one_one int), v, v ) 23.43/23.48 ( (zero_zero int), (zero_zero int), s1, s1 ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (div_div int) A_1) B)) (one_one int)))))) ) 23.43/23.48 ( (one_one int), (one_one int) ) 23.43/23.48 ( (zero_zero int), (one_one int) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less_eq rat) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int (fun int int) (div_div int) A_1) B))) (hAPP int rat (hAPP int (fun int rat) fract A_1) B))) ) 23.43/23.48 ( (one_one int), (one_one int) ) 23.43/23.48 ( (zero_zero int), (one_one int) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (hAPP real (fun real real) (inverse_divide real) X) (hAPP real real (abs_abs real) X)) (hAPP real real (sgn_sgn real) X)) ) 23.43/23.48 ( pi ) 23.43/23.48 ( (one_one real) ) 23.43/23.48 ( (zero_zero real) ) 23.43/23.48 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.48 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157122 $$unsorted) (BOUND_VARIABLE_157123 $$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_157122) BOUND_VARIABLE_157123))) (= (ti X_a BOUND_VARIABLE_157122) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (ord_min X_a) BOUND_VARIABLE_157123) BOUND_VARIABLE_157122))) ) 23.43/23.48 ( int, (one_one int), t ) 23.43/23.48 ( int, min, pls ) 23.43/23.48 ( int, min, min ) 23.43/23.48 ( int, (zero_zero int), pls ) 23.43/23.48 ( int, (zero_zero int), (one_one int) ) 23.43/23.48 ( int, (zero_zero int), min ) 23.43/23.48 ( int, (zero_zero int), s ) 23.43/23.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (zero_zero int), skv_4 ) 23.43/23.48 ( int, (zero_zero int), skv_5 ) 23.43/23.48 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.48 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( real, (zero_zero real), pi ) 23.43/23.48 ( 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)))) ) 23.43/23.48 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( real, (zero_zero real), skv_10 ) 23.43/23.48 ( real, (zero_zero real), skv_11 ) 23.43/23.48 ( real, (zero_zero real), skv_15 ) 23.43/23.48 ( real, (zero_zero real), skv_18 ) 23.43/23.48 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.43/23.48 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157180 $$unsorted) (BOUND_VARIABLE_157181 $$unsorted) (BOUND_VARIABLE_157182 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_157180))) (or (not (ordere1490568538miring X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157181) BOUND_VARIABLE_157182))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_157180))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_157181)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_157182))))))) ) 23.43/23.48 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.48 ) 23.43/23.48 (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)))) ) 23.43/23.48 ( rat ) 23.43/23.48 ( int ) 23.43/23.48 ( (fun int int) ) 23.43/23.48 ( nat ) 23.43/23.48 ( bool ) 23.43/23.48 ( real ) 23.43/23.48 ( (fun nat real) ) 23.43/23.48 ( (fun real real) ) 23.43/23.48 ( complex ) 23.43/23.48 ( (fun int bool) ) 23.43/23.48 ( (product_prod int int) ) 23.43/23.48 ( (fun (product_prod int int) int) ) 23.43/23.48 ( (fun int (fun int bool)) ) 23.43/23.48 ( (fun nat bool) ) 23.43/23.48 ( (fun (product_prod int int) bool) ) 23.43/23.48 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.43/23.48 ( (fun real bool) ) 23.43/23.48 ( quickcheck_code_int ) 23.43/23.48 ( code_code_numeral ) 23.43/23.48 ( (fun int (fun int (fun int bool))) ) 23.43/23.48 ( (fun int real) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_157248 $$unsorted) (BOUND_VARIABLE_157249 $$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_157249))) (or (not (real_normed_vector X_b)) (not (topological_space X_a)) (= (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_157248)) (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_157248) (zero_zero X_b)) _let_4))))))))) ) 23.43/23.48 ( 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)))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157282 $$unsorted) (BOUND_VARIABLE_157283 $$unsorted) (BOUND_VARIABLE_157284 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (ord_less X_a))) (let ((_let_3 (zero_zero X_a))) (let ((_let_4 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157282))) (let ((_let_5 (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_157284))) (let ((_let_6 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_3) _let_5)))) (let ((_let_7 (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_2 _let_5) _let_3)))) (let ((_let_8 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_157282) _let_5))) (or (not (number X_a)) (not (linord1117847801e_zero X_a)) (= (hBOOL (hAPP X_a bool _let_4 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_157283) _let_5))) (and (or _let_6 (and (or (not _let_7) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157283) _let_8))) (or _let_7 (hBOOL (hAPP X_a bool _let_4 _let_3))))) (or (not _let_6) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 _let_8) BOUND_VARIABLE_157283))))))))))))))) ) 23.43/23.48 ( real, (zero_zero real), pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((N $$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) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) N))) (= (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))))))) ) 23.43/23.48 ( pls ) 23.43/23.48 ( (one_one int) ) 23.43/23.48 ( min ) 23.43/23.48 ( s ) 23.43/23.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( (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) ) 23.43/23.48 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.43/23.48 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.48 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.48 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.43/23.48 ( skv_4 ) 23.43/23.48 ( skv_5 ) 23.43/23.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157360 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hAPP nat int (semiring_1_of_nat int) BOUND_VARIABLE_157360) (hAPP X_a int (archimedean_ceiling X_a) (hAPP nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_157360)))) ) 23.43/23.48 ( int, (zero_zero nat) ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, (one_one nat) ) 23.43/23.48 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.43/23.48 ( int, n ) 23.43/23.48 ( real, (zero_zero nat) ) 23.43/23.48 ( real, (one_one nat) ) 23.43/23.48 ) 23.43/23.48 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157422 $$unsorted) (BOUND_VARIABLE_157423 $$unsorted) (BOUND_VARIABLE_157424 $$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_157423) BOUND_VARIABLE_157424))) (not (= (ti X_a BOUND_VARIABLE_157423) (ti X_a BOUND_VARIABLE_157422))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157422) BOUND_VARIABLE_157424))))) ) 23.43/23.48 ( int, pls, (zero_zero int), pls ) 23.43/23.48 ( int, min, min, min ) 23.43/23.48 ( int, s, min, (zero_zero int) ) 23.43/23.48 ( int, s1, (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))) ) 23.43/23.48 ( int, m, 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))) ) 23.43/23.48 ( int, t, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.48 ( int, v, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( int, w, (zero_zero int), min ) 23.43/23.48 ( int, y, 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))) ) 23.43/23.48 ( int, sa, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.48 ( int, x, 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))) ) 23.43/23.48 ( int, r, (zero_zero int), (one_one int) ) 23.43/23.48 ( int, m1, (one_one int), t ) 23.43/23.48 ( int, skv_14, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.43/23.48 ( nat, n, (zero_zero nat), n ) 23.43/23.48 ( nat, tn, (zero_zero nat), tn ) 23.43/23.48 ( real, pi, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.43/23.48 ) 23.43/23.49 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (div_div int))) (let ((_let_4 (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)) (= (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 X) _let_4)) _let_2) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 X) _let_2)) _let_4)))))))) ) 23.43/23.49 ( (one_one int) ) 23.43/23.49 ( (zero_zero int) ) 23.43/23.49 ) 23.43/23.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157490 $$unsorted) (BOUND_VARIABLE_157491 $$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_157491))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_157490))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157490) (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_157490) BOUND_VARIABLE_157491)) BOUND_VARIABLE_157491)))))) ) 23.43/23.49 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), m1 ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_21 ) 23.43/23.49 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.43/23.49 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.43/23.49 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.43/23.49 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.43/23.49 ( int, y, v ) 23.43/23.49 ( int, y, w ) 23.43/23.49 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.49 ( int, sa, v ) 23.43/23.49 ( int, sa, w ) 23.43/23.49 ( int, x, v ) 23.43/23.49 ( int, x, w ) 23.43/23.49 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.43/23.49 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.49 ( int, r, v ) 23.43/23.49 ( int, r, w ) 23.43/23.49 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.43/23.49 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.43/23.49 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.43/23.49 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.43/23.49 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.43/23.49 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.49 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.49 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.43/23.49 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.43/23.49 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.49 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.43/23.49 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.43/23.49 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.43/23.49 ( 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)))))) ) 23.43/23.49 ( 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 ) 23.43/23.49 ( complex, ii, ii ) 23.43/23.49 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.43/23.49 ( 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 ) 23.43/23.49 ) 23.43/23.49 (instantiation (forall ((Ta $$unsorted) (A_2 $$unsorted) (D $$unsorted) (BOUND_VARIABLE_157562 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ti int Ta))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) D))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) A_2))) (not (forall ((Xa_1 $$unsorted) (BOUND_VARIABLE_157525 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa_1) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_157525) A_2))) (not (= (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_157525) Xa_1) (ti int BOUND_VARIABLE_157562)))))) )) (= _let_1 (ti int BOUND_VARIABLE_157562)) (not (= _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_157562) D)))))) ) 23.43/23.49 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), s1 ) 23.43/23.49 ) 23.43/23.49 (instantiation (forall ((W $$unsorted) (V $$unsorted)) (let ((_let_0 (zero_zero int))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (hAPP int (fun int _let_1) posDivAlg (hAPP int int _let_2 W)))) (let ((_let_4 (hAPP int int _let_2 V))) (let ((_let_5 (hAPP int _let_1 _let_3 _let_4))) (let ((_let_6 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int _let_2 W)) _let_4)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) _let_4))) (and (or (not _let_6) (= (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) _let_0) (hAPP int int _let_2 W)) _let_5)) (or _let_6 (= _let_5 (hAPP _let_1 _let_1 (hAPP int (fun _let_1 _let_1) adjust _let_4) (hAPP int _let_1 _let_3 (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) _let_4)))))))))))))) ) 23.43/23.49 ( pls, pls ) 23.43/23.49 ( pls, (hAPP int int bit1 pls) ) 23.43/23.49 ) 23.43/23.49 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157682 $$unsorted) (BOUND_VARIABLE_157683 $$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_157682)) (hAPP X_a real _let_0 BOUND_VARIABLE_157683))) (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_157682) BOUND_VARIABLE_157683)))))) ) 23.43/23.49 ( 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) ) 23.43/23.49 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.49 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.49 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.49 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.43/23.49 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.43/23.49 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.43/23.49 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.43/23.49 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.43/23.49 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.43/23.49 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.43/23.49 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.43/23.49 ) 23.43/23.49 (instantiation (forall ((X_a $$unsorted)) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (zero_zero X_a))))) ) 23.43/23.49 ( rat ) 23.43/23.49 ( int ) 23.43/23.49 ( nat ) 23.43/23.49 ( bool ) 23.43/23.49 ( real ) 23.43/23.49 ( (filter nat) ) 23.43/23.49 ( complex ) 23.43/23.49 ( (fun int bool) ) 23.43/23.49 ( (product_prod int int) ) 23.43/23.49 ( (fun nat bool) ) 23.43/23.49 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.43/23.49 ( quickcheck_code_int ) 23.43/23.49 ( code_code_numeral ) 23.43/23.49 ( (product_prod real real) ) 23.43/23.49 ( (filter real) ) 23.43/23.49 ( (product_prod nat nat) ) 23.43/23.49 ( (fun nat rat) ) 23.52/23.53 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real (uminus_uminus real) pi)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 X) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos Y)) (hAPP real real cos X)))))) ) 23.52/23.53 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Xa $$unsorted)) (= (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (not (= (hAPP _let_0 int twoSqu1094008024sum2sq (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) A_4) B_4)) (ti int Xa)))) )) (hBOOL (hAPP int bool twoSqu1091635170sum2sq Xa))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 23.52/23.53 ( (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))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 23.52/23.53 ) 23.52/23.53 (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))) (= (= (hAPP int nat nat_1 Z) (hAPP int nat nat_1 Z_3)) (= (ti int Z) (ti int Z_3))))) ) 23.52/23.53 ( pls, (one_one int) ) 23.52/23.53 ( (one_one int), pls ) 23.52/23.53 ( (one_one int), (one_one int) ) 23.52/23.53 ( min, min ) 23.52/23.53 ( min, s ) 23.52/23.53 ( s, min ) 23.52/23.53 ( (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))) ) 23.52/23.53 ( (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))) ) 23.52/23.53 ( (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))) ) 23.52/23.53 ( skv_4, skv_4 ) 23.52/23.53 ( skv_4, skv_5 ) 23.52/23.53 ( skv_5, skv_4 ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_157881 $$unsorted) (BOUND_VARIABLE_157882 $$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_157881)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_157882)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_157881) BOUND_VARIABLE_157882)))))) ) 23.52/23.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.53 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( 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))))))))) ) 23.52/23.53 ( 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))) ) 23.52/23.53 ( 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))) ) 23.52/23.53 ( 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))) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((V_2 $$unsorted)) (= (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_2)) (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_2)))) ) 23.52/23.53 ( pls ) 23.52/23.53 ( (hAPP int int bit1 pls) ) 23.52/23.53 ( min ) 23.52/23.53 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.53 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (fun nat bool))) (let ((_let_2 (div_div nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_1 (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP nat bool (hAPP nat _let_1 (ord_less_eq nat) N) M))) (= (hAPP nat nat (hAPP nat _let_0 _let_2 M) N) (hAPP nat nat suc (hAPP nat nat (hAPP nat _let_0 _let_2 (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) M) N)) N))))))) ) 23.52/23.53 ( (hAPP int nat nat_1 t), (one_one nat) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Y $$unsorted) (X $$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))) (not (hBOOL (hAPP int bool _let_0 Y))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 X)) (hAPP int nat nat_1 Y)) (hAPP int nat nat_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) X) Y))))) ) 23.52/23.53 ( (one_one int), (one_one int) ) 23.52/23.53 ( (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)))) ) 23.52/23.53 ( (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) ) 23.52/23.53 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.52/23.53 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.52/23.53 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.52/23.53 ( (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.52/23.53 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.52/23.53 ( m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.52/23.53 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (one_one real))) (let ((_let_3 (fun nat _let_1))) (let ((_let_4 (fun _let_0 _let_0))) (let ((_let_5 (fun (fun nat nat) _let_0))) (let ((_let_6 (combb nat real nat))) (let ((_let_7 (combc nat nat nat))) (let ((_let_8 (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_7 (hAPP (fun nat nat) (fun nat (fun nat nat)) (hAPP (fun nat (fun nat nat)) (fun (fun nat nat) (fun nat (fun nat nat))) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP (fun nat (fun nat nat)) (fun nat (fun nat nat)) _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (abs_abs real) Xa)) _let_2))) (hBOOL (hAPP _let_0 bool (monoseq real) (hAPP _let_0 _let_0 (hAPP _let_3 _let_4 (combs nat real real) (hAPP _let_0 _let_3 (hAPP (fun real _let_1) (fun _let_0 _let_3) (combb real _let_1 nat) (times_times real)) (hAPP _let_0 _let_0 (hAPP _let_1 _let_4 (combb real real nat) (hAPP real _let_1 (inverse_divide real) _let_2)) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_5 _let_6 (real_1 nat)) _let_8)))) (hAPP (fun nat nat) _let_0 (hAPP _let_0 _let_5 _let_6 (hAPP real _let_0 (power_power real) Xa)) _let_8)))))))))))))) ) 23.52/23.53 ( (hAPP int real (number_number_of real) min) ) 23.52/23.53 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (hAPP real complex (of_real complex) X))) (= _let_0 (hAPP complex complex cnj _let_0))) ) 23.52/23.53 ( (hAPP int real (number_number_of real) min) ) 23.52/23.53 ( pi ) 23.52/23.53 ( (hAPP real real (uminus_uminus real) (one_one real)) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Z $$unsorted) (P_1 $$unsorted)) (or (not (forall ((N_1 $$unsorted)) (hBOOL (hAPP int bool P_1 (hAPP nat int (semiring_1_of_nat int) N_1))) )) (not (forall ((N_1 $$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_1))))) )) (hBOOL (hAPP int bool P_1 Z))) ) 23.52/23.53 ( pls, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 23.52/23.53 ( pls, (hAPP int (fun int bool) (ord_less int) pls) ) 23.52/23.53 ( pls, (hAPP int (fun int bool) (ord_less_eq int) min) ) 23.52/23.53 ( (one_one int), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 23.52/23.53 ( (one_one int), (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 23.52/23.53 ( (one_one int), nat_neg ) 23.52/23.53 ( (one_one int), nat_is_nat ) 23.52/23.53 ( (one_one int), (even_odd_even int) ) 23.52/23.53 ( min, (hAPP int (fun int bool) (ord_less int) min) ) 23.52/23.53 ( min, (hAPP int (fun int bool) (ord_less_eq int) pls) ) 23.52/23.53 ( min, (hAPP int (fun int bool) (ord_less int) pls) ) 23.52/23.53 ( min, (hAPP int (fun int bool) (ord_less_eq int) min) ) 23.52/23.53 ( (zero_zero int), (hAPP int (fun int bool) (ord_less int) min) ) 23.52/23.53 ( (zero_zero int), nat_neg ) 23.52/23.53 ( (zero_zero int), nat_is_nat ) 23.52/23.53 ( (zero_zero int), (even_odd_even int) ) 23.52/23.53 ( s, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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 ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5)) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_5) ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))) ) 23.52/23.53 ( (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)) ) 23.52/23.53 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), zprime ) 23.52/23.53 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), nat_is_nat ) 23.52/23.53 ( (hAPP int int (number_number_of int) min), (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)))) ) 23.52/23.53 ( (hAPP int int (number_number_of int) min), nat_neg ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) (zero_zero int)) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less int) m1) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))) ) 23.52/23.53 ( t, (hAPP int (fun int bool) (ord_less int) (one_one int)) ) 23.52/23.53 ( t, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)) ) 23.52/23.53 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) ) 23.52/23.53 ( (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)) ) 23.52/23.53 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), nat_is_nat ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))), twoSqu1091635170sum2sq ) 23.52/23.53 ( (hAPP 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)), (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)))) ) 23.52/23.53 ( (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 ) 23.52/23.53 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))), twoSqu1091635170sum2sq ) 23.52/23.53 ( skv_4, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 23.52/23.53 ( skv_5, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Ya $$unsorted) (Na $$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)) Na))) (= (hBOOL (hAPP real bool _let_0 Ya)) (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Ya)))))) ) 23.52/23.53 ( (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))) ) 23.52/23.53 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (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))) ) 23.52/23.53 ) 23.52/23.53 (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 Z_1) (ti int W))))) ) 23.52/23.53 ( pls, min ) 23.52/23.53 ( pls, (zero_zero int) ) 23.52/23.53 ( (one_one int), (zero_zero int) ) 23.52/23.53 ( (one_one int), t ) 23.52/23.53 ( min, pls ) 23.52/23.53 ( min, min ) 23.52/23.53 ( min, (zero_zero int) ) 23.52/23.53 ( (zero_zero int), pls ) 23.52/23.53 ( (zero_zero int), (one_one int) ) 23.52/23.53 ( (zero_zero int), min ) 23.52/23.53 ( (zero_zero int), s ) 23.52/23.53 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (zero_zero int), skv_4 ) 23.52/23.53 ( (zero_zero int), skv_5 ) 23.52/23.53 ( s, (zero_zero int) ) 23.52/23.53 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.52/23.53 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.52/23.53 ( t, (one_one int) ) 23.52/23.53 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.52/23.53 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.53 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.53 ( skv_4, (zero_zero int) ) 23.52/23.53 ( skv_5, (zero_zero int) ) 23.52/23.53 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.53 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (zero_zero real)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) (one_one real)))) (hBOOL (hAPP _let_0 bool (monoseq real) (hAPP real _let_0 (power_power real) Xa))))))) ) 23.52/23.53 ( (hAPP int real (number_number_of real) min) ) 23.52/23.53 ( pi ) 23.52/23.53 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (zero_zero real) ) 23.52/23.53 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.53 ( skv_10 ) 23.52/23.53 ( skv_11 ) 23.52/23.53 ( skv_15 ) 23.52/23.53 ( skv_18 ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158151 $$unsorted) (BOUND_VARIABLE_158152 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (inverse_divide X_a) (one_one X_a)))) (or (not (field_inverse_zero X_a)) (= (hAPP X_a X_a _let_2 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158151) BOUND_VARIABLE_158152)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_158151)) BOUND_VARIABLE_158152)))))) ) 23.52/23.53 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.53 ) 23.52/23.53 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158170 $$unsorted) (BOUND_VARIABLE_158171 $$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_158170) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_158171)) (hAPP X_a X_a (hAPP X_a _let_0 (minus_minus X_a) BOUND_VARIABLE_158170) BOUND_VARIABLE_158171)))) ) 23.52/23.53 ( int, (one_one int), pls ) 23.52/23.53 ( 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) ) 23.52/23.53 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.52/23.53 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.52/23.53 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.52/23.53 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.52/23.54 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.54 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.52/23.54 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.52/23.54 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158217 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a bool) (ord_less X_a) (zero_zero X_a)))) (or (not (linordered_idom X_a)) (= (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_158217)) (hBOOL (hAPP X_a bool _let_0 (hAPP X_a X_a (sgn_sgn X_a) BOUND_VARIABLE_158217)))))) ) 23.52/23.54 ( rat, (zero_zero rat) ) 23.52/23.54 ( real, (zero_zero real) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158252 $$unsorted) (BOUND_VARIABLE_158253 $$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_158252) BOUND_VARIABLE_158253))) (= (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_158252) BOUND_VARIABLE_158253))) (= (ti X_a BOUND_VARIABLE_158252) (ti X_a BOUND_VARIABLE_158253))))) ) 23.52/23.54 ( int, (one_one int), t ) 23.52/23.54 ( int, min, pls ) 23.52/23.54 ( int, min, min ) 23.52/23.54 ( int, min, (zero_zero int) ) 23.52/23.54 ( int, (zero_zero int), pls ) 23.52/23.54 ( int, (zero_zero int), (one_one int) ) 23.52/23.54 ( int, (zero_zero int), min ) 23.52/23.54 ( int, (zero_zero int), s ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (zero_zero int), skv_4 ) 23.52/23.54 ( int, (zero_zero int), skv_5 ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.54 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( nat, (zero_zero nat), n ) 23.52/23.54 ( nat, (zero_zero nat), tn ) 23.52/23.54 ( real, pi, (zero_zero real) ) 23.52/23.54 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.52/23.54 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( real, (zero_zero real), pi ) 23.52/23.54 ( 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)))) ) 23.52/23.54 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( real, (zero_zero real), skv_2 ) 23.52/23.54 ( real, (zero_zero real), skv_9 ) 23.52/23.54 ( real, (zero_zero real), skv_10 ) 23.52/23.54 ( real, (zero_zero real), skv_11 ) 23.52/23.54 ( real, (zero_zero real), skv_12 ) 23.52/23.54 ( real, (zero_zero real), skv_15 ) 23.52/23.54 ( real, (zero_zero real), skv_18 ) 23.52/23.54 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.52/23.54 ( 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) ) 23.52/23.54 ( 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 ) 23.52/23.54 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((A_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_0 (hAPP int (fun int rat) fract (zero_zero int)))) (= (hAPP int rat _let_0 C_1) (hAPP int rat _let_0 A_1))) ) 23.52/23.54 ( (one_one int), (one_one int) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((A_1 $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (not (forall ((X_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X_1))) (not (forall ((Y_1 $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) Y_1) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) Y_1))) (= X_1 Y_1)) )) (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) X_1) N)))) ))) ) 23.52/23.54 ( pi, n ) 23.52/23.54 ( (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)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), tn ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((K_4 $$unsorted)) (= (hAPP nat rat (semiring_1_of_nat rat) K_4) (hAPP int rat (hAPP int (fun int rat) fract (hAPP nat int (semiring_1_of_nat int) K_4)) (one_one int))) ) 23.52/23.54 ( (zero_zero nat) ) 23.52/23.54 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (one_one nat) ) 23.52/23.54 ( (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.54 ( n ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (hAPP real _let_0 (times_times real) (hAPP int real (number_number_of real) _let_1)))) (let ((_let_4 (hAPP real real _let_3 X))) (let ((_let_5 (hAPP real real tan X))) (or (= _let_2 (hAPP real real cos X)) (= _let_2 (hAPP real real cos _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_1)))) (hAPP real real tan _let_4))))))))) ) 23.52/23.54 ( pi ) 23.52/23.54 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (zero_zero real) ) 23.52/23.54 ( (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))))) ) 23.52/23.54 ( (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) ) 23.52/23.54 ( (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.52/23.54 ( (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))))) ) 23.52/23.54 ( (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)))) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted) (Xaa $$unsorted)) (= (= (hAPP real complex (of_real complex) Xaa) (hAPP real complex (hAPP real (fun real complex) complex_1 Xa) Ya)) (and (= Xa Xaa) (= (zero_zero real) Ya))) ) 23.52/23.54 ( (one_one real), (zero_zero real), pi ) 23.52/23.54 ( (zero_zero real), (one_one real), (hAPP int real (number_number_of real) min) ) 23.52/23.54 ( (zero_zero real), (zero_zero real), (hAPP real real (uminus_uminus real) (one_one real)) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 (ord_less real) (zero_zero real)) Xa))) (hBOOL (hAPP real bool (hAPP real _let_1 (hAPP _let_0 (fun real _let_1) (deriv real) sqrt) Xa) (hAPP real real (hAPP real _let_0 (inverse_divide real) (hAPP real real (inverse_inverse real) (hAPP real real sqrt Xa))) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 23.52/23.54 ( pi ) 23.52/23.54 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (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)))) ) 23.52/23.54 ( (one_one real) ) 23.52/23.54 ( (zero_zero real) ) 23.52/23.54 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.54 ( skv_2 ) 23.52/23.54 ( skv_9 ) 23.52/23.54 ( skv_12 ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((Na $$unsorted)) (= (not (hBOOL (hAPP nat bool (even_odd_even nat) Na))) (not (forall ((M_2 $$unsorted)) (not (= Na (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)))) ))) ) 23.52/23.54 ( (zero_zero nat) ) 23.52/23.54 ( (one_one nat) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158371 $$unsorted) (BOUND_VARIABLE_158372 $$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_158371) BOUND_VARIABLE_158372))) (hAPP X_a X_a (hAPP X_a _let_1 (plus_plus X_a) (hAPP X_a X_a _let_0 BOUND_VARIABLE_158371)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_158372))))))) ) 23.52/23.54 ( 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) ) 23.52/23.54 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.52/23.54 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.52/23.54 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.54 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.52/23.54 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.52/23.54 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((P_2 $$unsorted) (P_1 $$unsorted) (Xa $$unsorted)) (let ((_let_0 (hBOOL P_2))) (let ((_let_1 (hBOOL P_1))) (let ((_let_2 (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Xa))))) (or (and (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) Xa)) (= (not _let_0) _let_1)) (= (or _let_2 _let_1) (or _let_2 _let_0)))))) ) 23.52/23.54 ( (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (one_one int) ) 23.52/23.54 ( (hAPP nat bool (even_odd_even nat) (zero_zero nat)), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int nat (number_number_of nat) _let_1))) (let ((_let_3 (fun int bool))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int bool (hAPP int _let_3 (hAPP int (fun int _let_3) zcong (hAPP nat int (hAPP int _let_4 _let_5 s) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 s1) _let_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 _let_1))) m)) (one_one int))))))))), (one_one int) ) 23.52/23.54 ( (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_2 (hAPP int nat (number_number_of nat) _let_1))) (let ((_let_3 (fun int bool))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int bool (hAPP int _let_3 (hAPP int (fun int _let_3) zcong (hAPP nat int (hAPP int _let_4 _let_5 s) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 s1) _let_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 _let_1))) m)) (one_one int))))))))), (hAPP nat bool (even_odd_even nat) (zero_zero nat)), pls ) 23.52/23.54 ( (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (one_one int)), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.54 ( (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)) (one_one int)), (let ((_let_0 (fun int int))) (let ((_let_1 (number_number_of int))) (hAPP int bool (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 _let_1 (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) (hAPP int int _let_1 min)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( fTrue, fTrue, min ) 23.52/23.54 ( fTrue, (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), min ) 23.52/23.54 ( (let ((_let_0 (fun int int))) (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))), fTrue, s ) 23.52/23.54 ( (hAPP real bool (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))))), (hAPP real bool (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))))), skv_4 ) 23.52/23.54 ( (hAPP real bool (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))))), (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), skv_4 ) 23.52/23.54 ( (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP real bool (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))))), skv_5 ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158439 $$unsorted) (BOUND_VARIABLE_158440 $$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_158439) BOUND_VARIABLE_158440))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158440) (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_158440)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158439))))))) ) 23.52/23.54 ( int, (one_one int), t ) 23.52/23.54 ( int, min, min ) 23.52/23.54 ( int, min, (zero_zero int) ) 23.52/23.54 ( int, (zero_zero int), pls ) 23.52/23.54 ( int, (zero_zero int), (one_one int) ) 23.52/23.54 ( int, (zero_zero int), min ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( 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))) ) 23.52/23.54 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.54 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( nat, (zero_zero nat), n ) 23.52/23.54 ( nat, (zero_zero nat), tn ) 23.52/23.54 ( real, pi, (zero_zero real) ) 23.52/23.54 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( 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)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( real, (zero_zero real), pi ) 23.52/23.54 ( 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)))) ) 23.52/23.54 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( real, (zero_zero real), skv_2 ) 23.52/23.54 ( real, (zero_zero real), skv_9 ) 23.52/23.54 ( real, (zero_zero real), skv_12 ) 23.52/23.54 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.52/23.54 ( 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) ) 23.52/23.54 ( 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 ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((Ma $$unsorted)) (let ((_let_0 (one_one int))) (= (= _let_0 (hAPP int int (hAPP int (fun int int) legacy_zgcd (zero_zero int)) Ma)) (= _let_0 (hAPP int int (abs_abs int) Ma)))) ) 23.52/23.54 ( v ) 23.52/23.54 ( w ) 23.52/23.54 ( skv_14 ) 23.52/23.54 ( skv_20 ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158548 $$unsorted) (BOUND_VARIABLE_158549 $$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_158549))) (not (hBOOL (hAPP X_a bool _let_1 BOUND_VARIABLE_158548))) (= (= _let_0 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_158549) BOUND_VARIABLE_158548)) (and (= _let_0 (ti X_a BOUND_VARIABLE_158549)) (= _let_0 (ti X_a BOUND_VARIABLE_158548))))))) ) 23.52/23.54 ( 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)))) ) 23.52/23.54 ( 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) ) 23.52/23.54 ( int, (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.52/23.54 ( int, (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.52/23.54 ( int, v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.54 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.52/23.54 ( int, (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)))), (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.52/23.54 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.52/23.54 ( int, m1, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.52/23.54 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( nat, (one_one nat), (one_one nat) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((Xa $$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)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arccos) Xa))))) ) 23.52/23.54 ( pi ) 23.52/23.54 ( (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)))) ) 23.52/23.54 ( (one_one real) ) 23.52/23.54 ( (zero_zero real) ) 23.52/23.54 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.54 ( (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))))) ) 23.52/23.54 ( (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)) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (hAPP int nat (number_number_of nat) V))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) _let_0))) (= _let_0 (hAPP nat nat suc (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) _let_0) (one_one nat)))))) ) 23.52/23.54 ( pls ) 23.52/23.54 ( (hAPP int int bit1 pls) ) 23.52/23.54 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.54 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158595 $$unsorted) (BOUND_VARIABLE_158596 $$unsorted)) (let ((_let_0 (fun nat X_a))) (let ((_let_1 (power_power X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (comm_ring_1 X_a)) (hBOOL (hAPP nat bool (even_odd_even nat) BOUND_VARIABLE_158596)) (= (hAPP X_a X_a _let_2 (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158595) BOUND_VARIABLE_158596)) (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_158595)) BOUND_VARIABLE_158596)))))) ) 23.52/23.54 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158651 $$unsorted) (BOUND_VARIABLE_158652 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (ordered_ab_group_add X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158652) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158651))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_158651) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158652)))))))) ) 23.52/23.54 ( int, pls, min ) 23.52/23.54 ( int, pls, (zero_zero int) ) 23.52/23.54 ( int, (one_one int), min ) 23.52/23.54 ( int, (one_one int), (zero_zero int) ) 23.52/23.54 ( int, min, pls ) 23.52/23.54 ( int, min, (one_one int) ) 23.52/23.54 ( int, (zero_zero int), pls ) 23.52/23.54 ( int, (zero_zero int), (one_one int) ) 23.52/23.54 ) 23.52/23.54 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158673 $$unsorted) (BOUND_VARIABLE_158674 $$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_158674) _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_158674) BOUND_VARIABLE_158673)) _let_3))))))) ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.52/23.54 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.52/23.54 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.52/23.54 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.52/23.54 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.52/23.54 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.52/23.54 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.52/23.54 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.52/23.55 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.52/23.55 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.52/23.55 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158697 $$unsorted) (BOUND_VARIABLE_158698 $$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_158697) BOUND_VARIABLE_158698)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_158698)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_158697))))))) ) 23.52/23.55 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.52/23.55 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.52/23.55 ( 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)))), (one_one int) ) 23.52/23.55 ( 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) ) 23.52/23.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.52/23.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.52/23.55 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.52/23.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( nat, (one_one nat), (one_one nat) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X $$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) (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) (hAPP int nat (number_number_of nat) _let_0)))))))) (hAPP real real arctan X)))) ) 23.52/23.55 ( (hAPP int real (number_number_of real) min) ) 23.52/23.55 ( pi ) 23.52/23.55 ( (one_one real) ) 23.52/23.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( (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)))) ) 23.52/23.55 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X $$unsorted) (A_1 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP nat real (real_1 nat) X)) A_1))) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) X) (hAPP real nat natfloor A_1)))) ) 23.52/23.55 ( (zero_zero nat), pi ) 23.52/23.55 ( (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)))) ) 23.52/23.55 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( (zero_zero nat), skv_10 ) 23.52/23.55 ( (zero_zero nat), skv_11 ) 23.52/23.55 ( (zero_zero nat), skv_15 ) 23.52/23.55 ( (zero_zero nat), skv_18 ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158786 $$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 nat X_a (semiring_1_of_nat X_a) BOUND_VARIABLE_158786)) (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_158786)))) ) 23.52/23.55 ( int, (zero_zero nat) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (one_one nat) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, n ) 23.52/23.55 ( real, (zero_zero nat) ) 23.52/23.55 ( real, (one_one nat) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158810 $$unsorted) (BOUND_VARIABLE_158811 $$unsorted)) (let ((_let_0 (hAPP int (fun int bool) (ord_less_eq int) pls))) (let ((_let_1 (number_number_of X_a))) (or (not (number_semiring X_a)) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_158811))) (not (hBOOL (hAPP int bool _let_0 BOUND_VARIABLE_158810))) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP int X_a _let_1 BOUND_VARIABLE_158811)) (hAPP int X_a _let_1 BOUND_VARIABLE_158810)) (hAPP int X_a _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_158811) BOUND_VARIABLE_158810)))))) ) 23.52/23.55 ( int, pls, (hAPP int int bit1 pls) ) 23.52/23.55 ( nat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158853 $$unsorted) (BOUND_VARIABLE_158854 $$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_158853)) BOUND_VARIABLE_158854)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) BOUND_VARIABLE_158853) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_158854))))) ) 23.52/23.55 ( real, (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (zero_zero int), pi ) 23.52/23.55 ( 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)))) ) 23.52/23.55 ( real, (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (zero_zero int), skv_2 ) 23.52/23.55 ( real, (zero_zero int), skv_9 ) 23.52/23.55 ( real, (zero_zero int), skv_12 ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP real nat natceiling X)) (one_one nat)) (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (plus_plus real) X) (one_one real))))) ) 23.52/23.55 ( pi ) 23.52/23.55 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( (one_one real) ) 23.52/23.55 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( skv_10 ) 23.52/23.55 ( skv_11 ) 23.52/23.55 ( skv_15 ) 23.52/23.55 ( skv_18 ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158876 $$unsorted)) (or (not (archim1727834104eiling X_a)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_158876) (hAPP int X_a (ring_1_of_int X_a) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_158876))))) ) 23.52/23.55 ( int, (one_one int) ) 23.52/23.55 ( int, min ) 23.52/23.55 ( int, (zero_zero int) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.52/23.55 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (zero_zero real) ) 23.52/23.55 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, skv_10 ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((Xa $$unsorted)) (= (= (zero_zero real) (hAPP real real sin Xa)) (or (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (not (= Xa (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_1)) (hAPP real real (hAPP real _let_0 (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) )) (not (forall ((N_1 $$unsorted)) (let ((_let_0 (fun real real))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) N_1))) (not (= Xa (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real _let_0 (times_times real) (hAPP nat real (real_1 nat) N_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)))))))))) )))) ) 23.52/23.55 ( pi ) 23.52/23.55 ( (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)))) ) 23.52/23.55 ( (zero_zero real) ) 23.52/23.55 ( (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))))) ) 23.52/23.55 ( (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) ) 23.52/23.55 ( (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))))) ) 23.52/23.55 ( (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)))) ) 23.52/23.55 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP nat (fun nat nat) (minus_minus nat) Ma))) (= (hAPP nat nat (hAPP (fun nat nat) (fun nat nat) (hAPP nat (fun (fun nat nat) (fun nat nat)) (nat_case nat) (zero_zero nat)) (combi nat)) (hAPP nat nat _let_0 Na)) (hAPP nat nat _let_0 (hAPP nat nat suc Na)))) ) 23.52/23.55 ( (hAPP int nat nat_1 t), (zero_zero nat) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_158921 $$unsorted) (BOUND_VARIABLE_158922 $$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_158922))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_158921))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_158922) BOUND_VARIABLE_158921))))) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.52/23.55 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.52/23.55 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.52/23.55 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.52/23.55 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.52/23.55 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.52/23.55 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.52/23.55 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.52/23.55 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.52/23.55 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.52/23.55 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.52/23.55 ) 23.52/23.55 (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)))))) ) 23.52/23.55 ( pls ) 23.52/23.55 ( (hAPP int int bit1 pls) ) 23.52/23.55 ( min ) 23.52/23.55 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.55 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (norm_norm complex))) (= (hAPP complex real _let_0 (hAPP complex complex cnj Z_1)) (hAPP complex real _let_0 Z_1))) ) 23.52/23.55 ( (zero_zero complex) ) 23.52/23.55 ( ii ) 23.52/23.55 ( (one_one complex) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159007 $$unsorted) (BOUND_VARIABLE_159008 $$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_159007) BOUND_VARIABLE_159008))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_159007))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_159008)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_159007))))))) ) 23.52/23.55 ( int, (one_one int), t ) 23.52/23.55 ( int, min, min ) 23.52/23.55 ( int, min, (zero_zero int) ) 23.52/23.55 ( int, (zero_zero int), pls ) 23.52/23.55 ( int, (zero_zero int), (one_one int) ) 23.52/23.55 ( int, (zero_zero int), min ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.55 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( nat, (zero_zero nat), n ) 23.52/23.55 ( nat, (zero_zero nat), tn ) 23.52/23.55 ( real, pi, (zero_zero real) ) 23.52/23.55 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (zero_zero real), pi ) 23.52/23.55 ( 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)))) ) 23.52/23.55 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (zero_zero real), skv_2 ) 23.52/23.55 ( real, (zero_zero real), skv_9 ) 23.52/23.55 ( real, (zero_zero real), skv_12 ) 23.52/23.55 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.52/23.55 ( 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) ) 23.52/23.55 ( 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 ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((B $$unsorted)) (let ((_let_0 (hAPP int int (number_number_of int) min))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (zero_zero int)) B))) (= _let_0 (hAPP int int (hAPP int (fun int int) (div_div int) _let_0) B)))) ) 23.52/23.55 ( pls ) 23.52/23.55 ( (one_one int) ) 23.52/23.55 ( min ) 23.52/23.55 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.55 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159107 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (minus_minus X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_159107)) (one_one X_a)) (hAPP int X_a _let_0 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_159107) (hAPP int int (uminus_uminus int) (hAPP int int bit1 pls))))))) ) 23.52/23.55 ( code_code_numeral, pls ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (sgn_sgn int))) (= (hAPP rat rat (sgn_sgn rat) (hAPP int rat (hAPP int (fun int rat) fract A_1) B)) (hAPP int rat (ring_1_of_int rat) (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int _let_0 A_1)) (hAPP int int _let_0 B))))) ) 23.52/23.55 ( (one_one int), (one_one int) ) 23.52/23.55 ( (zero_zero int), (one_one int) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159141 $$unsorted) (BOUND_VARIABLE_159142 $$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_159142))) (= (hAPP nat X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_159141)) BOUND_VARIABLE_159142) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159141) BOUND_VARIABLE_159142))))) ) 23.52/23.55 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((A_3 $$unsorted) (P_4 $$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_3) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_4) A_3)) (= (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_3) P_4)))))))) ) 23.52/23.55 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159229 $$unsorted)) (or (not (division_ring X_a)) (= (ti X_a BOUND_VARIABLE_159229) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_159229) (one_one X_a)))) ) 23.52/23.55 ( int, pls ) 23.52/23.55 ( int, min ) 23.52/23.55 ( int, s ) 23.52/23.55 ( int, s1 ) 23.52/23.55 ( int, m ) 23.52/23.55 ( int, t ) 23.52/23.55 ( int, v ) 23.52/23.55 ( int, w ) 23.52/23.55 ( int, y ) 23.52/23.55 ( int, sa ) 23.52/23.55 ( int, x ) 23.52/23.55 ( int, r ) 23.52/23.55 ( int, m1 ) 23.52/23.55 ( int, skv_14 ) 23.52/23.55 ( int, skv_20 ) 23.52/23.55 ( (fun int int), bit1 ) 23.52/23.55 ( (fun int int), bit0 ) 23.52/23.55 ( (fun int int), succ ) 23.52/23.55 ( (fun int int), pred ) 23.52/23.55 ( (fun int int), (fact_fact int) ) 23.52/23.55 ( (fun int int), zfact ) 23.52/23.55 ( nat, n ) 23.52/23.55 ( nat, tn ) 23.52/23.55 ( bool, fTrue ) 23.52/23.55 ( bool, fFalse ) 23.52/23.55 ( real, pi ) 23.52/23.55 ( real, (one_one real) ) 23.52/23.55 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.55 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( (fun nat real), (real_1 nat) ) 23.52/23.55 ( (fun nat real), cos_coeff ) 23.52/23.55 ( (fun nat real), sin_coeff ) 23.52/23.55 ( (fun real real), sin ) 23.52/23.55 ( (fun real real), cos ) 23.52/23.55 ( (fun real real), sqrt ) 23.52/23.55 ( (fun real real), tan ) 23.52/23.55 ( (fun real real), ln ) 23.52/23.55 ( (fun real real), arctan ) 23.52/23.55 ( (fun real real), arcsin ) 23.52/23.55 ( (fun real real), arccos ) 23.52/23.55 ( (fun nat nat), suc ) 23.52/23.55 ( (fun nat nat), (fact_fact nat) ) 23.52/23.55 ( (fun nat nat), nat_size ) 23.52/23.55 ( (fun nat nat), (size_size nat) ) 23.52/23.55 ( (fun nat nat), fact ) 23.52/23.55 ( (filter nat), sequentially ) 23.52/23.55 ( (fun int (fun int rat)), fract ) 23.52/23.55 ( complex, ii ) 23.52/23.55 ( (fun int bool), zOdd ) 23.52/23.55 ( (fun int bool), zprime ) 23.52/23.55 ( (fun int bool), zEven ) 23.52/23.55 ( (fun int bool), nat_neg ) 23.52/23.55 ( (fun int bool), nat_is_nat ) 23.52/23.55 ( (fun int bool), (even_odd_even int) ) 23.52/23.55 ( (fun int bool), twoSqu1091635170sum2sq ) 23.52/23.55 ( (fun int (fun int int)), legacy_zgcd ) 23.52/23.55 ( (fun int (fun int int)), (gcd_gcd int) ) 23.52/23.55 ( (fun int (fun int int)), inv ) 23.52/23.55 ( (fun int (fun int int)), multInv ) 23.52/23.55 ( (fun int (fun int int)), legendre ) 23.52/23.55 ( (fun int (fun int int)), standardRes ) 23.52/23.55 ( (fun int (fun int int)), nat_tsub ) 23.52/23.55 ( (fun int (fun int int)), z3div ) 23.52/23.55 ( (fun int (fun int int)), z3mod ) 23.52/23.55 ( (fun int (fun int int)), int_lcm ) 23.52/23.55 ( (fun int (fun int int)), int_gcd ) 23.52/23.55 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.52/23.55 ( (fun bool bool), fNot ) 23.52/23.55 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.52/23.55 ( (fun bool (fun bool bool)), fconj ) 23.52/23.55 ( (fun bool (fun bool bool)), fdisj ) 23.52/23.55 ( (fun bool (fun bool bool)), fimplies ) 23.52/23.55 ( (fun int (fun int bool)), quadRes ) 23.52/23.55 ( (fun int (fun int bool)), d22set ) 23.52/23.55 ( (fun int (fun int bool)), norRRset ) 23.52/23.55 ( (fun int (fun int bool)), sRStar ) 23.52/23.55 ( (fun int (fun int bool)), sr ) 23.52/23.55 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.52/23.55 ( (fun nat bool), (even_odd_even nat) ) 23.52/23.55 ( (fun nat bool), prime ) 23.52/23.55 ( (fun real complex), cis ) 23.52/23.55 ( (fun nat (fun nat bool)), coprime ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.52/23.55 ( (fun (product_prod int int) bool), frac_1 ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.52/23.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.52/23.55 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.52/23.55 ( (fun (fun int bool) bool), nat_nat_set ) 23.52/23.55 ( (fun nat (fun real real)), root ) 23.52/23.55 ( (fun real (fun real real)), log ) 23.52/23.55 ( (fun real (fun real real)), powr ) 23.52/23.55 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.52/23.55 ( (fun complex complex), cnj ) 23.52/23.55 ( (fun complex complex), expi ) 23.52/23.55 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.52/23.55 ( (fun nat (fun nat nat)), nat_gcd ) 23.52/23.55 ( (fun nat (fun nat nat)), nat_lcm ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.52/23.55 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.52/23.55 ( (fun int (fun (fun int bool) bool)), resSet ) 23.52/23.55 ( (fun int nat), nat_1 ) 23.52/23.55 ( (fun int nat), phi ) 23.52/23.55 ( (fun complex real), re ) 23.52/23.55 ( (fun complex real), im ) 23.52/23.55 ( (fun complex real), arg ) 23.52/23.55 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.52/23.55 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.52/23.55 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.52/23.55 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.52/23.55 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.52/23.55 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.52/23.55 ( (fun (product_prod nat nat) bool), pred_nat ) 23.52/23.55 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.52/23.55 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.52/23.55 ( (fun (fun int bool) int), (the int) ) 23.52/23.55 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.52/23.55 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.52/23.55 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.52/23.55 ( (fun real (fun real complex)), rcis ) 23.52/23.55 ( (fun real (fun real complex)), complex_1 ) 23.52/23.55 ( (fun int (fun int (fun int bool))), zcong ) 23.52/23.55 ( (fun int (fun int (fun int bool))), wset ) 23.52/23.55 ( (fun int (fun int (fun int bool))), noXRRset ) 23.52/23.55 ( (fun int (fun int (fun int bool))), bnorRset ) 23.52/23.55 ( (fun int (fun int (fun int bool))), zcongm ) 23.52/23.55 ( (fun real nat), natceiling ) 23.52/23.55 ( (fun real nat), natfloor ) 23.52/23.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.52/23.55 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.52/23.55 ( (fun int real), (real_1 int) ) 23.52/23.55 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.52/23.55 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.52/23.55 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.52/23.55 ( (fun complex nat), (size_size complex) ) 23.52/23.55 ( (fun complex nat), complex_size ) 23.52/23.55 ( (fun (fun nat rat) bool), vanishes ) 23.52/23.55 ( (fun (product_prod int int) rat), frct ) 23.52/23.55 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.52/23.55 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.52/23.55 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.52/23.55 ( (fun rat real), ratreal ) 23.52/23.55 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.52/23.55 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.52/23.55 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.52/23.55 ( (fun rat (product_prod int int)), quotient_of ) 23.52/23.55 ( (fun int (fun nat nat)), nat_aux ) 23.52/23.55 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.52/23.55 ( (fun int (list int)), quickc666637781d_zero ) 23.52/23.55 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.52/23.55 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.52/23.55 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.52/23.55 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.52/23.55 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.52/23.55 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.52/23.55 ( (fun code_code_numeral int), code_int_of ) 23.52/23.55 ) 23.52/23.55 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_159249 $$unsorted) (BOUND_VARIABLE_159250 $$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_a)) (not (topological_space X_b)) (= (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_159249) (hAPP X_a X_b BOUND_VARIABLE_159249 BOUND_VARIABLE_159250)) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_159250))) (hBOOL (hAPP X_a bool (hAPP _let_2 (fun X_a bool) (isCont X_a X_b) BOUND_VARIABLE_159249) BOUND_VARIABLE_159250))))))) ) 23.52/23.55 ( rat, rat, (sgn_sgn rat), (zero_zero rat) ) 23.52/23.55 ( rat, int, (hAPP int (fun int rat) fract (zero_zero int)), (one_one int) ) 23.52/23.55 ( rat, int, (hAPP int (fun int rat) fract (one_one int)), (one_one int) ) 23.52/23.55 ( 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))) ) 23.52/23.55 ( int, int, bit1, pls ) 23.52/23.55 ( int, int, bit1, (hAPP int int bit1 pls) ) 23.52/23.55 ( int, int, bit1, min ) 23.52/23.55 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.55 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.55 ( int, int, bit1, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, int, bit1, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.52/23.55 ( 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)))))) ) 23.52/23.55 ( 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))))))) ) 23.52/23.55 ( int, int, (uminus_uminus int), pls ) 23.52/23.55 ( int, int, (uminus_uminus int), (one_one int) ) 23.52/23.55 ( int, int, (uminus_uminus int), min ) 23.52/23.55 ( int, int, bit0, pls ) 23.52/23.55 ( int, int, bit0, (hAPP int int bit1 pls) ) 23.52/23.55 ( int, int, bit0, min ) 23.52/23.55 ( int, int, bit0, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.55 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.55 ( int, int, bit0, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, int, succ, pls ) 23.52/23.55 ( int, int, succ, min ) 23.52/23.55 ( int, int, (number_number_of int), pls ) 23.52/23.55 ( int, int, (number_number_of int), (hAPP int int bit1 pls) ) 23.52/23.55 ( int, int, (number_number_of int), min ) 23.52/23.55 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.55 ( int, int, (number_number_of int), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.55 ( int, int, (number_number_of int), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.55 ( 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 ) 23.52/23.55 ( 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) ) 23.52/23.55 ( int, int, (abs_abs int), v ) 23.52/23.55 ( int, int, (abs_abs int), w ) 23.52/23.55 ( int, int, (abs_abs int), skv_14 ) 23.52/23.55 ( int, int, (abs_abs int), skv_20 ) 23.52/23.55 ( int, int, (hAPP int (fun int int) legendre (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.55 ( int, int, pred, pls ) 23.52/23.55 ( int, int, pred, min ) 23.52/23.55 ( 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)))), (hAPP int int (abs_abs int) w) ) 23.52/23.55 ( 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)))), (hAPP int int (abs_abs int) v) ) 23.52/23.55 ( 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)))), (hAPP int int (abs_abs int) skv_14) ) 23.52/23.55 ( 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)))), (hAPP int int (abs_abs int) skv_20) ) 23.52/23.55 ( int, int, (fact_fact int), (one_one int) ) 23.52/23.55 ( int, int, (fact_fact int), (zero_zero int) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (plus_plus int) (one_one int)), (hAPP nat int (semiring_1_of_nat int) n) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), m1 ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), skv_3 ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (minus_minus int) y), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) sa), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) sa), v ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) sa), w ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.55 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_0 (times_times int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP nat int (hAPP int _let_2 _let_3 x) _let_1)) (hAPP nat int (hAPP int _let_2 _let_3 y) _let_1))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) x), v ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) x), w ) 23.52/23.55 ( 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) x) v))), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) y), v ) 23.52/23.55 ( int, int, (hAPP int (fun int int) (times_times int) y), w ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 x) v)) (hAPP int int (hAPP int _let_0 _let_2 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) x) w))), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.52/23.56 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( 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 ) 23.52/23.56 ( 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))))), m1 ) 23.52/23.56 ( 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))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.52/23.56 ( 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_21 ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (times_times int) r), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (times_times int) r), v ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (times_times int) r), w ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), v ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), v ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))))), w ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))))), w ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), v ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))))), w ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int 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((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_2 r) v)))))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w))))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP 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) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (times_times int) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int _let_0 (minus_minus 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))) m1)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.52/23.56 ( 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) r) v))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w)))))), m1 ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (let ((_let_4 (minus_minus int))) (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 (times_times int) r) w))), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (minus_minus int) x), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.52/23.56 ( 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) ) 23.52/23.56 ( 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) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.52/23.56 ( int, int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int 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(semiring_1_of_nat int) n)) ) 23.52/23.56 ( int, int, (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( int, nat, (semiring_1_of_nat int), (zero_zero nat) ) 23.52/23.56 ( int, nat, (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( int, nat, (semiring_1_of_nat int), (one_one nat) ) 23.52/23.56 ( int, nat, 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(hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( int, nat, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int 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pls))))) m)) (one_one int))) m1))) ) 23.52/23.56 ( (fun int int), int, (minus_minus int), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.52/23.56 ( (fun int int), int, legendre, (hAPP int int (number_number_of int) min) ) 23.52/23.56 ( (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) ) 23.52/23.56 ( (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))) ) 23.52/23.56 ( nat, int, (number_number_of nat), pls ) 23.52/23.56 ( nat, int, (number_number_of nat), (hAPP int int bit1 pls) ) 23.52/23.56 ( nat, int, (number_number_of nat), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.56 ( nat, int, (number_number_of nat), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.56 ( nat, int, nat_1, (one_one int) ) 23.52/23.56 ( nat, int, nat_1, (zero_zero int) ) 23.52/23.56 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( nat, int, nat_1, t ) 23.52/23.56 ( nat, int, nat_1, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.56 ( nat, nat, suc, (zero_zero nat) ) 23.52/23.56 ( nat, nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 23.52/23.56 ( nat, nat, suc, (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 23.52/23.56 ( nat, nat, (fact_fact nat), (zero_zero nat) ) 23.52/23.56 ( nat, nat, (fact_fact nat), (one_one nat) ) 23.52/23.56 ( nat, nat, nat_size, (zero_zero nat) ) 23.52/23.56 ( nat, nat, (size_size nat), (zero_zero nat) ) 23.52/23.56 ( nat, nat, fact, (zero_zero nat) ) 23.52/23.56 ( nat, nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (one_one nat) ) 23.52/23.56 ( nat, nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (one_one nat) ) 23.52/23.56 ( nat, real, natceiling, (one_one real) ) 23.52/23.56 ( nat, real, natceiling, (zero_zero real) ) 23.52/23.56 ( nat, real, natfloor, (one_one real) ) 23.52/23.56 ( nat, real, natfloor, (zero_zero real) ) 23.52/23.56 ( nat, code_code_numeral, code_c271388182l_size, (zero_zero code_code_numeral) ) 23.52/23.56 ( nat, code_code_numeral, (size_size code_code_numeral), (zero_zero code_code_numeral) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (one_one int) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) (zero_zero int)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), (one_one int) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), s ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_4 ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (zero_zero int)), skv_5 ) 23.52/23.56 ( bool, int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun nat int))) (let ((_let_3 (power_power int))) (hAPP int _let_1 (hAPP int (fun int _let_1) zcong (hAPP nat int (hAPP int _let_2 _let_3 s) _let_0)) (hAPP nat int (hAPP int _let_2 _let_3 s1) _let_0)))))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) (one_one int)), t ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( bool, int, zprime, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( 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) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), min ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) min), (zero_zero int) ) 23.52/23.56 ( bool, int, nat_neg, (one_one int) ) 23.52/23.56 ( bool, int, nat_neg, (zero_zero int) ) 23.52/23.56 ( bool, int, nat_neg, (hAPP int int (number_number_of int) min) ) 23.52/23.56 ( bool, int, nat_is_nat, (one_one int) ) 23.52/23.56 ( bool, int, nat_is_nat, (zero_zero int) ) 23.52/23.56 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.56 ( bool, int, nat_is_nat, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) (one_one int)), t ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (dvd_dvd int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), pls ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) pls), min ) 23.52/23.56 ( bool, int, (even_odd_even int), (one_one int) ) 23.52/23.56 ( bool, int, (even_odd_even int), (zero_zero int) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), pls ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) pls), min ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) n))))))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( bool, int, twoSqu1091635170sum2sq, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (one_one int))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) _let_2)) (hAPP int int (hAPP int _let_0 _let_1 _let_2) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)))))))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), pls ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq int) min), min ) 23.52/23.56 ( 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))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) m1), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.56 ( 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) (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)) ) 23.52/23.56 ( bool, int, (hAPP int (fun int bool) (ord_less int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( 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))) ) 23.52/23.56 ( bool, int, (let ((_let_0 (fun int bool))) (hAPP int _let_0 (hAPP int (fun int _let_0) zcong s1) skv_5)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.57 ( bool, int, (hAPP int (fun int bool) (ord_less int) skv_5), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.57 ( 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_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.52/23.57 ( bool, int, (hAPP int (fun int bool) (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.52/23.57 ( bool, nat, (even_odd_even nat), (zero_zero nat) ) 23.52/23.57 ( bool, nat, (even_odd_even nat), (one_one nat) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), n ) 23.52/23.57 ( bool, nat, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), tn ) 23.52/23.57 ( bool, nat, prime, (zero_zero nat) ) 23.52/23.57 ( bool, nat, prime, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( bool, nat, prime, (hAPP nat nat suc (zero_zero nat)) ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), pi ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_2 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_9 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) (zero_zero real)), skv_12 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), pi ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_10 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_11 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_15 ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)), skv_18 ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less real) pi), (zero_zero real) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( bool, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real bool) (sums real) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _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)))), (one_one real) ) 23.52/23.57 ( 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 ) 23.52/23.57 ( 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 ) 23.52/23.57 ( 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) ) 23.52/23.57 ( bool, real, (hAPP real (fun real bool) (ord_less_eq real) skv_10), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( bool, (filter nat), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (fun (filter nat) bool))) (hAPP real _let_2 (hAPP _let_0 (fun real _let_2) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) (zero_zero real))))), sequentially ) 23.52/23.57 ( bool, (filter nat), (trivial_limit nat), sequentially ) 23.52/23.57 ( 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)) ) 23.52/23.57 ( bool, (fun int bool), (hAPP int (fun (fun int bool) bool) (member int) (one_one int)), zEven ) 23.52/23.57 ( bool, (fun nat bool), (finite_finite_1 nat), (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( real, rat, ratreal, (one_one rat) ) 23.52/23.57 ( real, rat, ratreal, (zero_zero rat) ) 23.52/23.57 ( real, int, (number_number_of real), min ) 23.52/23.57 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.52/23.57 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.52/23.57 ( real, int, (number_number_of real), (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( real, int, (number_number_of real), (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.57 ( 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)))))))) ) 23.52/23.57 ( real, int, (real_1 int), (one_one int) ) 23.52/23.57 ( real, int, (real_1 int), (zero_zero int) ) 23.52/23.57 ( real, nat, (real_1 nat), (zero_zero nat) ) 23.52/23.57 ( real, nat, (real_1 nat), (one_one nat) ) 23.52/23.57 ( real, real, sin, pi ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, sin, (zero_zero real) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, sin, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.52/23.57 ( real, real, cos, pi ) 23.52/23.57 ( real, real, cos, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, cos, (zero_zero real) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, cos, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.52/23.57 ( real, real, cos, skv_10 ) 23.52/23.57 ( real, real, (hAPP real (fun real real) (inverse_divide real) pi), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( real, 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)))) ) 23.52/23.57 ( real, real, (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)))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, (uminus_uminus real), (one_one real) ) 23.52/23.57 ( 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) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( 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))))))))) ) 23.52/23.57 ( real, real, (sgn_sgn real), (zero_zero real) ) 23.52/23.57 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.52/23.57 ( real, real, sqrt, (one_one real) ) 23.52/23.57 ( real, real, sqrt, (zero_zero real) ) 23.52/23.57 ( real, real, sqrt, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( real, real, tan, pi ) 23.52/23.57 ( real, real, tan, (zero_zero real) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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)))) ) 23.52/23.57 ( real, real, ln, (one_one real) ) 23.52/23.57 ( real, real, (inverse_inverse real), (zero_zero real) ) 23.52/23.57 ( real, real, (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.52/23.57 ( real, real, (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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.52/23.57 ( real, real, arctan, (one_one real) ) 23.52/23.57 ( real, real, arctan, (zero_zero real) ) 23.52/23.57 ( 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))))) ) 23.52/23.57 ( 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)))))))))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( 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))) ) 23.52/23.57 ( real, real, (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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 ) 23.52/23.57 ( 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)))))) ) 23.52/23.57 ( real, real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real _let_1 (minus_minus real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2))))))))), (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))))))))))) ) 23.63/23.60 ( real, (fun nat real), (suminf real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 23.63/23.60 ( real, complex, re, (zero_zero complex) ) 23.63/23.60 ( real, complex, re, ii ) 23.63/23.60 ( real, complex, re, (one_one complex) ) 23.63/23.60 ( real, complex, im, (zero_zero complex) ) 23.63/23.60 ( real, complex, im, ii ) 23.63/23.60 ( real, complex, im, (one_one complex) ) 23.63/23.61 ( real, (fun real bool), (the real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2)))))))))))))) ) 23.63/23.61 ( (fun nat real), real, (power_power real), (hAPP int real (number_number_of real) min) ) 23.63/23.61 ( (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)))) ) 23.63/23.61 ( (fun nat real), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP (fun real _let_1) (fun _let_0 _let_2) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min))))))), (one_one real) ) 23.63/23.61 ( (fun nat real), (fun nat real), (diffs real), sin_coeff ) 23.63/23.61 ( (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))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 23.63/23.61 ( (fun nat real), (fun nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (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) 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nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))) ) 23.63/23.61 ( (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 ) 23.63/23.61 ( (fun real real), nat, root, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.63/23.61 ( (fun real real), real, (inverse_divide real), pi ) 23.63/23.61 ( (fun real real), real, (inverse_divide real), (one_one real) ) 23.63/23.61 ( (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)))) ) 23.63/23.61 ( (fun real real), real, (inverse_divide real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.63/23.61 ( (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)))) ) 23.63/23.61 ( (fun real real), real, (times_times real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.63/23.61 ( (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)))) ) 23.63/23.61 ( (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))))) ) 23.63/23.61 ( (fun real real), real, (minus_minus real), (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.63/23.61 ( (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 ) 23.63/23.61 ( (fun nat nat), nat, (plus_plus nat), (one_one nat) ) 23.63/23.61 ( (fun nat nat), nat, (minus_minus nat), (hAPP int nat nat_1 t) ) 23.63/23.61 ( (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))) ) 23.63/23.61 ( (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) ) 23.63/23.61 ( (fun (filter nat) bool), real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 (fun real (fun (filter nat) bool)) (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 _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))))), (zero_zero real) ) 23.63/23.61 ( (fun real (fun (filter nat) bool)), (fun nat real), (tendsto nat real), (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.63/23.61 ( (fun int rat), int, fract, (one_one int) ) 23.63/23.61 ( (fun int rat), int, fract, (zero_zero int) ) 23.63/23.61 ( complex, int, (number_number_of complex), min ) 23.63/23.61 ( complex, int, (number_number_of complex), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.63/23.61 ( 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))) ) 23.63/23.61 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (one_one real) ) 23.63/23.61 ( complex, real, (hAPP real (fun real complex) complex_1 (zero_zero real)), (zero_zero real) ) 23.63/23.61 ( complex, real, (of_real complex), (hAPP int real (number_number_of real) min) ) 23.63/23.61 ( complex, real, (of_real complex), pi ) 23.63/23.61 ( complex, real, (of_real complex), (hAPP real real (uminus_uminus real) (one_one real)) ) 23.63/23.61 ( complex, real, cis, (zero_zero real) ) 23.63/23.61 ( complex, real, (hAPP real (fun real complex) complex_1 (one_one real)), (zero_zero real) ) 23.63/23.61 ( complex, complex, cnj, (zero_zero complex) ) 23.63/23.61 ( complex, complex, cnj, ii ) 23.63/23.61 ( complex, complex, cnj, (one_one complex) ) 23.63/23.61 ( complex, complex, (hAPP complex (fun complex complex) (times_times complex) ii), ii ) 23.63/23.61 ( complex, complex, (uminus_uminus complex), ii ) 23.63/23.61 ( complex, complex, (uminus_uminus complex), (one_one complex) ) 23.63/23.61 ( complex, complex, expi, (zero_zero complex) ) 23.63/23.61 ( 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))) ) 23.63/23.61 ( complex, complex, (inverse_inverse complex), ii ) 23.63/23.61 ( 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) ) 23.63/23.61 ( 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 ) 23.63/23.61 ( (fun int bool), int, (ord_less int), (one_one int) ) 23.63/23.61 ( (fun int bool), int, (ord_less int), min ) 23.63/23.61 ( (fun int bool), int, (ord_less int), (zero_zero int) ) 23.63/23.61 ( (fun int bool), int, (ord_less int), s ) 23.63/23.61 ( (fun int bool), int, (ord_less int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.63/23.61 ( (fun int bool), int, (ord_less int), t ) 23.63/23.61 ( (fun int bool), int, (ord_less int), m1 ) 23.63/23.61 ( (fun int bool), int, (ord_less int), skv_4 ) 23.63/23.61 ( (fun int bool), int, (ord_less int), skv_5 ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq int), (one_one int) ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq int), min ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq int), (zero_zero int) ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.63/23.61 ( (fun int bool), int, (ord_less_eq 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.63/23.61 ( (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)))) ) 23.63/23.61 ( (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) ) 23.63/23.61 ( (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) ) 23.63/23.61 ( (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))) ) 23.63/23.61 ( (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))) ) 23.63/23.61 ( (fun int bool), int, (dvd_dvd int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.63/23.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), s ) 23.63/23.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_4 ) 23.63/23.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong s1), skv_5 ) 23.63/23.61 ( (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) ) 23.63/23.61 ( (fun int bool), int, (hAPP int (fun int (fun int bool)) zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))), (hAPP int int (number_number_of int) min) ) 23.63/23.61 ( (fun int bool), (fun int bool), (collect int), (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun int _let_1))) (let ((_let_4 (fun _let_0 _let_1))) (let ((_let_5 (fun int _let_4))) (hAPP _let_3 _let_1 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real bool))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun int real))) (let ((_let_5 (fun int _let_0))) (let ((_let_6 (fun _let_4 (fun int bool)))) (let ((_let_7 (fun real (fun int (fun int bool))))) (let ((_let_8 (fun int _let_4))) (let ((_let_9 (fun _let_8 (fun int (fun int bool))))) (let ((_let_10 (fun real _let_9))) (let ((_let_11 (fun real _let_6))) (let ((_let_12 (fun _let_4 _let_4))) (let ((_let_13 (fun int _let_12))) (hAPP _let_8 _let_7 (hAPP _let_10 (fun _let_8 _let_7) (combc real _let_8 (fun int (fun int bool))) (hAPP _let_11 _let_10 (hAPP (fun _let_6 _let_9) (fun _let_11 _let_10) (combb _let_6 _let_9 real) (combb _let_4 (fun int bool) int)) (hAPP _let_3 _let_11 (hAPP (fun _let_2 _let_6) (fun _let_3 _let_11) (combb _let_2 _let_6 real) (combb real bool int)) (fequal real)))) (hAPP _let_4 _let_8 (hAPP _let_13 (fun _let_4 _let_8) (combc int _let_4 _let_4) (hAPP _let_5 _let_13 (hAPP (fun _let_0 _let_12) (fun _let_5 _let_13) (combb _let_0 _let_12 int) (combb real real int)) (hAPP _let_4 _let_5 (hAPP (fun real _let_0) (fun _let_4 _let_5) (combb real _let_0 int) (inverse_divide real)) _let_1))) _let_1)))))))))))))))) ) 23.66/23.67 ( (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)))) ) 23.66/23.67 ( (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)))))) ) 23.66/23.67 ( (fun int (fun int real)), (fun int real), (let ((_let_0 (fun real real))) (let ((_let_1 (fun int real))) (let ((_let_2 (fun int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_4 (fun _let_1 (fun int _let_1)) (combc int _let_1 _let_1) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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))))))))), (real_1 int) ) 23.66/23.67 ( (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 _let_1 _let_0))) (let ((_let_3 (fun (fun int _let_1) (fun int _let_0)))) (hAPP (fun _let_2 _let_3) (fun (fun real _let_2) (fun real _let_3)) (combb _let_2 _let_3 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)))))) ) 23.66/23.67 ( (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 real) (fun int bool)))) (let ((_let_3 (fun (fun int (fun int real)) (fun int (fun int bool))))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (fun real _let_2))) (hAPP _let_5 _let_4 (hAPP (fun _let_2 _let_3) (fun _let_5 _let_4) (combb _let_2 _let_3 real) (combb (fun int real) (fun int bool) int)) (hAPP _let_1 _let_5 (hAPP (fun _let_0 _let_2) (fun _let_1 _let_5) (combb _let_0 _let_2 real) (combb real bool int)) (fequal real))))))))) ) 23.66/23.67 ( (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) ) 23.66/23.67 ( (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) ) 23.66/23.67 ( (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) ) 23.66/23.67 ( (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))))) ) 23.66/23.67 ( (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 int _let_0))) (let ((_let_3 (fun _let_1 _let_1))) (let ((_let_4 (fun int _let_3))) (hAPP _let_2 _let_4 (hAPP (fun _let_0 _let_3) (fun _let_2 _let_4) (combb _let_0 _let_3 int) (combb real real int)) (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)))))))) ) 23.66/23.67 ( (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) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159306 $$unsorted) (BOUND_VARIABLE_159307 $$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_159306)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_159307)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) BOUND_VARIABLE_159307) (zero_zero X_a)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159307) BOUND_VARIABLE_159306)))))) ) 23.66/23.67 ( int, pls, min ) 23.66/23.67 ( int, pls, (zero_zero int) ) 23.66/23.67 ( int, (one_one int), (zero_zero int) ) 23.66/23.67 ( int, min, min ) 23.66/23.67 ( int, min, (zero_zero int) ) 23.66/23.67 ( int, s, (zero_zero int) ) 23.66/23.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.66/23.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.66/23.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.66/23.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.66/23.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.66/23.67 ( int, t, (one_one int) ) 23.66/23.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.66/23.67 ( int, skv_4, (zero_zero int) ) 23.66/23.67 ( int, skv_5, (zero_zero int) ) 23.66/23.67 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( real, pi, (zero_zero real) ) 23.66/23.67 ( 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)))) ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.66/23.67 ( real, (hAPP real real (hAPP 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) ) 23.66/23.67 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.66/23.67 ( real, skv_10, (zero_zero real) ) 23.66/23.67 ( real, skv_11, (zero_zero real) ) 23.66/23.67 ( real, skv_15, (zero_zero real) ) 23.66/23.67 ( real, skv_18, (zero_zero real) ) 23.66/23.67 ) 23.66/23.67 (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)))))) ) 23.66/23.67 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.66/23.67 ( 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))) ) 23.66/23.67 ( v, y ) 23.66/23.67 ( v, sa ) 23.66/23.67 ( v, x ) 23.66/23.67 ( v, r ) 23.66/23.67 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.67 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.67 ( w, y ) 23.66/23.67 ( w, sa ) 23.66/23.67 ( w, x ) 23.66/23.67 ( w, r ) 23.66/23.67 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.67 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.67 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.66/23.67 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.67 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.66/23.67 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( skv_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))) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159340 $$unsorted) (BOUND_VARIABLE_159341 $$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 X_a X_a (uminus_uminus X_a) (hAPP int X_a _let_2 BOUND_VARIABLE_159340))) BOUND_VARIABLE_159341) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP int X_a _let_2 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_159340))) BOUND_VARIABLE_159341)))))) ) 23.66/23.67 ( int, pls, (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))) m1))) ) 23.66/23.67 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.67 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.67 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.66/23.67 ( int, pls, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159364 $$unsorted) (BOUND_VARIABLE_159365 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (metric_space X_a)) (not (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_159364) BOUND_VARIABLE_159365) sequentially))) (hBOOL (hAPP _let_1 bool (cauchy X_a) BOUND_VARIABLE_159364))))) ) 23.66/23.67 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), (zero_zero real) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159397 $$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_159397) _let_0)))) ) 23.66/23.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.67 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.67 ( int, y ) 23.66/23.67 ( int, sa ) 23.66/23.67 ( int, x ) 23.66/23.67 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.66/23.67 ( int, r ) 23.66/23.67 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.67 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.67 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( int, skv_13 ) 23.66/23.67 ( int, skv_19 ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.67 ( 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))))) ) 23.66/23.67 ( complex, ii ) 23.66/23.67 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.67 ( 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)) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159414 $$unsorted) (BOUND_VARIABLE_159415 $$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_159415))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_159414))) (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_159415) BOUND_VARIABLE_159414))))) ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 23.66/23.67 ( 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)))) ) 23.66/23.67 ( 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))) ) 23.66/23.67 ( 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)))) ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 23.66/23.67 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 23.66/23.67 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 23.66/23.67 ( 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) ) 23.66/23.67 ) 23.66/23.67 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (dvd_dvd int) X) Y))) (= (hAPP int int (abs_abs int) X) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) Y))) ) 23.66/23.68 ( (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))), (hAPP 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)) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (not (= _let_0 (hAPP real real sqrt X))) (= _let_0 X))) ) 23.66/23.68 ( pi ) 23.66/23.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( (one_one real) ) 23.66/23.68 ( (zero_zero real) ) 23.66/23.68 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.68 ( skv_10 ) 23.66/23.68 ( skv_11 ) 23.66/23.68 ( skv_15 ) 23.66/23.68 ( skv_18 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((Z_1 $$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))))) ) 23.66/23.68 ( pls ) 23.66/23.68 ( (one_one int) ) 23.66/23.68 ( min ) 23.66/23.68 ( (zero_zero int) ) 23.66/23.68 ( s ) 23.66/23.68 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ( t ) 23.66/23.68 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.68 ( skv_4 ) 23.66/23.68 ( skv_5 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (sgn_div_norm X_a)) (= _let_0 (ti (fun X_a real) _let_0)))) ) 23.66/23.68 ( rat ) 23.66/23.68 ( int ) 23.66/23.68 ( nat ) 23.66/23.68 ( real ) 23.66/23.68 ( complex ) 23.66/23.68 ( (fun real bool) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((B $$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))) (= (hAPP int int (hAPP int (fun int int) (div_mod int) A_1) B) (ti int A_1)))) ) 23.66/23.68 ( pls, (zero_zero int) ) 23.66/23.68 ( (one_one int), (zero_zero int) ) 23.66/23.68 ( min, min ) 23.66/23.68 ( min, (zero_zero int) ) 23.66/23.68 ( (zero_zero int), min ) 23.66/23.68 ( (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))), (zero_zero int) ) 23.66/23.68 ( (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 ) 23.66/23.68 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( (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 ) 23.66/23.68 ( (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 ) 23.66/23.68 ( (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_5 ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.66/23.68 ( t, (one_one int) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 (hAPP int int succ V))))) ) 23.66/23.68 ( pls ) 23.66/23.68 ( (hAPP int int bit1 pls) ) 23.66/23.68 ( (one_one int) ) 23.66/23.68 ( min ) 23.66/23.68 ( (zero_zero int) ) 23.66/23.68 ( s ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( t ) 23.66/23.68 ( m1 ) 23.66/23.68 ( skv_4 ) 23.66/23.68 ( skv_5 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (one_one nat))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) _let_0) (hAPP int nat (number_number_of nat) V))))) ) 23.66/23.68 ( pls ) 23.66/23.68 ( (hAPP int int bit1 pls) ) 23.66/23.68 ( (one_one int) ) 23.66/23.68 ( min ) 23.66/23.68 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.68 ( (zero_zero int) ) 23.66/23.68 ( s ) 23.66/23.68 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( t ) 23.66/23.68 ( m1 ) 23.66/23.68 ( skv_4 ) 23.66/23.68 ( skv_5 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159541 $$unsorted) (BOUND_VARIABLE_159542 $$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_159541) BOUND_VARIABLE_159542))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_159542)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_159541))))))) ) 23.66/23.68 ( int, pls, pls ) 23.66/23.68 ( int, pls, (one_one int) ) 23.66/23.68 ( int, (one_one int), pls ) 23.66/23.68 ( int, (one_one int), (one_one int) ) 23.66/23.68 ( int, (one_one int), t ) 23.66/23.68 ( int, min, pls ) 23.66/23.68 ( int, min, min ) 23.66/23.68 ( int, (zero_zero int), pls ) 23.66/23.68 ( int, (zero_zero int), (one_one int) ) 23.66/23.68 ( int, (zero_zero int), min ) 23.66/23.68 ( int, (zero_zero int), s ) 23.66/23.68 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.68 ( int, (zero_zero int), skv_4 ) 23.66/23.68 ( int, (zero_zero int), skv_5 ) 23.66/23.68 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.68 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.66/23.68 ( 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))) ) 23.66/23.68 ( real, (zero_zero real), pi ) 23.66/23.68 ( 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)))) ) 23.66/23.68 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( real, (zero_zero real), skv_10 ) 23.66/23.68 ( real, (zero_zero real), skv_11 ) 23.66/23.68 ( real, (zero_zero real), skv_15 ) 23.66/23.68 ( real, (zero_zero real), skv_18 ) 23.66/23.68 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.66/23.68 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((P_5 $$unsorted)) (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (hAPP int int bit0 _let_0))) (let ((_let_2 (number_number_of int))) (let ((_let_3 (ti int P_5))) (or (not (hBOOL (hAPP int bool zprime P_5))) (= (hAPP int int _let_2 _let_1) _let_3) (= (hAPP int int _let_2 (hAPP int int bit1 _let_0)) _let_3) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int _let_2 (hAPP int int bit1 _let_1))) P_5))))))) ) 23.66/23.68 ( pls ) 23.66/23.68 ( min ) 23.66/23.68 ( s ) 23.66/23.68 ( s1 ) 23.66/23.68 ( m ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.68 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ( t ) 23.66/23.68 ( v ) 23.66/23.68 ( w ) 23.66/23.68 ( y ) 23.66/23.68 ( sa ) 23.66/23.68 ( x ) 23.66/23.68 ( r ) 23.66/23.68 ( m1 ) 23.66/23.68 ( skv_14 ) 23.66/23.68 ( skv_20 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((Ya $$unsorted) (Xa $$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) zOdd))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Ya) zOdd))) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP int int (hAPP int (fun int int) (minus_minus int) Xa) Ya)) zEven)))))) ) 23.66/23.68 ( (hAPP int int (number_number_of int) min), (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (times_times int) y) v), (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.66/23.68 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (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))) m1))) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), y ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), x ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (= (hAPP real real cos (hAPP real real (hAPP real _let_0 (minus_minus real) X) Y)) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real cos Y)) (hAPP real real cos X))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real sin Y)) (hAPP real real sin X)))))) ) 23.66/23.68 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 (zero_zero real)) Y))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X) pi))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos X)) (hAPP real real cos Y))))))) ) 23.66/23.68 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((Y $$unsorted) (X $$unsorted) (P_5 $$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) (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) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) X) P_5))) (not (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) P_5) Y)))))) ) 23.66/23.68 ( 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))) ) 23.66/23.68 ( s, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.68 ( s1, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.68 ( skv_16, (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) min) (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) min)))) ) 23.66/23.68 ( rat ) 23.66/23.68 ( int ) 23.66/23.68 ( nat ) 23.66/23.68 ( real ) 23.66/23.68 ( complex ) 23.66/23.68 ( quickcheck_code_int ) 23.66/23.68 ( code_code_numeral ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159639 $$unsorted) (BOUND_VARIABLE_159640 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (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_eq X_a) (hAPP int X_a _let_0 BOUND_VARIABLE_159639)) (hAPP int X_a _let_0 BOUND_VARIABLE_159640))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_159639) BOUND_VARIABLE_159640))))) ) 23.66/23.68 ( int, pls, pls ) 23.66/23.68 ( int, pls, (hAPP int int bit1 pls) ) 23.66/23.68 ( int, pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.68 ( int, pls, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((Xa $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) min)) Xa))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) (one_one real)))) (hBOOL (hAPP real bool (hAPP (fun real real) _let_0 (isCont real real) arcsin) Xa))))) ) 23.66/23.68 ( pi ) 23.66/23.68 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( (one_one real) ) 23.66/23.68 ( (zero_zero real) ) 23.66/23.68 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.66/23.68 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((R_3 $$unsorted) (S_3 $$unsorted)) (let ((_let_0 (fun real real))) (= (hAPP real real (hAPP real _let_0 (minus_minus real) R_3) S_3) (hAPP real real (hAPP real _let_0 (plus_plus real) R_3) (hAPP real real (uminus_uminus real) S_3)))) ) 23.66/23.68 ( (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (hAPP real real arctan (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))))))))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int int bit1 pls))) (let ((_let_2 (number_number_of nat))) (let ((_let_3 (hAPP int nat _let_2 (hAPP int int bit0 _let_1)))) (let ((_let_4 (times_times int))) (let ((_let_5 (minus_minus int))) (let ((_let_6 (hAPP int int bit1 _let_1))) (let ((_let_7 (hAPP int nat _let_2 _let_6))) (let ((_let_8 (hAPP int _let_0 _let_4 (hAPP int int (number_number_of int) _let_6)))) (let ((_let_9 (hAPP int (fun nat int) (power_power int) A_1))) (let ((_let_10 (hAPP int (fun nat int) (power_power int) B))) (= (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_5 A_1) B)) _let_7) (hAPP int int (hAPP int _let_0 _let_5 (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_5 (hAPP nat int _let_9 _let_7)) (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int _let_8 (hAPP nat int _let_9 _let_3))) B))) (hAPP int int (hAPP int _let_0 _let_4 (hAPP int int _let_8 A_1)) (hAPP nat int _let_10 _let_3)))) (hAPP nat int _let_10 _let_7)))))))))))))) ) 23.66/23.68 ( y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.66/23.68 ( x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.66/23.68 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.66/23.68 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.66/23.68 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (and (= (one_one real) Ya) (= (zero_zero real) Xa)) (= ii (hAPP real complex (hAPP real (fun real complex) complex_1 Xa) Ya))) ) 23.66/23.68 ( (one_one real), (zero_zero real) ) 23.66/23.68 ( (zero_zero real), (one_one real) ) 23.66/23.68 ( (zero_zero real), (zero_zero real) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159695 $$unsorted) (BOUND_VARIABLE_159696 $$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_159695) BOUND_VARIABLE_159696))) (hAPP X_a X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a _let_0 BOUND_VARIABLE_159695)) (hAPP X_a X_a _let_0 BOUND_VARIABLE_159696)))))))) ) 23.66/23.68 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.66/23.68 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.66/23.68 ( 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) ) 23.66/23.68 ( 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) ) 23.66/23.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.66/23.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.66/23.68 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.66/23.68 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.68 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.66/23.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.68 ( nat, (one_one nat), (one_one nat) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159717 $$unsorted)) (or (not (number_ring X_a)) (= (ti X_a BOUND_VARIABLE_159717) (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_159717))) ) 23.66/23.68 ( int, pls ) 23.66/23.68 ( int, min ) 23.66/23.68 ( int, s ) 23.66/23.68 ( int, s1 ) 23.66/23.68 ( int, m ) 23.66/23.68 ( int, t ) 23.66/23.68 ( int, v ) 23.66/23.68 ( int, w ) 23.66/23.68 ( int, y ) 23.66/23.68 ( int, sa ) 23.66/23.68 ( int, x ) 23.66/23.68 ( int, r ) 23.66/23.68 ( int, m1 ) 23.66/23.68 ( int, skv_14 ) 23.66/23.68 ( int, skv_20 ) 23.66/23.68 ( (fun int int), bit1 ) 23.66/23.68 ( (fun int int), bit0 ) 23.66/23.68 ( (fun int int), succ ) 23.66/23.68 ( (fun int int), pred ) 23.66/23.68 ( (fun int int), (fact_fact int) ) 23.66/23.68 ( (fun int int), zfact ) 23.66/23.68 ( nat, n ) 23.66/23.68 ( nat, tn ) 23.66/23.68 ( bool, fTrue ) 23.66/23.68 ( bool, fFalse ) 23.66/23.68 ( real, pi ) 23.66/23.68 ( (fun nat real), (real_1 nat) ) 23.66/23.68 ( (fun nat real), cos_coeff ) 23.66/23.68 ( (fun nat real), sin_coeff ) 23.66/23.68 ( (fun real real), sin ) 23.66/23.68 ( (fun real real), cos ) 23.66/23.68 ( (fun real real), sqrt ) 23.66/23.68 ( (fun real real), tan ) 23.66/23.68 ( (fun real real), ln ) 23.66/23.68 ( (fun real real), arctan ) 23.66/23.68 ( (fun real real), arcsin ) 23.66/23.68 ( (fun real real), arccos ) 23.66/23.68 ( (fun nat nat), suc ) 23.66/23.68 ( (fun nat nat), (fact_fact nat) ) 23.66/23.68 ( (fun nat nat), nat_size ) 23.66/23.68 ( (fun nat nat), (size_size nat) ) 23.66/23.68 ( (fun nat nat), fact ) 23.66/23.68 ( (filter nat), sequentially ) 23.66/23.68 ( (fun int (fun int rat)), fract ) 23.66/23.68 ( complex, ii ) 23.66/23.68 ( (fun int bool), zOdd ) 23.66/23.68 ( (fun int bool), zprime ) 23.66/23.68 ( (fun int bool), zEven ) 23.66/23.68 ( (fun int bool), nat_neg ) 23.66/23.68 ( (fun int bool), nat_is_nat ) 23.66/23.68 ( (fun int bool), (even_odd_even int) ) 23.66/23.68 ( (fun int bool), twoSqu1091635170sum2sq ) 23.66/23.68 ( (fun int (fun int int)), legacy_zgcd ) 23.66/23.68 ( (fun int (fun int int)), (gcd_gcd int) ) 23.66/23.68 ( (fun int (fun int int)), inv ) 23.66/23.68 ( (fun int (fun int int)), multInv ) 23.66/23.68 ( (fun int (fun int int)), legendre ) 23.66/23.68 ( (fun int (fun int int)), standardRes ) 23.66/23.68 ( (fun int (fun int int)), nat_tsub ) 23.66/23.68 ( (fun int (fun int int)), z3div ) 23.66/23.68 ( (fun int (fun int int)), z3mod ) 23.66/23.68 ( (fun int (fun int int)), int_lcm ) 23.66/23.68 ( (fun int (fun int int)), int_gcd ) 23.66/23.68 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.66/23.68 ( (fun bool bool), fNot ) 23.66/23.68 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.66/23.68 ( (fun bool (fun bool bool)), fconj ) 23.66/23.68 ( (fun bool (fun bool bool)), fdisj ) 23.66/23.68 ( (fun bool (fun bool bool)), fimplies ) 23.66/23.68 ( (fun int (fun int bool)), quadRes ) 23.66/23.68 ( (fun int (fun int bool)), d22set ) 23.66/23.68 ( (fun int (fun int bool)), norRRset ) 23.66/23.68 ( (fun int (fun int bool)), sRStar ) 23.66/23.68 ( (fun int (fun int bool)), sr ) 23.66/23.68 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.66/23.68 ( (fun nat bool), (even_odd_even nat) ) 23.66/23.68 ( (fun nat bool), prime ) 23.66/23.68 ( (fun real complex), cis ) 23.66/23.68 ( (fun nat (fun nat bool)), coprime ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.66/23.68 ( (fun (product_prod int int) bool), frac_1 ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.66/23.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.66/23.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.66/23.68 ( (fun (fun int bool) bool), nat_nat_set ) 23.66/23.68 ( (fun nat (fun real real)), root ) 23.66/23.68 ( (fun real (fun real real)), log ) 23.66/23.68 ( (fun real (fun real real)), powr ) 23.66/23.68 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.66/23.68 ( (fun complex complex), cnj ) 23.66/23.68 ( (fun complex complex), expi ) 23.66/23.68 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.66/23.68 ( (fun nat (fun nat nat)), nat_gcd ) 23.66/23.68 ( (fun nat (fun nat nat)), nat_lcm ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.66/23.68 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.66/23.68 ( (fun int (fun (fun int bool) bool)), resSet ) 23.66/23.68 ( (fun int nat), nat_1 ) 23.66/23.68 ( (fun int nat), phi ) 23.66/23.68 ( (fun complex real), re ) 23.66/23.68 ( (fun complex real), im ) 23.66/23.68 ( (fun complex real), arg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.66/23.68 ( (fun (product_prod nat nat) bool), pred_nat ) 23.66/23.68 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.66/23.68 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.66/23.68 ( (fun (fun int bool) int), (the int) ) 23.66/23.68 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.66/23.68 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.66/23.68 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.66/23.68 ( (fun real (fun real complex)), rcis ) 23.66/23.68 ( (fun real (fun real complex)), complex_1 ) 23.66/23.68 ( (fun int (fun int (fun int bool))), zcong ) 23.66/23.68 ( (fun int (fun int (fun int bool))), wset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), noXRRset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), bnorRset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), zcongm ) 23.66/23.68 ( (fun real nat), natceiling ) 23.66/23.68 ( (fun real nat), natfloor ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.66/23.68 ( (fun int real), (real_1 int) ) 23.66/23.68 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.66/23.68 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.66/23.68 ( (fun complex nat), (size_size complex) ) 23.66/23.68 ( (fun complex nat), complex_size ) 23.66/23.68 ( (fun (fun nat rat) bool), vanishes ) 23.66/23.68 ( (fun (product_prod int int) rat), frct ) 23.66/23.68 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.66/23.68 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.66/23.68 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.66/23.68 ( (fun rat real), ratreal ) 23.66/23.68 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.66/23.68 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.66/23.68 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.66/23.68 ( (fun rat (product_prod int int)), quotient_of ) 23.66/23.68 ( (fun int (fun nat nat)), nat_aux ) 23.66/23.68 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.66/23.68 ( (fun int (list int)), quickc666637781d_zero ) 23.66/23.68 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.66/23.68 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.66/23.68 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.66/23.68 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.66/23.68 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.66/23.68 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.66/23.68 ( (fun code_code_numeral int), code_int_of ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun nat nat))) (let ((_let_2 (minus_minus nat))) (or (not (= _let_0 (hAPP nat nat (hAPP nat _let_1 _let_2 M) N))) (not (= _let_0 (hAPP nat nat (hAPP nat _let_1 _let_2 N) M))) (= M N))))) ) 23.66/23.68 ( (one_one nat), (hAPP int nat nat_1 t) ) 23.66/23.68 ( (hAPP int nat nat_1 t), (one_one nat) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (Xa $$unsorted)) (let ((_let_0 (fun X_a (fun X_a bool)))) (= (ti X_a Xa) (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)) Xa)))) ) 23.66/23.68 ( int, pls ) 23.66/23.68 ( int, min ) 23.66/23.68 ( int, (zero_zero int) ) 23.66/23.68 ( int, s ) 23.66/23.68 ( int, s1 ) 23.66/23.68 ( int, m ) 23.66/23.68 ( int, t ) 23.66/23.68 ( int, v ) 23.66/23.68 ( int, w ) 23.66/23.68 ( int, y ) 23.66/23.68 ( int, sa ) 23.66/23.68 ( int, x ) 23.66/23.68 ( int, r ) 23.66/23.68 ( int, m1 ) 23.66/23.68 ( int, skv_14 ) 23.66/23.68 ( int, skv_20 ) 23.66/23.68 ( (fun int int), bit1 ) 23.66/23.68 ( (fun int int), bit0 ) 23.66/23.68 ( (fun int int), succ ) 23.66/23.68 ( (fun int int), pred ) 23.66/23.68 ( (fun int int), (fact_fact int) ) 23.66/23.68 ( (fun int int), zfact ) 23.66/23.68 ( nat, (zero_zero nat) ) 23.66/23.68 ( nat, n ) 23.66/23.68 ( nat, tn ) 23.66/23.68 ( bool, fTrue ) 23.66/23.68 ( bool, fFalse ) 23.66/23.68 ( real, pi ) 23.66/23.68 ( (fun nat real), (real_1 nat) ) 23.66/23.68 ( (fun nat real), cos_coeff ) 23.66/23.68 ( (fun nat real), sin_coeff ) 23.66/23.68 ( (fun real real), sin ) 23.66/23.68 ( (fun real real), cos ) 23.66/23.68 ( (fun real real), sqrt ) 23.66/23.68 ( (fun real real), tan ) 23.66/23.68 ( (fun real real), ln ) 23.66/23.68 ( (fun real real), arctan ) 23.66/23.68 ( (fun real real), arcsin ) 23.66/23.68 ( (fun real real), arccos ) 23.66/23.68 ( (fun nat nat), suc ) 23.66/23.68 ( (fun nat nat), (fact_fact nat) ) 23.66/23.68 ( (fun nat nat), nat_size ) 23.66/23.68 ( (fun nat nat), (size_size nat) ) 23.66/23.68 ( (fun nat nat), fact ) 23.66/23.68 ( (filter nat), sequentially ) 23.66/23.68 ( (fun int (fun int rat)), fract ) 23.66/23.68 ( complex, ii ) 23.66/23.68 ( (fun int bool), zOdd ) 23.66/23.68 ( (fun int bool), zprime ) 23.66/23.68 ( (fun int bool), zEven ) 23.66/23.68 ( (fun int bool), nat_neg ) 23.66/23.68 ( (fun int bool), nat_is_nat ) 23.66/23.68 ( (fun int bool), (even_odd_even int) ) 23.66/23.68 ( (fun int bool), twoSqu1091635170sum2sq ) 23.66/23.68 ( (fun int (fun int int)), legacy_zgcd ) 23.66/23.68 ( (fun int (fun int int)), (gcd_gcd int) ) 23.66/23.68 ( (fun int (fun int int)), inv ) 23.66/23.68 ( (fun int (fun int int)), multInv ) 23.66/23.68 ( (fun int (fun int int)), legendre ) 23.66/23.68 ( (fun int (fun int int)), standardRes ) 23.66/23.68 ( (fun int (fun int int)), nat_tsub ) 23.66/23.68 ( (fun int (fun int int)), z3div ) 23.66/23.68 ( (fun int (fun int int)), z3mod ) 23.66/23.68 ( (fun int (fun int int)), int_lcm ) 23.66/23.68 ( (fun int (fun int int)), int_gcd ) 23.66/23.68 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.66/23.68 ( (fun bool bool), fNot ) 23.66/23.68 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.66/23.68 ( (fun bool (fun bool bool)), fconj ) 23.66/23.68 ( (fun bool (fun bool bool)), fdisj ) 23.66/23.68 ( (fun bool (fun bool bool)), fimplies ) 23.66/23.68 ( (fun int (fun int bool)), quadRes ) 23.66/23.68 ( (fun int (fun int bool)), d22set ) 23.66/23.68 ( (fun int (fun int bool)), norRRset ) 23.66/23.68 ( (fun int (fun int bool)), sRStar ) 23.66/23.68 ( (fun int (fun int bool)), sr ) 23.66/23.68 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.66/23.68 ( (fun nat bool), (even_odd_even nat) ) 23.66/23.68 ( (fun nat bool), prime ) 23.66/23.68 ( (fun real complex), cis ) 23.66/23.68 ( (fun nat (fun nat bool)), coprime ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.66/23.68 ( (fun (product_prod int int) bool), frac_1 ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.66/23.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.66/23.68 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.66/23.68 ( (fun (fun int bool) bool), nat_nat_set ) 23.66/23.68 ( (fun nat (fun real real)), root ) 23.66/23.68 ( (fun real (fun real real)), log ) 23.66/23.68 ( (fun real (fun real real)), powr ) 23.66/23.68 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.66/23.68 ( (fun complex complex), cnj ) 23.66/23.68 ( (fun complex complex), expi ) 23.66/23.68 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.66/23.68 ( (fun nat (fun nat nat)), nat_gcd ) 23.66/23.68 ( (fun nat (fun nat nat)), nat_lcm ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.66/23.68 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.66/23.68 ( (fun int (fun (fun int bool) bool)), resSet ) 23.66/23.68 ( (fun int nat), nat_1 ) 23.66/23.68 ( (fun int nat), phi ) 23.66/23.68 ( (fun complex real), re ) 23.66/23.68 ( (fun complex real), im ) 23.66/23.68 ( (fun complex real), arg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.66/23.68 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.66/23.68 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.66/23.68 ( (fun (product_prod nat nat) bool), pred_nat ) 23.66/23.68 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.66/23.68 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.66/23.68 ( (fun (fun int bool) int), (the int) ) 23.66/23.68 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.66/23.68 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.66/23.68 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.66/23.68 ( (fun real (fun real complex)), rcis ) 23.66/23.68 ( (fun real (fun real complex)), complex_1 ) 23.66/23.68 ( (fun int (fun int (fun int bool))), zcong ) 23.66/23.68 ( (fun int (fun int (fun int bool))), wset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), noXRRset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), bnorRset ) 23.66/23.68 ( (fun int (fun int (fun int bool))), zcongm ) 23.66/23.68 ( (fun real nat), natceiling ) 23.66/23.68 ( (fun real nat), natfloor ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.66/23.68 ( (fun int real), (real_1 int) ) 23.66/23.68 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.66/23.68 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.66/23.68 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.66/23.68 ( (fun complex nat), (size_size complex) ) 23.66/23.68 ( (fun complex nat), complex_size ) 23.66/23.68 ( (fun (fun nat rat) bool), vanishes ) 23.66/23.68 ( (fun (product_prod int int) rat), frct ) 23.66/23.68 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.66/23.68 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.66/23.68 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.66/23.68 ( (fun rat real), ratreal ) 23.66/23.68 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.66/23.68 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.66/23.68 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.66/23.68 ( (fun rat (product_prod int int)), quotient_of ) 23.66/23.68 ( (fun int (fun nat nat)), nat_aux ) 23.66/23.68 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.66/23.68 ( (fun int (list int)), quickc666637781d_zero ) 23.66/23.68 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.66/23.68 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.66/23.68 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.66/23.68 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.66/23.68 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.66/23.68 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.66/23.68 ( (fun code_code_numeral int), code_int_of ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (uminus_uminus real))) (let ((_let_1 (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 (hAPP real real _let_1 X)) (hAPP real real _let_1 (hAPP real real _let_0 X)))))) ) 23.66/23.68 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (C_1 $$unsorted) (D_3 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (fun real complex))) (let ((_let_3 (hAPP real _let_0 _let_1 A_1))) (let ((_let_4 (hAPP real _let_0 _let_1 B))) (= (hAPP real complex (hAPP real _let_2 complex_1 (hAPP real real (hAPP real _let_0 (minus_minus real) (hAPP real real _let_3 C_1)) (hAPP real real _let_4 D_3))) (hAPP real real (hAPP real _let_0 (plus_plus real) (hAPP real real _let_3 D_3)) (hAPP real real _let_4 C_1))) (hAPP complex complex (hAPP complex (fun complex complex) (times_times complex) (hAPP real complex (hAPP real _let_2 complex_1 A_1) B)) (hAPP real complex (hAPP real _let_2 complex_1 C_1) D_3)))))))) ) 23.66/23.68 ( (zero_zero real), (one_one real), (zero_zero real), (one_one real) ) 23.66/23.68 ) 23.66/23.68 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159815 $$unsorted) (BOUND_VARIABLE_159816 $$unsorted) (BOUND_VARIABLE_159817 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_159817))) (or (not (linord581940658strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_159817))) (= (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_159815) BOUND_VARIABLE_159816)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_159815)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_159816)))))))) ) 23.66/23.69 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((Ma $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (= (or (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less nat) Ma) Na)) (= Ma Na)) (hBOOL (hAPP nat bool (hAPP nat _let_0 (ord_less_eq nat) Ma) Na)))) ) 23.66/23.69 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( (zero_zero nat), n ) 23.66/23.69 ( (zero_zero nat), tn ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((N $$unsorted)) (= N (hAPP real nat natfloor (hAPP nat real (real_1 nat) N))) ) 23.66/23.69 ( (zero_zero nat) ) 23.66/23.69 ( (one_one nat) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_159905 $$unsorted) (BOUND_VARIABLE_159906 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (field_inverse_zero X_a)) (not (real_normed_field X_a)) (= (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_159905) BOUND_VARIABLE_159906)) (hAPP real real (hAPP real (fun real real) (inverse_divide real) (hAPP X_a real _let_0 BOUND_VARIABLE_159905)) (hAPP X_a real _let_0 BOUND_VARIABLE_159906))))) ) 23.66/23.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.69 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( real, (one_one real), (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( 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))))))))) ) 23.66/23.69 ( 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))) ) 23.66/23.69 ( 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))) ) 23.66/23.69 ( 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))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((K_4 $$unsorted)) (= (ti int K_4) (hAPP int int (hAPP int (fun int int) (plus_plus int) K_4) pls)) ) 23.66/23.69 ( pls ) 23.66/23.69 ( (one_one int) ) 23.66/23.69 ( min ) 23.66/23.69 ( s ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( s1 ) 23.66/23.69 ( m ) 23.66/23.69 ( (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) ) 23.66/23.69 ( t ) 23.66/23.69 ( v ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( w ) 23.66/23.69 ( y ) 23.66/23.69 ( sa ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.66/23.69 ( x ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.69 ( r ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.66/23.69 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.66/23.69 ( m1 ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( skv_14 ) 23.66/23.69 ( skv_20 ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_159928 $$unsorted) (BOUND_VARIABLE_159929 $$unsorted)) (let ((_let_0 (fun (filter X_a) bool))) (let ((_let_1 (fun X_a X_b))) (let ((_let_2 (fun X_a real))) (or (not (real_normed_vector X_b)) (not (hBOOL (hAPP (filter X_a) bool (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (tendsto X_a real) (hAPP _let_1 _let_2 (hAPP (fun X_b real) (fun _let_1 _let_2) (combb X_b real X_a) (norm_norm X_b)) BOUND_VARIABLE_159928)) (zero_zero real)) BOUND_VARIABLE_159929))) (hBOOL (hAPP (filter X_a) bool (hAPP X_b _let_0 (hAPP _let_1 (fun X_b _let_0) (tendsto X_a X_b) BOUND_VARIABLE_159928) (zero_zero X_b)) BOUND_VARIABLE_159929)))))) ) 23.66/23.69 ( nat, real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))), sequentially ) 23.66/23.69 ( real, real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real _let_0))) (hAPP _let_0 _let_0 (hAPP _let_1 (fun _let_0 _let_0) (combs real real real) (hAPP _let_0 _let_1 (hAPP _let_1 (fun _let_0 _let_1) (combb real _let_0 real) (inverse_divide real)) cos)) sin))), (hAPP real (filter real) (at real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((B $$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)))) ) 23.66/23.69 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.66/23.69 ( 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))) ) 23.66/23.69 ( v, y ) 23.66/23.69 ( v, sa ) 23.66/23.69 ( v, x ) 23.66/23.69 ( v, r ) 23.66/23.69 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.69 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.69 ( w, y ) 23.66/23.69 ( w, sa ) 23.66/23.69 ( w, x ) 23.66/23.69 ( w, r ) 23.66/23.69 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.69 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.69 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.66/23.69 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.69 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.66/23.69 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.69 ( skv_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))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((Ya $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_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)))))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_2))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_2) (fun _let_3 _let_6) (combb bool _let_2 real) fconj))) (let ((_let_10 (combc real real bool))) (= (hAPP real real arctan Ya) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 (hAPP real real (uminus_uminus real) _let_1)))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) _let_1))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) tan)) Ya)))))))))))))))) ) 23.66/23.69 ( (one_one real) ) 23.66/23.69 ( (zero_zero real) ) 23.66/23.69 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.66/23.69 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) (one_one real)) (hAPP int real (number_number_of real) (hAPP int int 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)))))))))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (one_one real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (= _let_0 A_1) (= _let_0 (hAPP real real (hAPP real (fun real real) log A_1) A_1)))) ) 23.66/23.69 ( pi ) 23.66/23.69 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( skv_2 ) 23.66/23.69 ( skv_9 ) 23.66/23.69 ( skv_12 ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (not (hBOOL (hAPP int bool _let_0 Y))) (hBOOL (hAPP int bool _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) X) Y))))) ) 23.66/23.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.66/23.69 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( (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 ) 23.66/23.69 ( (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))), m1 ) 23.66/23.69 ( (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.66/23.69 ( (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_21 ) 23.66/23.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.66/23.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.66/23.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.66/23.69 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.66/23.69 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.66/23.69 ( y, v ) 23.66/23.69 ( y, w ) 23.66/23.69 ( sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( sa, v ) 23.66/23.69 ( sa, w ) 23.66/23.69 ( x, v ) 23.66/23.69 ( x, w ) 23.66/23.69 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.66/23.69 ( r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( r, v ) 23.66/23.69 ( r, w ) 23.66/23.69 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.66/23.69 ( (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.66/23.69 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.66/23.69 ( (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.66/23.69 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.66/23.69 ( skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160085 $$unsorted)) (let ((_let_0 (number_number_of X_a))) (or (not (number_ring X_a)) (= (hAPP int X_a _let_0 (hAPP int int pred BOUND_VARIABLE_160085)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (hAPP X_a X_a (uminus_uminus X_a) (one_one X_a))) (hAPP int X_a _let_0 BOUND_VARIABLE_160085))))) ) 23.66/23.69 ( int, pls ) 23.66/23.69 ( real, pls ) 23.66/23.69 ( complex, pls ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((Nat $$unsorted) (Nat_5 $$unsorted)) (= (= (hAPP nat nat suc Nat) (hAPP nat nat suc Nat_5)) (= Nat Nat_5)) ) 23.66/23.69 ( (zero_zero nat), (zero_zero nat) ) 23.66/23.69 ( (zero_zero nat), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.69 ( (hAPP nat nat suc (zero_zero nat)), (zero_zero nat) ) 23.66/23.69 ( (hAPP nat nat suc (zero_zero nat)), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 23.66/23.69 ( (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))), (zero_zero nat) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160108 $$unsorted)) (or (not (preorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_160108) BOUND_VARIABLE_160108)))) ) 23.66/23.69 ( int, (one_one int) ) 23.66/23.69 ( int, min ) 23.66/23.69 ( int, (zero_zero int) ) 23.66/23.69 ( int, s ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( int, t ) 23.66/23.69 ( int, m1 ) 23.66/23.69 ( int, skv_4 ) 23.66/23.69 ( int, skv_5 ) 23.66/23.69 ( nat, (zero_zero nat) ) 23.66/23.69 ( real, pi ) 23.66/23.69 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( real, (one_one real) ) 23.66/23.69 ( real, (zero_zero real) ) 23.66/23.69 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.66/23.69 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160150 $$unsorted) (BOUND_VARIABLE_160151 $$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_160150) BOUND_VARIABLE_160151)))) (not (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160151))) (hBOOL (hAPP X_a bool _let_0 BOUND_VARIABLE_160150)))) ) 23.66/23.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.66/23.69 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( 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 ) 23.66/23.69 ( 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))), m1 ) 23.66/23.69 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.66/23.69 ( 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_21 ) 23.66/23.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.66/23.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.66/23.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.66/23.69 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.66/23.69 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.66/23.69 ( int, y, v ) 23.66/23.69 ( int, y, w ) 23.66/23.69 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( int, sa, v ) 23.66/23.69 ( int, sa, w ) 23.66/23.69 ( int, x, v ) 23.66/23.69 ( int, x, w ) 23.66/23.69 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.66/23.69 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( int, r, v ) 23.66/23.69 ( int, r, w ) 23.66/23.69 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.66/23.69 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.66/23.69 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.66/23.69 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.66/23.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.66/23.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.66/23.69 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.66/23.69 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.66/23.69 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.66/23.69 ( 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)))))) ) 23.66/23.69 ( 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 ) 23.66/23.69 ( complex, ii, ii ) 23.66/23.69 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.66/23.69 ( 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 ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (cauchy X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun (fun nat X_a) bool) _let_0)))) ) 23.66/23.69 ( rat ) 23.66/23.69 ( int ) 23.66/23.69 ( (fun int int) ) 23.66/23.69 ( nat ) 23.66/23.69 ( bool ) 23.66/23.69 ( real ) 23.66/23.69 ( (fun real real) ) 23.66/23.69 ( (fun nat nat) ) 23.66/23.69 ( complex ) 23.66/23.69 ( (product_prod int int) ) 23.66/23.69 ( (fun bool bool) ) 23.66/23.69 ( (fun nat bool) ) 23.66/23.69 ( (fun nat (fun nat bool)) ) 23.66/23.69 ( (fun nat (product_prod int int)) ) 23.66/23.69 ( (product_prod real real) ) 23.66/23.69 ( (product_prod nat nat) ) 23.66/23.69 ( (fun (product_prod nat nat) bool) ) 23.66/23.69 ( (fun nat (fun (product_prod nat nat) bool)) ) 23.66/23.69 ( (fun nat (product_prod nat nat)) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((A_3 $$unsorted) (P_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int (fun int bool)))) (let ((_let_2 (fun (fun int bool) bool))) (let ((_let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool zprime P_4))) (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_3) P_4))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int _let_1 zcong A_3) (zero_zero int)) P_4)) (hBOOL (hAPP int bool (hAPP int (fun int bool) quadRes P_4) A_3)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (hAPP int _let_1 zcong (hAPP (fun int bool) int (hAPP _let_0 (fun (fun int bool) int) (big_co302546470etprod int int) (combi int)) (hAPP _let_2 (fun int bool) (complete_Sup_Sup (fun int bool)) (hAPP int _let_2 (hAPP int (fun int _let_2) setS A_3) P_4)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) A_3) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_4) (one_one int))) _let_3)))) P_4))))))) ) 23.66/23.69 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((K_4 $$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)))))) ) 23.66/23.69 ( pls, min, pls ) 23.66/23.69 ( pls, (zero_zero int), min ) 23.66/23.69 ( (one_one int), (zero_zero int), pls ) 23.66/23.69 ( min, min, min ) 23.66/23.69 ( t, (zero_zero int), (one_one int) ) 23.66/23.69 ) 23.66/23.69 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160294 $$unsorted) (BOUND_VARIABLE_160295 $$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_160295) _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_160295) BOUND_VARIABLE_160294)) _let_3))))))) ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.66/23.69 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.66/23.69 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.66/23.69 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.66/23.69 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.66/23.69 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.66/23.70 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.66/23.70 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.66/23.70 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.66/23.70 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.66/23.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.66/23.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.66/23.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.66/23.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.66/23.70 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.66/23.70 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less int) (zero_zero int)) Ma))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (dvd_dvd int) Ma) Na)) (= (hAPP int int (hAPP int (fun int int) legacy_zgcd Na) Ma) (ti int Ma))))) ) 23.66/23.70 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160321 $$unsorted) (BOUND_VARIABLE_160322 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_160321) (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_160322)) (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_160321)) (hAPP int int (number_number_of int) BOUND_VARIABLE_160322))))) ) 23.66/23.70 ( nat, (zero_zero nat), (hAPP int int bit1 pls) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160378 $$unsorted) (BOUND_VARIABLE_160379 $$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))) (let ((_let_4 (fun X_a X_a))) (let ((_let_5 (times_times X_a))) (let ((_let_6 (abs_abs X_a))) (or (not (ordered_ring_abs X_a)) (and (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_160378))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160378) _let_2)))) (and (not (hBOOL (hAPP X_a bool _let_3 BOUND_VARIABLE_160379))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160379) _let_2)))) (= (hAPP X_a X_a _let_6 (hAPP X_a X_a (hAPP X_a _let_4 _let_5 BOUND_VARIABLE_160379) BOUND_VARIABLE_160378)) (hAPP X_a X_a (hAPP X_a _let_4 _let_5 (hAPP X_a X_a _let_6 BOUND_VARIABLE_160379)) (hAPP X_a X_a _let_6 BOUND_VARIABLE_160378))))))))))) ) 23.66/23.70 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.66/23.70 ( 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))) ) 23.66/23.70 ( int, v, y ) 23.66/23.70 ( int, v, sa ) 23.66/23.70 ( int, v, x ) 23.66/23.70 ( int, v, r ) 23.66/23.70 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.70 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.70 ( int, w, y ) 23.66/23.70 ( int, w, sa ) 23.66/23.70 ( int, w, x ) 23.66/23.70 ( int, w, r ) 23.66/23.70 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.66/23.70 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.66/23.70 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.66/23.70 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.66/23.70 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, skv_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))) ) 23.66/23.70 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( 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))))) ) 23.66/23.70 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( 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)))) ) 23.66/23.70 ( complex, ii, ii ) 23.66/23.70 ( 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)) ) 23.66/23.70 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160420 $$unsorted) (BOUND_VARIABLE_160421 $$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_160420) BOUND_VARIABLE_160421))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) (zero_zero X_a)) BOUND_VARIABLE_160420))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_160421)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_160420))))))) ) 23.66/23.70 ( int, (one_one int), t ) 23.66/23.70 ( int, min, pls ) 23.66/23.70 ( int, min, min ) 23.66/23.70 ( int, (zero_zero int), pls ) 23.66/23.70 ( int, (zero_zero int), (one_one int) ) 23.66/23.70 ( int, (zero_zero int), min ) 23.66/23.70 ( int, (zero_zero int), s ) 23.66/23.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (zero_zero int), skv_4 ) 23.66/23.70 ( int, (zero_zero int), skv_5 ) 23.66/23.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.66/23.70 ( 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))) ) 23.66/23.70 ( real, (zero_zero real), pi ) 23.66/23.70 ( 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)))) ) 23.66/23.70 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( real, (zero_zero real), skv_10 ) 23.66/23.70 ( real, (zero_zero real), skv_11 ) 23.66/23.70 ( real, (zero_zero real), skv_15 ) 23.66/23.70 ( real, (zero_zero real), skv_18 ) 23.66/23.70 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.66/23.70 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160641 $$unsorted) (BOUND_VARIABLE_160642 $$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_160641))) (let ((_let_3 (hAPP nat nat suc BOUND_VARIABLE_160642))) (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_160642))) (hAPP nat X_a BOUND_VARIABLE_160641 _let_3)))))))) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) s), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) s1), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (semiring_1_of_nat int), (zero_zero nat) ) 23.66/23.70 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (semiring_1_of_nat int), (hAPP nat nat suc (hAPP nat nat suc (zero_zero nat))) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) v), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) w), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) x), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) y), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2))))))))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v))))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))))), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) skv_6), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) skv_7), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) skv_16), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) skv_23), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( int, (hAPP int (fun nat int) (power_power int) skv_24), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( (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)) ) 23.66/23.70 ( nat, suc, (zero_zero nat) ) 23.66/23.70 ( nat, suc, (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( nat, (fact_fact nat), (zero_zero nat) ) 23.66/23.70 ( nat, (hAPP nat (fun nat nat) (plus_plus nat) (one_one nat)), (zero_zero nat) ) 23.66/23.70 ( nat, (hAPP nat (fun nat nat) (minus_minus nat) (hAPP int nat nat_1 t)), (zero_zero nat) ) 23.66/23.70 ( bool, (even_odd_even nat), (zero_zero nat) ) 23.66/23.70 ( bool, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( bool, prime, (zero_zero nat) ) 23.66/23.70 ( bool, prime, (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( real, (real_1 nat), (zero_zero nat) ) 23.66/23.70 ( (fun real real), root, (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ( (fun nat nat), (plus_plus nat), (zero_zero nat) ) 23.66/23.70 ( (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)) ) 23.66/23.70 ( (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) ) 23.66/23.70 ( complex, (hAPP complex (fun nat complex) (power_power complex) ii), (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X $$unsorted)) (= (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (times_times real) X) X)) (hAPP real real (abs_abs real) X)) ) 23.66/23.70 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.66/23.70 ( (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))))) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((Xa $$unsorted) (Na $$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) Na))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (zero_zero real)) Xa))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP int real (number_number_of real) Na)) Xa)) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat (number_number_of nat) Na)) (hAPP real nat natfloor Xa))))))) ) 23.66/23.70 ( pi, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (dist_dist X_a))) (or (not (metric_space X_a)) (= _let_0 (ti (fun X_a (fun X_a real)) _let_0)))) ) 23.66/23.70 ( rat ) 23.66/23.70 ( int ) 23.66/23.70 ( nat ) 23.66/23.70 ( real ) 23.66/23.70 ( complex ) 23.66/23.70 ( (fun real bool) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((N $$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))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (one_one int)) (hAPP int int (fact_fact int) N)))))) ) 23.66/23.70 ( pls ) 23.66/23.70 ( (one_one int) ) 23.66/23.70 ( min ) 23.66/23.70 ( (zero_zero int) ) 23.66/23.70 ( s ) 23.66/23.70 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.70 ( skv_4 ) 23.66/23.70 ( skv_5 ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160849 $$unsorted) (BOUND_VARIABLE_160850 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (uminus_uminus X_a))) (or (not (boolean_algebra X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160849) (hAPP X_a X_a _let_2 BOUND_VARIABLE_160850)))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160850) (hAPP X_a X_a _let_2 BOUND_VARIABLE_160849))))))) ) 23.66/23.70 ( int, pls, min ) 23.66/23.70 ( int, pls, (zero_zero int) ) 23.66/23.70 ( int, (one_one int), min ) 23.66/23.70 ( int, (one_one int), (zero_zero int) ) 23.66/23.70 ( int, min, pls ) 23.66/23.70 ( int, min, (one_one int) ) 23.66/23.70 ( int, (zero_zero int), pls ) 23.66/23.70 ( int, (zero_zero int), (one_one int) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160872 $$unsorted)) (let ((_let_0 (fun X_a bool))) (or (not (number_ring X_a)) (not (field_char_0 X_a)) (hBOOL (hAPP _let_0 bool (hAPP X_a (fun _let_0 bool) (member X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_160872)) (field_char_0_Rats X_a))))) ) 23.66/23.70 ( int, pls ) 23.66/23.70 ( int, (hAPP int int bit1 pls) ) 23.66/23.70 ( int, min ) 23.66/23.70 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.70 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.66/23.70 ( nat, pls ) 23.66/23.70 ( nat, (hAPP int int bit1 pls) ) 23.66/23.70 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.70 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.66/23.70 ( real, min ) 23.66/23.70 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.70 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.66/23.70 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.66/23.70 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.66/23.70 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 23.66/23.70 ( complex, min ) 23.66/23.70 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.66/23.70 ( quickcheck_code_int, pls ) 23.66/23.70 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 23.66/23.70 ( quickcheck_code_int, (one_one int) ) 23.66/23.70 ( code_code_numeral, pls ) 23.66/23.70 ( code_code_numeral, (hAPP int int bit1 pls) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((Va $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less nat))) (let ((_let_2 (hAPP int int (number_number_of int) (hAPP int int pred Va)))) (= (or (hBOOL (hAPP int bool nat_neg _let_2)) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat nat_1 _let_2)) Na))) (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 (hAPP int nat (number_number_of nat) Va)) (hAPP nat nat suc Na))))))) ) 23.66/23.70 ( pls, (hAPP nat nat suc (zero_zero nat)) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160894 $$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_160894))) (= _let_0 (ti X_a BOUND_VARIABLE_160894)))) ) 23.66/23.70 ( int, pls ) 23.66/23.70 ( int, min ) 23.66/23.70 ( int, s ) 23.66/23.70 ( int, s1 ) 23.66/23.70 ( int, m ) 23.66/23.70 ( int, t ) 23.66/23.70 ( int, v ) 23.66/23.70 ( int, w ) 23.66/23.70 ( int, y ) 23.66/23.70 ( int, sa ) 23.66/23.70 ( int, x ) 23.66/23.70 ( int, r ) 23.66/23.70 ( int, m1 ) 23.66/23.70 ( int, skv_14 ) 23.66/23.70 ( int, skv_20 ) 23.66/23.70 ( (fun int int), bit1 ) 23.66/23.70 ( (fun int int), bit0 ) 23.66/23.70 ( (fun int int), succ ) 23.66/23.70 ( (fun int int), pred ) 23.66/23.70 ( (fun int int), (fact_fact int) ) 23.66/23.70 ( (fun int int), zfact ) 23.66/23.70 ( nat, n ) 23.66/23.70 ( nat, tn ) 23.66/23.70 ( bool, fTrue ) 23.66/23.70 ( bool, fFalse ) 23.66/23.70 ( real, pi ) 23.66/23.70 ( (fun nat real), (real_1 nat) ) 23.66/23.70 ( (fun nat real), cos_coeff ) 23.66/23.70 ( (fun nat real), sin_coeff ) 23.66/23.70 ( (fun real real), sin ) 23.66/23.70 ( (fun real real), cos ) 23.66/23.70 ( (fun real real), sqrt ) 23.66/23.70 ( (fun real real), tan ) 23.66/23.70 ( (fun real real), ln ) 23.66/23.70 ( (fun real real), arctan ) 23.66/23.70 ( (fun real real), arcsin ) 23.66/23.70 ( (fun real real), arccos ) 23.66/23.70 ( (fun nat nat), suc ) 23.66/23.70 ( (fun nat nat), (fact_fact nat) ) 23.66/23.70 ( (fun nat nat), nat_size ) 23.66/23.70 ( (fun nat nat), (size_size nat) ) 23.66/23.70 ( (fun nat nat), fact ) 23.66/23.70 ( (filter nat), sequentially ) 23.66/23.70 ( (fun int (fun int rat)), fract ) 23.66/23.70 ( complex, ii ) 23.66/23.70 ( (fun int bool), zOdd ) 23.66/23.70 ( (fun int bool), zprime ) 23.66/23.70 ( (fun int bool), zEven ) 23.66/23.70 ( (fun int bool), nat_neg ) 23.66/23.70 ( (fun int bool), nat_is_nat ) 23.66/23.70 ( (fun int bool), (even_odd_even int) ) 23.66/23.70 ( (fun int bool), twoSqu1091635170sum2sq ) 23.66/23.70 ( (fun int (fun int int)), legacy_zgcd ) 23.66/23.70 ( (fun int (fun int int)), (gcd_gcd int) ) 23.66/23.70 ( (fun int (fun int int)), inv ) 23.66/23.70 ( (fun int (fun int int)), multInv ) 23.66/23.70 ( (fun int (fun int int)), legendre ) 23.66/23.70 ( (fun int (fun int int)), standardRes ) 23.66/23.70 ( (fun int (fun int int)), nat_tsub ) 23.66/23.70 ( (fun int (fun int int)), z3div ) 23.66/23.70 ( (fun int (fun int int)), z3mod ) 23.66/23.70 ( (fun int (fun int int)), int_lcm ) 23.66/23.70 ( (fun int (fun int int)), int_gcd ) 23.66/23.70 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.66/23.70 ( (fun bool bool), fNot ) 23.66/23.70 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.66/23.70 ( (fun bool (fun bool bool)), fconj ) 23.66/23.70 ( (fun bool (fun bool bool)), fdisj ) 23.66/23.70 ( (fun bool (fun bool bool)), fimplies ) 23.66/23.70 ( (fun int (fun int bool)), quadRes ) 23.66/23.70 ( (fun int (fun int bool)), d22set ) 23.66/23.70 ( (fun int (fun int bool)), norRRset ) 23.66/23.70 ( (fun int (fun int bool)), sRStar ) 23.66/23.70 ( (fun int (fun int bool)), sr ) 23.66/23.70 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.66/23.70 ( (fun nat bool), (even_odd_even nat) ) 23.66/23.70 ( (fun nat bool), prime ) 23.66/23.70 ( (fun real complex), cis ) 23.66/23.70 ( (fun nat (fun nat bool)), coprime ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.66/23.70 ( (fun (product_prod int int) bool), frac_1 ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.66/23.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.66/23.70 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.66/23.70 ( (fun (fun int bool) bool), nat_nat_set ) 23.66/23.70 ( (fun nat (fun real real)), root ) 23.66/23.70 ( (fun real (fun real real)), log ) 23.66/23.70 ( (fun real (fun real real)), powr ) 23.66/23.70 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.66/23.70 ( (fun complex complex), cnj ) 23.66/23.70 ( (fun complex complex), expi ) 23.66/23.70 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.66/23.70 ( (fun nat (fun nat nat)), nat_gcd ) 23.66/23.70 ( (fun nat (fun nat nat)), nat_lcm ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.66/23.70 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.66/23.70 ( (fun int (fun (fun int bool) bool)), resSet ) 23.66/23.70 ( (fun int nat), nat_1 ) 23.66/23.70 ( (fun int nat), phi ) 23.66/23.70 ( (fun complex real), re ) 23.66/23.70 ( (fun complex real), im ) 23.66/23.70 ( (fun complex real), arg ) 23.66/23.70 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.66/23.70 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.66/23.70 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.66/23.70 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.66/23.70 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.66/23.70 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.66/23.70 ( (fun (product_prod nat nat) bool), pred_nat ) 23.66/23.70 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.66/23.70 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.66/23.70 ( (fun (fun int bool) int), (the int) ) 23.66/23.70 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.66/23.70 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.66/23.70 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.66/23.70 ( (fun real (fun real complex)), rcis ) 23.66/23.70 ( (fun real (fun real complex)), complex_1 ) 23.66/23.70 ( (fun int (fun int (fun int bool))), zcong ) 23.66/23.70 ( (fun int (fun int (fun int bool))), wset ) 23.66/23.70 ( (fun int (fun int (fun int bool))), noXRRset ) 23.66/23.70 ( (fun int (fun int (fun int bool))), bnorRset ) 23.66/23.70 ( (fun int (fun int (fun int bool))), zcongm ) 23.66/23.70 ( (fun real nat), natceiling ) 23.66/23.70 ( (fun real nat), natfloor ) 23.66/23.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.66/23.70 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.66/23.70 ( (fun int real), (real_1 int) ) 23.66/23.70 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.66/23.70 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.66/23.70 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.66/23.70 ( (fun complex nat), (size_size complex) ) 23.66/23.70 ( (fun complex nat), complex_size ) 23.66/23.70 ( (fun (fun nat rat) bool), vanishes ) 23.66/23.70 ( (fun (product_prod int int) rat), frct ) 23.66/23.70 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.66/23.70 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.66/23.70 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.66/23.70 ( (fun rat real), ratreal ) 23.66/23.70 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.66/23.70 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.66/23.70 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.66/23.70 ( (fun rat (product_prod int int)), quotient_of ) 23.66/23.70 ( (fun int (fun nat nat)), nat_aux ) 23.66/23.70 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.66/23.70 ( (fun int (list int)), quickc666637781d_zero ) 23.66/23.70 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.66/23.70 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.66/23.70 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.66/23.70 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.66/23.70 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.66/23.70 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.66/23.70 ( (fun code_code_numeral int), code_int_of ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((N $$unsorted)) (= (hAPP real real cos (hAPP real real (hAPP real (fun real real) (times_times real) pi) (hAPP nat real (real_1 nat) N))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP int real (number_number_of real) min)) N)) ) 23.66/23.70 ( (zero_zero nat) ) 23.66/23.70 ( (one_one nat) ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160918 $$unsorted) (BOUND_VARIABLE_160919 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n1866405975lgebra X_a)) (= (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_160918) BOUND_VARIABLE_160919)) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP X_a real _let_0 BOUND_VARIABLE_160918)) (hAPP X_a real _let_0 BOUND_VARIABLE_160919))))) ) 23.66/23.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.66/23.70 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( 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))), t ) 23.66/23.70 ( 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))), m1 ) 23.66/23.70 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.66/23.70 ( 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))), skv_21 ) 23.66/23.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.66/23.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.66/23.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.66/23.70 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.66/23.70 ( int, y, v ) 23.66/23.70 ( int, y, w ) 23.66/23.70 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, sa, v ) 23.66/23.70 ( int, sa, w ) 23.66/23.70 ( int, x, v ) 23.66/23.70 ( int, x, w ) 23.66/23.70 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.66/23.70 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, r, v ) 23.66/23.70 ( int, r, w ) 23.66/23.70 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.66/23.70 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.66/23.70 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.66/23.70 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.66/23.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.66/23.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.66/23.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.66/23.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.66/23.70 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.66/23.70 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.66/23.70 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.66/23.70 ( 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)))))) ) 23.66/23.70 ( 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))))), pi ) 23.66/23.70 ( complex, ii, ii ) 23.66/23.70 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.66/23.70 ( 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)), ii ) 23.66/23.70 ) 23.66/23.70 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160938 $$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 BOUND_VARIABLE_160938) _let_0) (hAPP nat X_a (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_160938)) _let_0)))))) ) 23.66/23.70 ( int, pls ) 23.66/23.70 ( int, (one_one int) ) 23.66/23.70 ( int, min ) 23.66/23.70 ( int, s ) 23.66/23.70 ( int, s1 ) 23.66/23.70 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.66/23.70 ( int, v ) 23.66/23.70 ( int, w ) 23.66/23.70 ( int, y ) 23.66/23.70 ( int, x ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.66/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.76/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.76/23.70 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.76/23.71 ( int, skv_6 ) 23.76/23.71 ( int, skv_7 ) 23.76/23.71 ( int, skv_16 ) 23.76/23.71 ( int, skv_23 ) 23.76/23.71 ( int, skv_24 ) 23.76/23.71 ( 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)))) ) 23.76/23.71 ( real, (one_one real) ) 23.76/23.71 ( 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) ) 23.76/23.71 ( complex, ii ) 23.76/23.71 ( complex, (one_one complex) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160951 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_160951) (hAPP int X_a (number_number_of X_a) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_160951)) (one_one int))))) ) 23.76/23.71 ( int, (one_one int) ) 23.76/23.71 ( int, min ) 23.76/23.71 ( int, (zero_zero int) ) 23.76/23.71 ( int, s ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.71 ( int, t ) 23.76/23.71 ( int, m1 ) 23.76/23.71 ( int, skv_4 ) 23.76/23.71 ( int, skv_5 ) 23.76/23.71 ( nat, (zero_zero nat) ) 23.76/23.71 ( real, pi ) 23.76/23.71 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( real, (one_one real) ) 23.76/23.71 ( real, (zero_zero real) ) 23.76/23.71 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.76/23.71 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (ord_less int))) (let ((_let_1 (hAPP int (fun int bool) _let_0 (zero_zero int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool _let_1 Na))) (= (hAPP int int (hAPP int (fun int int) (minus_minus int) Na) (one_one int)) (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_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_4 _let_4 (combc int int bool) _let_0) Na)))))))))))) ) 23.76/23.71 ( pls ) 23.76/23.71 ( (one_one int) ) 23.76/23.71 ( min ) 23.76/23.71 ( (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)))) ) 23.76/23.71 ( (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))) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.71 ( y ) 23.76/23.71 ( x ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.76/23.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.76/23.71 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.76/23.71 ( (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))) m1))) ) 23.76/23.71 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160975 $$unsorted) (BOUND_VARIABLE_160976 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) BOUND_VARIABLE_160975) (hAPP int X_a (ring_1_of_int X_a) BOUND_VARIABLE_160976))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP X_a int (archim2085082626_floor X_a) BOUND_VARIABLE_160975)) BOUND_VARIABLE_160976)))) ) 23.76/23.71 ( real, pi, (zero_zero int) ) 23.76/23.71 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero int) ) 23.76/23.71 ( real, (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))), (zero_zero int) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_160999 $$unsorted) (BOUND_VARIABLE_161000 $$unsorted) (BOUND_VARIABLE_161001 $$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_161001))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_160999) (hAPP X_a X_a (hAPP X_a _let_2 (times_times X_a) BOUND_VARIABLE_161000) BOUND_VARIABLE_161001)))) (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_160999) BOUND_VARIABLE_161001)) BOUND_VARIABLE_161000)))))) ) 23.76/23.71 ( int, min, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.76/23.71 ( int, (zero_zero int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.76/23.71 ( 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))) ) 23.76/23.71 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.76/23.71 ( 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)), (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_0 (fun int rat))) (let ((_let_1 (product_prod int int))) (let ((_let_2 (hAPP int rat (hAPP int _let_0 fract A_1) B))) (or (not (= (hAPP int _let_1 (hAPP int (fun int _let_1) (product_Pair int int) P_5) Q_3) (hAPP rat _let_1 quotient_of _let_2))) (= _let_2 (hAPP int rat (hAPP int _let_0 fract P_5) Q_3)))))) ) 23.76/23.71 ( (one_one int), (one_one int), (zero_zero int), (one_one int) ) 23.76/23.71 ( (zero_zero int), (one_one int), (one_one int), (one_one int) ) 23.76/23.71 ( (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161060 $$unsorted) (BOUND_VARIABLE_161061 $$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_161060) BOUND_VARIABLE_161061) (ti X_a BOUND_VARIABLE_161060)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_161061)))) ) 23.76/23.71 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.76/23.71 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.76/23.71 ( 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)))), (one_one int) ) 23.76/23.71 ( 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) ) 23.76/23.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.76/23.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.76/23.71 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.76/23.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( nat, (one_one nat), (one_one nat) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Na $$unsorted) (P_1 $$unsorted)) (or (hBOOL (hAPP nat bool P_1 (zero_zero nat))) (not (hBOOL (hAPP nat bool P_1 Na))) (not (forall ((K_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 K_1))) (not (forall ((I_2 $$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 (hAPP nat (fun nat bool) (ord_less_eq nat) K_1) Na)))) ))) ) 23.76/23.71 ( (zero_zero nat), (even_odd_even nat) ) 23.76/23.71 ( (zero_zero nat), prime ) 23.76/23.71 ( (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)) ) 23.76/23.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), prime ) 23.76/23.71 ( (one_one nat), (even_odd_even nat) ) 23.76/23.71 ( (hAPP nat nat suc (zero_zero nat)), prime ) 23.76/23.71 ( n, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 23.76/23.71 ( tn, (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Ya $$unsorted) (Xa $$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 Xa))) (not (hBOOL (hAPP int bool _let_2 Ya))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) (hAPP int nat nat_1 Xa)) (hAPP int nat nat_1 Ya))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 Xa) Ya))))))) ) 23.76/23.71 ( pls, min ) 23.76/23.71 ( pls, (zero_zero int) ) 23.76/23.71 ( (one_one int), (zero_zero int) ) 23.76/23.71 ( min, min ) 23.76/23.71 ( min, (zero_zero int) ) 23.76/23.71 ( s, (zero_zero int) ) 23.76/23.71 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.76/23.71 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.76/23.71 ( t, (one_one int) ) 23.76/23.71 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.76/23.71 ( skv_4, (zero_zero int) ) 23.76/23.71 ( skv_5, (zero_zero int) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (exp X_a))) (or (not (real_normed_field X_a)) (not (banach X_a)) (= _let_0 (ti (fun X_a X_a) _let_0)))) ) 23.76/23.71 ( int ) 23.76/23.71 ( (fun int int) ) 23.76/23.71 ( nat ) 23.76/23.71 ( bool ) 23.76/23.71 ( real ) 23.76/23.71 ( (fun nat real) ) 23.76/23.71 ( (fun real real) ) 23.76/23.71 ( complex ) 23.76/23.71 ( (fun int bool) ) 23.76/23.71 ( (product_prod int int) ) 23.76/23.71 ( (fun (product_prod int int) int) ) 23.76/23.71 ( (fun int (fun int bool)) ) 23.76/23.71 ( (fun nat bool) ) 23.76/23.71 ( (fun (product_prod int int) bool) ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.76/23.71 ( (fun real bool) ) 23.76/23.71 ( code_code_numeral ) 23.76/23.71 ( (fun int (fun int (fun int bool))) ) 23.76/23.71 ( (fun int real) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$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)))) ) 23.76/23.71 ( int ) 23.76/23.71 ( (fun int int) ) 23.76/23.71 ( nat ) 23.76/23.71 ( bool ) 23.76/23.71 ( real ) 23.76/23.71 ( (fun nat real) ) 23.76/23.71 ( (fun real real) ) 23.76/23.71 ( complex ) 23.76/23.71 ( (fun int bool) ) 23.76/23.71 ( (product_prod int int) ) 23.76/23.71 ( (fun (product_prod int int) int) ) 23.76/23.71 ( (fun int (fun int bool)) ) 23.76/23.71 ( (fun nat bool) ) 23.76/23.71 ( (fun (product_prod int int) bool) ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.76/23.71 ( (fun real bool) ) 23.76/23.71 ( code_code_numeral ) 23.76/23.71 ( (fun int (fun int (fun int bool))) ) 23.76/23.71 ( (fun int real) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161192 $$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 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_161192)) BOUND_VARIABLE_161192)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_161192)))))) ) 23.76/23.71 ( int, pls ) 23.76/23.71 ( int, (one_one int) ) 23.76/23.71 ( int, min ) 23.76/23.71 ( int, s ) 23.76/23.71 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.71 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.71 ( int, skv_4 ) 23.76/23.71 ( int, skv_5 ) 23.76/23.71 ( real, pi ) 23.76/23.71 ( 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)))) ) 23.76/23.71 ( real, (one_one real) ) 23.76/23.71 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.71 ( 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) ) 23.76/23.71 ( real, skv_10 ) 23.76/23.71 ( real, skv_11 ) 23.76/23.71 ( real, skv_15 ) 23.76/23.71 ( real, skv_18 ) 23.76/23.71 ( complex, ii ) 23.76/23.71 ( complex, (one_one complex) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (fun nat nat))) (let ((_let_1 (one_one nat))) (or (= (zero_zero nat) N) (= _let_1 (hAPP nat nat (hAPP nat _let_0 (gcd_gcd nat) (hAPP nat nat (hAPP nat _let_0 (minus_minus nat) N) _let_1)) N))))) ) 23.76/23.71 ( (hAPP int nat nat_1 t) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161255 $$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_161255) (one_one X_a))) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP X_a int _let_0 BOUND_VARIABLE_161255)) (one_one int))))) ) 23.76/23.71 ( 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)))) ) 23.76/23.71 ( int, y ) 23.76/23.71 ( int, x ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.76/23.71 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.76/23.71 ( 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))) m1))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.76/23.71 ( nat, (hAPP int nat nat_1 t) ) 23.76/23.71 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))) ) 23.76/23.71 ( code_code_numeral, (zero_zero code_code_numeral) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161273 $$unsorted)) (let ((_let_0 (sgn_sgn X_a))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_161273))) (or (not (linordered_idom X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))))) ) 23.76/23.71 ( rat, (zero_zero rat) ) 23.76/23.71 ( real, (zero_zero real) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161291 $$unsorted)) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_161291)) (zero_zero X_a))))) ) 23.76/23.71 ( int, v ) 23.76/23.71 ( int, w ) 23.76/23.71 ( int, skv_14 ) 23.76/23.71 ( int, skv_20 ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Y $$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)) (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))))) ) 23.76/23.71 ( (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)))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (div_mod X_a))) (or (not (semiring_div X_a)) (= _let_0 (ti (fun X_a (fun X_a X_a)) _let_0)))) ) 23.76/23.71 ( int ) 23.76/23.71 ( (fun int int) ) 23.76/23.71 ( nat ) 23.76/23.71 ( bool ) 23.76/23.71 ( real ) 23.76/23.71 ( (fun nat real) ) 23.76/23.71 ( (fun real real) ) 23.76/23.71 ( complex ) 23.76/23.71 ( (fun int bool) ) 23.76/23.71 ( (product_prod int int) ) 23.76/23.71 ( (fun (product_prod int int) int) ) 23.76/23.71 ( (fun int (fun int bool)) ) 23.76/23.71 ( (fun nat bool) ) 23.76/23.71 ( (fun (product_prod int int) bool) ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.76/23.71 ( (fun real bool) ) 23.76/23.71 ( quickcheck_code_int ) 23.76/23.71 ( code_code_numeral ) 23.76/23.71 ( (fun int (fun int (fun int bool))) ) 23.76/23.71 ( (fun int real) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((A_1 $$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))) ) 23.76/23.71 ( min ) 23.76/23.71 ( s ) 23.76/23.71 ( s1 ) 23.76/23.71 ( m ) 23.76/23.71 ( t ) 23.76/23.71 ( v ) 23.76/23.71 ( w ) 23.76/23.71 ( y ) 23.76/23.71 ( sa ) 23.76/23.71 ( x ) 23.76/23.71 ( r ) 23.76/23.71 ( m1 ) 23.76/23.71 ( skv_14 ) 23.76/23.71 ( skv_20 ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161393 $$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_161393) (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_161393)))))) ) 23.76/23.71 ( 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)))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161414 $$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_161414)) (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_161414) (zero_zero X_a)) sequentially))))))) ) 23.76/23.71 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Q_3 $$unsorted)) (let ((_let_0 (one_one rat))) (let ((_let_1 (hAPP rat rat (sgn_sgn rat) Q_3))) (let ((_let_2 (hBOOL (hAPP rat bool (hAPP rat (fun rat bool) (ord_less rat) (zero_zero rat)) Q_3)))) (or (= (zero_zero rat) Q_3) (and (or (not _let_2) (= _let_0 _let_1)) (or _let_2 (= _let_1 (hAPP rat rat (uminus_uminus rat) _let_0)))))))) ) 23.76/23.71 ( (zero_zero rat) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (number_number_of int))) (let ((_let_4 (hAPP int int _let_3 (hAPP int int bit0 (hAPP int int bit1 pls))))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) _let_4) P_5))) (not (hBOOL (hAPP int bool zprime P_5))) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int _let_2 zcong X) (zero_zero int)) P_5)) (hBOOL (hAPP int bool (hAPP int _let_1 quadRes P_5) X)) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int _let_2 zcong (hAPP nat int (hAPP int (fun nat int) (power_power int) X) (hAPP int nat nat_1 (hAPP int int (hAPP int _let_0 (div_div int) (hAPP int int (hAPP int _let_0 (minus_minus int) P_5) (one_one int))) _let_4)))) (hAPP int int _let_3 min)) P_5)))))))) ) 23.76/23.71 ( (hAPP int int (number_number_of int) min), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161541 $$unsorted) (BOUND_VARIABLE_161542 $$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_161542)) BOUND_VARIABLE_161541)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_161541)) BOUND_VARIABLE_161542))))))) ) 23.76/23.71 ( int, pls, pls ) 23.76/23.71 ( int, pls, (one_one int) ) 23.76/23.71 ( int, pls, min ) 23.76/23.71 ( int, pls, s ) 23.76/23.71 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.71 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.71 ( int, pls, skv_4 ) 23.76/23.71 ( int, pls, skv_5 ) 23.76/23.71 ( int, (one_one int), pls ) 23.76/23.71 ( int, (one_one int), min ) 23.76/23.71 ( int, min, pls ) 23.76/23.71 ( int, min, (one_one int) ) 23.76/23.71 ( int, s, pls ) 23.76/23.71 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), pls ) 23.76/23.71 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), pls ) 23.76/23.71 ( int, skv_4, pls ) 23.76/23.71 ( int, skv_5, pls ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((Z_1 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (power_power real))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (= (hAPP complex real (norm_norm complex) Z_1) (hAPP real real sqrt (hAPP real real (hAPP real (fun real real) (plus_plus real) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real re Z_1)) _let_2)) (hAPP nat real (hAPP real _let_0 _let_1 (hAPP complex real im Z_1)) _let_2))))))) ) 23.76/23.71 ( (zero_zero complex) ) 23.76/23.71 ( ii ) 23.76/23.71 ( (one_one complex) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (not (hBOOL (hAPP nat bool (even_odd_even nat) X))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (div_mod nat) X) (hAPP nat nat suc (hAPP nat nat suc _let_0)))))) ) 23.76/23.71 ( (zero_zero nat) ) 23.76/23.71 ( (one_one nat) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((N $$unsorted)) (let ((_let_0 (zero_zero nat))) (or (= _let_0 N) (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) N)))) ) 23.76/23.71 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.71 ( n ) 23.76/23.71 ( tn ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161581 $$unsorted) (BOUND_VARIABLE_161582 $$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_161581) BOUND_VARIABLE_161582))) (not (forall ((K_1 $$unsorted)) (not (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_161581) K_1) (ti X_a BOUND_VARIABLE_161582))) ))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)) ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.76/23.71 ) 23.76/23.71 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161612 $$unsorted)) (or (not (monoid_mult X_a)) (= (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_161612) (one_one nat)) (ti X_a BOUND_VARIABLE_161612))) ) 23.76/23.71 ( int, pls ) 23.76/23.71 ( int, min ) 23.76/23.71 ( int, s ) 23.76/23.71 ( int, s1 ) 23.76/23.71 ( int, m ) 23.76/23.71 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.71 ( int, t ) 23.76/23.71 ( int, v ) 23.76/23.71 ( int, w ) 23.76/23.71 ( int, y ) 23.76/23.71 ( int, sa ) 23.76/23.71 ( int, x ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.76/23.71 ( int, r ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.76/23.71 ( int, m1 ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.76/23.71 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.76/23.71 ( int, skv_6 ) 23.76/23.71 ( int, skv_7 ) 23.76/23.71 ( int, skv_14 ) 23.76/23.71 ( int, skv_16 ) 23.76/23.71 ( int, skv_20 ) 23.76/23.71 ( int, skv_23 ) 23.76/23.71 ( int, skv_24 ) 23.76/23.71 ( (fun int int), bit1 ) 23.76/23.71 ( (fun int int), bit0 ) 23.76/23.71 ( (fun int int), succ ) 23.76/23.71 ( (fun int int), pred ) 23.76/23.71 ( (fun int int), (fact_fact int) ) 23.76/23.71 ( (fun int int), zfact ) 23.76/23.71 ( nat, n ) 23.76/23.71 ( nat, tn ) 23.76/23.71 ( bool, fTrue ) 23.76/23.71 ( bool, fFalse ) 23.76/23.71 ( real, (hAPP int real (number_number_of real) min) ) 23.76/23.71 ( real, pi ) 23.76/23.71 ( 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)))) ) 23.76/23.71 ( (fun nat real), (real_1 nat) ) 23.76/23.71 ( (fun nat real), cos_coeff ) 23.76/23.71 ( (fun nat real), sin_coeff ) 23.76/23.71 ( (fun real real), sin ) 23.76/23.71 ( (fun real real), cos ) 23.76/23.71 ( (fun real real), sqrt ) 23.76/23.71 ( (fun real real), tan ) 23.76/23.71 ( (fun real real), ln ) 23.76/23.71 ( (fun real real), arctan ) 23.76/23.71 ( (fun real real), arcsin ) 23.76/23.71 ( (fun real real), arccos ) 23.76/23.71 ( (fun nat nat), suc ) 23.76/23.71 ( (fun nat nat), (fact_fact nat) ) 23.76/23.71 ( (fun nat nat), nat_size ) 23.76/23.71 ( (fun nat nat), (size_size nat) ) 23.76/23.71 ( (fun nat nat), fact ) 23.76/23.71 ( (filter nat), sequentially ) 23.76/23.71 ( (fun int (fun int rat)), fract ) 23.76/23.71 ( complex, ii ) 23.76/23.71 ( (fun int bool), zOdd ) 23.76/23.71 ( (fun int bool), zprime ) 23.76/23.71 ( (fun int bool), zEven ) 23.76/23.71 ( (fun int bool), nat_neg ) 23.76/23.71 ( (fun int bool), nat_is_nat ) 23.76/23.71 ( (fun int bool), (even_odd_even int) ) 23.76/23.71 ( (fun int bool), twoSqu1091635170sum2sq ) 23.76/23.71 ( (fun int (fun int int)), legacy_zgcd ) 23.76/23.71 ( (fun int (fun int int)), (gcd_gcd int) ) 23.76/23.71 ( (fun int (fun int int)), inv ) 23.76/23.71 ( (fun int (fun int int)), multInv ) 23.76/23.71 ( (fun int (fun int int)), legendre ) 23.76/23.71 ( (fun int (fun int int)), standardRes ) 23.76/23.71 ( (fun int (fun int int)), nat_tsub ) 23.76/23.71 ( (fun int (fun int int)), z3div ) 23.76/23.71 ( (fun int (fun int int)), z3mod ) 23.76/23.71 ( (fun int (fun int int)), int_lcm ) 23.76/23.71 ( (fun int (fun int int)), int_gcd ) 23.76/23.71 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.76/23.71 ( (fun bool bool), fNot ) 23.76/23.71 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.76/23.71 ( (fun bool (fun bool bool)), fconj ) 23.76/23.71 ( (fun bool (fun bool bool)), fdisj ) 23.76/23.71 ( (fun bool (fun bool bool)), fimplies ) 23.76/23.71 ( (fun int (fun int bool)), quadRes ) 23.76/23.71 ( (fun int (fun int bool)), d22set ) 23.76/23.71 ( (fun int (fun int bool)), norRRset ) 23.76/23.71 ( (fun int (fun int bool)), sRStar ) 23.76/23.71 ( (fun int (fun int bool)), sr ) 23.76/23.71 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.76/23.71 ( (fun nat bool), (even_odd_even nat) ) 23.76/23.71 ( (fun nat bool), prime ) 23.76/23.71 ( (fun real complex), cis ) 23.76/23.71 ( (fun nat (fun nat bool)), coprime ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.76/23.71 ( (fun (product_prod int int) bool), frac_1 ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.76/23.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.76/23.71 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.76/23.71 ( (fun (fun int bool) bool), nat_nat_set ) 23.76/23.71 ( (fun nat (fun real real)), root ) 23.76/23.71 ( (fun real (fun real real)), log ) 23.76/23.71 ( (fun real (fun real real)), powr ) 23.76/23.71 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.76/23.71 ( (fun complex complex), cnj ) 23.76/23.71 ( (fun complex complex), expi ) 23.76/23.71 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.76/23.71 ( (fun nat (fun nat nat)), nat_gcd ) 23.76/23.71 ( (fun nat (fun nat nat)), nat_lcm ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.76/23.71 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.76/23.71 ( (fun int (fun (fun int bool) bool)), resSet ) 23.76/23.71 ( (fun int nat), nat_1 ) 23.76/23.71 ( (fun int nat), phi ) 23.76/23.71 ( (fun complex real), re ) 23.76/23.71 ( (fun complex real), im ) 23.76/23.71 ( (fun complex real), arg ) 23.76/23.71 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.76/23.71 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.76/23.71 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.76/23.71 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.76/23.71 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.76/23.71 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.76/23.71 ( (fun (product_prod nat nat) bool), pred_nat ) 23.76/23.71 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.76/23.71 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.76/23.71 ( (fun (fun int bool) int), (the int) ) 23.76/23.71 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.76/23.71 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.76/23.71 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.76/23.71 ( (fun real (fun real complex)), rcis ) 23.76/23.71 ( (fun real (fun real complex)), complex_1 ) 23.76/23.71 ( (fun int (fun int (fun int bool))), zcong ) 23.76/23.71 ( (fun int (fun int (fun int bool))), wset ) 23.76/23.71 ( (fun int (fun int (fun int bool))), noXRRset ) 23.76/23.71 ( (fun int (fun int (fun int bool))), bnorRset ) 23.76/23.71 ( (fun int (fun int (fun int bool))), zcongm ) 23.76/23.71 ( (fun real nat), natceiling ) 23.76/23.71 ( (fun real nat), natfloor ) 23.76/23.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.76/23.71 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.76/23.71 ( (fun int real), (real_1 int) ) 23.76/23.71 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.76/23.71 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.76/23.71 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.76/23.71 ( (fun complex nat), (size_size complex) ) 23.76/23.71 ( (fun complex nat), complex_size ) 23.76/23.71 ( (fun (fun nat rat) bool), vanishes ) 23.76/23.71 ( (fun (product_prod int int) rat), frct ) 23.76/23.71 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.76/23.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.76/23.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.76/23.72 ( (fun rat real), ratreal ) 23.76/23.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.76/23.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.76/23.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.76/23.72 ( (fun rat (product_prod int int)), quotient_of ) 23.76/23.72 ( (fun int (fun nat nat)), nat_aux ) 23.76/23.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.76/23.72 ( (fun int (list int)), quickc666637781d_zero ) 23.76/23.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.76/23.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.76/23.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.76/23.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.76/23.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.76/23.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.76/23.72 ( (fun code_code_numeral int), code_int_of ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_0 (fun int int))) (= (hAPP int int (hAPP int _let_0 legacy_zgcd M) N) (hAPP int int (hAPP int _let_0 legacy_zgcd (hAPP int int (hAPP int _let_0 (plus_plus int) M) (hAPP int int (hAPP int _let_0 (times_times int) N) K_4))) N))) ) 23.76/23.72 ( (one_one int), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), y, w ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), sa, w ) 23.76/23.72 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (Xa $$unsorted) (Ya $$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) Xa)))) (hAPP X_b _let_3 (fequal X_b) Ya)))) (hAPP X_b _let_1 (hAPP X_a (fun X_b _let_1) (product_Pair X_a X_b) Xa) Ya))))))))))) ) 23.76/23.72 ( int, int, (one_one int), (one_one int) ) 23.76/23.72 ( int, int, (zero_zero int), (one_one int) ) 23.76/23.72 ( int, int, s, (one_one int) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161634 $$unsorted) (BOUND_VARIABLE_161635 $$unsorted) (BOUND_VARIABLE_161636 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_161634))) (or (not (linord20386208strict X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161635) BOUND_VARIABLE_161636))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_161634))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a _let_2 BOUND_VARIABLE_161635)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_161636))))))) ) 23.76/23.72 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (zero_zero nat))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun real bool))) (let ((_let_3 (hAPP nat _let_1 root Na))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) _let_0) Na))) (not (hBOOL (hAPP nat bool (even_odd_even nat) Na))) (not (hBOOL (hAPP real bool (hAPP real _let_2 (ord_less real) Xa) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_2 (hAPP _let_1 (fun real _let_2) (deriv real) _let_3) Xa) (hAPP real real (inverse_inverse real) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP real real (uminus_uminus real) (hAPP nat real (real_1 nat) Na))) (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real _let_3 Xa)) (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) Na) (hAPP nat nat suc _let_0)))))))))))) ) 23.76/23.72 ( (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))) ) 23.76/23.72 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( (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))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161690 $$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) BOUND_VARIABLE_161690)) (= _let_0 (ti X_a BOUND_VARIABLE_161690))))) ) 23.76/23.72 ( int, pls ) 23.76/23.72 ( int, min ) 23.76/23.72 ( int, s ) 23.76/23.72 ( int, s1 ) 23.76/23.72 ( int, m ) 23.76/23.72 ( int, t ) 23.76/23.72 ( int, v ) 23.76/23.72 ( int, w ) 23.76/23.72 ( int, y ) 23.76/23.72 ( int, sa ) 23.76/23.72 ( int, x ) 23.76/23.72 ( int, r ) 23.76/23.72 ( int, m1 ) 23.76/23.72 ( int, skv_14 ) 23.76/23.72 ( int, skv_20 ) 23.76/23.72 ( (fun int int), bit1 ) 23.76/23.72 ( (fun int int), bit0 ) 23.76/23.72 ( (fun int int), succ ) 23.76/23.72 ( (fun int int), pred ) 23.76/23.72 ( (fun int int), (fact_fact int) ) 23.76/23.72 ( (fun int int), zfact ) 23.76/23.72 ( nat, n ) 23.76/23.72 ( nat, tn ) 23.76/23.72 ( bool, fTrue ) 23.76/23.72 ( bool, fFalse ) 23.76/23.72 ( real, pi ) 23.76/23.72 ( real, (zero_zero real) ) 23.76/23.72 ( (fun nat real), (real_1 nat) ) 23.76/23.72 ( (fun nat real), cos_coeff ) 23.76/23.72 ( (fun nat real), sin_coeff ) 23.76/23.72 ( (fun real real), sin ) 23.76/23.72 ( (fun real real), cos ) 23.76/23.72 ( (fun real real), sqrt ) 23.76/23.72 ( (fun real real), tan ) 23.76/23.72 ( (fun real real), ln ) 23.76/23.72 ( (fun real real), arctan ) 23.76/23.72 ( (fun real real), arcsin ) 23.76/23.72 ( (fun real real), arccos ) 23.76/23.72 ( (fun nat nat), suc ) 23.76/23.72 ( (fun nat nat), (fact_fact nat) ) 23.76/23.72 ( (fun nat nat), nat_size ) 23.76/23.72 ( (fun nat nat), (size_size nat) ) 23.76/23.72 ( (fun nat nat), fact ) 23.76/23.72 ( (filter nat), sequentially ) 23.76/23.72 ( (fun int (fun int rat)), fract ) 23.76/23.72 ( complex, ii ) 23.76/23.72 ( (fun int bool), zOdd ) 23.76/23.72 ( (fun int bool), zprime ) 23.76/23.72 ( (fun int bool), zEven ) 23.76/23.72 ( (fun int bool), nat_neg ) 23.76/23.72 ( (fun int bool), nat_is_nat ) 23.76/23.72 ( (fun int bool), (even_odd_even int) ) 23.76/23.72 ( (fun int bool), twoSqu1091635170sum2sq ) 23.76/23.72 ( (fun int (fun int int)), legacy_zgcd ) 23.76/23.72 ( (fun int (fun int int)), (gcd_gcd int) ) 23.76/23.72 ( (fun int (fun int int)), inv ) 23.76/23.72 ( (fun int (fun int int)), multInv ) 23.76/23.72 ( (fun int (fun int int)), legendre ) 23.76/23.72 ( (fun int (fun int int)), standardRes ) 23.76/23.72 ( (fun int (fun int int)), nat_tsub ) 23.76/23.72 ( (fun int (fun int int)), z3div ) 23.76/23.72 ( (fun int (fun int int)), z3mod ) 23.76/23.72 ( (fun int (fun int int)), int_lcm ) 23.76/23.72 ( (fun int (fun int int)), int_gcd ) 23.76/23.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.76/23.72 ( (fun bool bool), fNot ) 23.76/23.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.76/23.72 ( (fun bool (fun bool bool)), fconj ) 23.76/23.72 ( (fun bool (fun bool bool)), fdisj ) 23.76/23.72 ( (fun bool (fun bool bool)), fimplies ) 23.76/23.72 ( (fun int (fun int bool)), quadRes ) 23.76/23.72 ( (fun int (fun int bool)), d22set ) 23.76/23.72 ( (fun int (fun int bool)), norRRset ) 23.76/23.72 ( (fun int (fun int bool)), sRStar ) 23.76/23.72 ( (fun int (fun int bool)), sr ) 23.76/23.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.76/23.72 ( (fun nat bool), (even_odd_even nat) ) 23.76/23.72 ( (fun nat bool), prime ) 23.76/23.72 ( (fun real complex), cis ) 23.76/23.72 ( (fun nat (fun nat bool)), coprime ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.76/23.72 ( (fun (product_prod int int) bool), frac_1 ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.76/23.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.76/23.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.76/23.72 ( (fun (fun int bool) bool), nat_nat_set ) 23.76/23.72 ( (fun nat (fun real real)), root ) 23.76/23.72 ( (fun real (fun real real)), log ) 23.76/23.72 ( (fun real (fun real real)), powr ) 23.76/23.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.76/23.72 ( (fun complex complex), cnj ) 23.76/23.72 ( (fun complex complex), expi ) 23.76/23.72 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.76/23.72 ( (fun nat (fun nat nat)), nat_gcd ) 23.76/23.72 ( (fun nat (fun nat nat)), nat_lcm ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.76/23.72 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.76/23.72 ( (fun int (fun (fun int bool) bool)), resSet ) 23.76/23.72 ( (fun int nat), nat_1 ) 23.76/23.72 ( (fun int nat), phi ) 23.76/23.72 ( (fun complex real), re ) 23.76/23.72 ( (fun complex real), im ) 23.76/23.72 ( (fun complex real), arg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.76/23.72 ( (fun (product_prod nat nat) bool), pred_nat ) 23.76/23.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.76/23.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.76/23.72 ( (fun (fun int bool) int), (the int) ) 23.76/23.72 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.76/23.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.76/23.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.76/23.72 ( (fun real (fun real complex)), rcis ) 23.76/23.72 ( (fun real (fun real complex)), complex_1 ) 23.76/23.72 ( (fun int (fun int (fun int bool))), zcong ) 23.76/23.72 ( (fun int (fun int (fun int bool))), wset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), noXRRset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), bnorRset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), zcongm ) 23.76/23.72 ( (fun real nat), natceiling ) 23.76/23.72 ( (fun real nat), natfloor ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.76/23.72 ( (fun int real), (real_1 int) ) 23.76/23.72 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.76/23.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.76/23.72 ( (fun complex nat), (size_size complex) ) 23.76/23.72 ( (fun complex nat), complex_size ) 23.76/23.72 ( (fun (fun nat rat) bool), vanishes ) 23.76/23.72 ( (fun (product_prod int int) rat), frct ) 23.76/23.72 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.76/23.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.76/23.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.76/23.72 ( (fun rat real), ratreal ) 23.76/23.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.76/23.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.76/23.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.76/23.72 ( (fun rat (product_prod int int)), quotient_of ) 23.76/23.72 ( (fun int (fun nat nat)), nat_aux ) 23.76/23.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.76/23.72 ( (fun int (list int)), quickc666637781d_zero ) 23.76/23.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.76/23.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.76/23.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.76/23.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.76/23.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.76/23.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.76/23.72 ( (fun code_code_numeral int), code_int_of ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161706 $$unsorted) (BOUND_VARIABLE_161707 $$unsorted) (BOUND_VARIABLE_161708 $$unsorted) (BOUND_VARIABLE_161709 $$unsorted)) (let ((_let_0 (fun X_a X_a))) (let ((_let_1 (plus_plus X_a))) (let ((_let_2 (times_times X_a))) (or (not (semiring X_a)) (= (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_161706) BOUND_VARIABLE_161707)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 BOUND_VARIABLE_161708) BOUND_VARIABLE_161707)) BOUND_VARIABLE_161709)) (hAPP X_a X_a (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (hAPP X_a _let_0 _let_2 (hAPP X_a X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161706) BOUND_VARIABLE_161708)) BOUND_VARIABLE_161707)) BOUND_VARIABLE_161709)))))) ) 23.76/23.72 ( int, (one_one int), (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP nat int (semiring_1_of_nat int) n), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.76/23.72 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161785 $$unsorted)) (or (not (number_ring X_a)) (not (linordered_idom X_a)) (= (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) (hAPP int int bit1 pls)) BOUND_VARIABLE_161785)) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) (one_one X_a)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_161785))))) ) 23.76/23.72 ( int, pls ) 23.76/23.72 ( int, (hAPP int int bit1 pls) ) 23.76/23.72 ( int, min ) 23.76/23.72 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ( nat, pls ) 23.76/23.72 ( nat, (hAPP int int bit1 pls) ) 23.76/23.72 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ( real, min ) 23.76/23.72 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.72 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 23.76/23.72 ( complex, min ) 23.76/23.72 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( quickcheck_code_int, pls ) 23.76/23.72 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 23.76/23.72 ( quickcheck_code_int, (one_one int) ) 23.76/23.72 ( code_code_numeral, pls ) 23.76/23.72 ( code_code_numeral, (hAPP int int bit1 pls) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((A_1 $$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 (hAPP int _let_1 (hAPP int _let_2 posDivAlg A_1) B))) (let ((_let_4 (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) A_1) B)))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) _let_0) B))) (and (or _let_4 (= (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_3)) (or (not _let_4) (= _let_3 (hAPP int _let_1 (hAPP int _let_2 (product_Pair int int) _let_0) A_1)))))))))) ) 23.76/23.72 ( (one_one int), t ) 23.76/23.72 ( min, min ) 23.76/23.72 ( min, (zero_zero int) ) 23.76/23.72 ( (zero_zero int), pls ) 23.76/23.72 ( (zero_zero int), (one_one int) ) 23.76/23.72 ( (zero_zero int), min ) 23.76/23.72 ( (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))) ) 23.76/23.72 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (= (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat _let_0 V)) (one_one nat)) (hAPP int nat _let_0 (hAPP int int succ V))))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (hAPP int int bit1 pls) ) 23.76/23.72 ( (one_one int) ) 23.76/23.72 ( min ) 23.76/23.72 ( (zero_zero int) ) 23.76/23.72 ( s ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( t ) 23.76/23.72 ( m1 ) 23.76/23.72 ( skv_4 ) 23.76/23.72 ( skv_5 ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((V $$unsorted)) (let ((_let_0 (one_one nat))) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls))) (= _let_0 (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat (number_number_of nat) V)) _let_0)))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (hAPP int int bit1 pls) ) 23.76/23.72 ( (one_one int) ) 23.76/23.72 ( min ) 23.76/23.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (zero_zero int) ) 23.76/23.72 ( s ) 23.76/23.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( t ) 23.76/23.72 ( m1 ) 23.76/23.72 ( skv_4 ) 23.76/23.72 ( skv_5 ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$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)))) ) 23.76/23.72 ( rat ) 23.76/23.72 ( int ) 23.76/23.72 ( nat ) 23.76/23.72 ( real ) 23.76/23.72 ( complex ) 23.76/23.72 ( quickcheck_code_int ) 23.76/23.72 ( code_code_numeral ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_161926 $$unsorted) (BOUND_VARIABLE_161927 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (order X_a)) (= (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161927) BOUND_VARIABLE_161926)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_161926) BOUND_VARIABLE_161927))) (= (ti X_a BOUND_VARIABLE_161927) (ti X_a BOUND_VARIABLE_161926)))))) ) 23.76/23.72 ( int, pls, min ) 23.76/23.72 ( int, pls, (zero_zero int) ) 23.76/23.72 ( int, (one_one int), (zero_zero int) ) 23.76/23.72 ( int, (one_one int), t ) 23.76/23.72 ( int, min, pls ) 23.76/23.72 ( int, min, min ) 23.76/23.72 ( int, min, (zero_zero int) ) 23.76/23.72 ( int, (zero_zero int), pls ) 23.76/23.72 ( int, (zero_zero int), (one_one int) ) 23.76/23.72 ( int, (zero_zero int), min ) 23.76/23.72 ( int, (zero_zero int), s ) 23.76/23.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( int, (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.72 ( int, (zero_zero int), skv_4 ) 23.76/23.72 ( int, (zero_zero int), skv_5 ) 23.76/23.72 ( int, s, (zero_zero int) ) 23.76/23.72 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero int) ) 23.76/23.72 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) w)) ) 23.76/23.72 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) v)) ) 23.76/23.72 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_14)) ) 23.76/23.72 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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)))) (hAPP int int (abs_abs int) skv_20)) ) 23.76/23.72 ( int, t, (one_one int) ) 23.76/23.72 ( int, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (zero_zero int) ) 23.76/23.72 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( int, skv_4, (zero_zero int) ) 23.76/23.72 ( int, skv_5, (zero_zero int) ) 23.76/23.72 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( real, pi, (zero_zero real) ) 23.76/23.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.76/23.72 ( 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)))) ) 23.76/23.72 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_10 ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( 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) ) 23.76/23.72 ( real, (zero_zero real), pi ) 23.76/23.72 ( 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)))) ) 23.76/23.72 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( real, (zero_zero real), skv_10 ) 23.76/23.72 ( real, (zero_zero real), skv_11 ) 23.76/23.72 ( real, (zero_zero real), skv_15 ) 23.76/23.72 ( real, (zero_zero real), skv_18 ) 23.76/23.72 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.76/23.72 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.76/23.72 ( real, skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( real, skv_10, (zero_zero real) ) 23.76/23.72 ( real, skv_11, (zero_zero real) ) 23.76/23.72 ( real, skv_15, (zero_zero real) ) 23.76/23.72 ( real, skv_18, (zero_zero real) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) K_2))) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) ))) ))) ) 23.76/23.72 ( real ) 23.76/23.72 ( complex ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162022 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_n1866405975lgebra X_a)) (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_162022)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_162022)) (hAPP real real (inverse_inverse real) (hAPP X_a real _let_0 BOUND_VARIABLE_162022))))) ) 23.76/23.72 ( int, pls ) 23.76/23.72 ( int, min ) 23.76/23.72 ( int, s ) 23.76/23.72 ( int, s1 ) 23.76/23.72 ( int, m ) 23.76/23.72 ( int, t ) 23.76/23.72 ( int, v ) 23.76/23.72 ( int, w ) 23.76/23.72 ( int, y ) 23.76/23.72 ( int, sa ) 23.76/23.72 ( int, x ) 23.76/23.72 ( int, r ) 23.76/23.72 ( int, m1 ) 23.76/23.72 ( int, skv_14 ) 23.76/23.72 ( int, skv_20 ) 23.76/23.72 ( (fun int int), bit1 ) 23.76/23.72 ( (fun int int), bit0 ) 23.76/23.72 ( (fun int int), succ ) 23.76/23.72 ( (fun int int), pred ) 23.76/23.72 ( (fun int int), (fact_fact int) ) 23.76/23.72 ( (fun int int), zfact ) 23.76/23.72 ( nat, n ) 23.76/23.72 ( nat, tn ) 23.76/23.72 ( bool, fTrue ) 23.76/23.72 ( bool, fFalse ) 23.76/23.72 ( real, pi ) 23.76/23.72 ( real, (zero_zero real) ) 23.76/23.72 ( (fun nat real), (real_1 nat) ) 23.76/23.72 ( (fun nat real), cos_coeff ) 23.76/23.72 ( (fun nat real), sin_coeff ) 23.76/23.72 ( (fun real real), sin ) 23.76/23.72 ( (fun real real), cos ) 23.76/23.72 ( (fun real real), sqrt ) 23.76/23.72 ( (fun real real), tan ) 23.76/23.72 ( (fun real real), ln ) 23.76/23.72 ( (fun real real), arctan ) 23.76/23.72 ( (fun real real), arcsin ) 23.76/23.72 ( (fun real real), arccos ) 23.76/23.72 ( (fun nat nat), suc ) 23.76/23.72 ( (fun nat nat), (fact_fact nat) ) 23.76/23.72 ( (fun nat nat), nat_size ) 23.76/23.72 ( (fun nat nat), (size_size nat) ) 23.76/23.72 ( (fun nat nat), fact ) 23.76/23.72 ( (filter nat), sequentially ) 23.76/23.72 ( (fun int (fun int rat)), fract ) 23.76/23.72 ( complex, ii ) 23.76/23.72 ( (fun int bool), zOdd ) 23.76/23.72 ( (fun int bool), zprime ) 23.76/23.72 ( (fun int bool), zEven ) 23.76/23.72 ( (fun int bool), nat_neg ) 23.76/23.72 ( (fun int bool), nat_is_nat ) 23.76/23.72 ( (fun int bool), (even_odd_even int) ) 23.76/23.72 ( (fun int bool), twoSqu1091635170sum2sq ) 23.76/23.72 ( (fun int (fun int int)), legacy_zgcd ) 23.76/23.72 ( (fun int (fun int int)), (gcd_gcd int) ) 23.76/23.72 ( (fun int (fun int int)), inv ) 23.76/23.72 ( (fun int (fun int int)), multInv ) 23.76/23.72 ( (fun int (fun int int)), legendre ) 23.76/23.72 ( (fun int (fun int int)), standardRes ) 23.76/23.72 ( (fun int (fun int int)), nat_tsub ) 23.76/23.72 ( (fun int (fun int int)), z3div ) 23.76/23.72 ( (fun int (fun int int)), z3mod ) 23.76/23.72 ( (fun int (fun int int)), int_lcm ) 23.76/23.72 ( (fun int (fun int int)), int_gcd ) 23.76/23.72 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.76/23.72 ( (fun bool bool), fNot ) 23.76/23.72 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.76/23.72 ( (fun bool (fun bool bool)), fconj ) 23.76/23.72 ( (fun bool (fun bool bool)), fdisj ) 23.76/23.72 ( (fun bool (fun bool bool)), fimplies ) 23.76/23.72 ( (fun int (fun int bool)), quadRes ) 23.76/23.72 ( (fun int (fun int bool)), d22set ) 23.76/23.72 ( (fun int (fun int bool)), norRRset ) 23.76/23.72 ( (fun int (fun int bool)), sRStar ) 23.76/23.72 ( (fun int (fun int bool)), sr ) 23.76/23.72 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.76/23.72 ( (fun nat bool), (even_odd_even nat) ) 23.76/23.72 ( (fun nat bool), prime ) 23.76/23.72 ( (fun real complex), cis ) 23.76/23.72 ( (fun nat (fun nat bool)), coprime ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.76/23.72 ( (fun (product_prod int int) bool), frac_1 ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.76/23.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.76/23.72 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.76/23.72 ( (fun (fun int bool) bool), nat_nat_set ) 23.76/23.72 ( (fun nat (fun real real)), root ) 23.76/23.72 ( (fun real (fun real real)), log ) 23.76/23.72 ( (fun real (fun real real)), powr ) 23.76/23.72 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.76/23.72 ( (fun complex complex), cnj ) 23.76/23.72 ( (fun complex complex), expi ) 23.76/23.72 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.76/23.72 ( (fun nat (fun nat nat)), nat_gcd ) 23.76/23.72 ( (fun nat (fun nat nat)), nat_lcm ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.76/23.72 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.76/23.72 ( (fun int (fun (fun int bool) bool)), resSet ) 23.76/23.72 ( (fun int nat), nat_1 ) 23.76/23.72 ( (fun int nat), phi ) 23.76/23.72 ( (fun complex real), re ) 23.76/23.72 ( (fun complex real), im ) 23.76/23.72 ( (fun complex real), arg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.76/23.72 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.76/23.72 ( (fun (product_prod nat nat) bool), pred_nat ) 23.76/23.72 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.76/23.72 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.76/23.72 ( (fun (fun int bool) int), (the int) ) 23.76/23.72 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.76/23.72 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.76/23.72 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.76/23.72 ( (fun real (fun real complex)), rcis ) 23.76/23.72 ( (fun real (fun real complex)), complex_1 ) 23.76/23.72 ( (fun int (fun int (fun int bool))), zcong ) 23.76/23.72 ( (fun int (fun int (fun int bool))), wset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), noXRRset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), bnorRset ) 23.76/23.72 ( (fun int (fun int (fun int bool))), zcongm ) 23.76/23.72 ( (fun real nat), natceiling ) 23.76/23.72 ( (fun real nat), natfloor ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.76/23.72 ( (fun int real), (real_1 int) ) 23.76/23.72 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.76/23.72 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.76/23.72 ( (fun complex nat), (size_size complex) ) 23.76/23.72 ( (fun complex nat), complex_size ) 23.76/23.72 ( (fun (fun nat rat) bool), vanishes ) 23.76/23.72 ( (fun (product_prod int int) rat), frct ) 23.76/23.72 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.76/23.72 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.76/23.72 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.76/23.72 ( (fun rat real), ratreal ) 23.76/23.72 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.76/23.72 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.76/23.72 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.76/23.72 ( (fun rat (product_prod int int)), quotient_of ) 23.76/23.72 ( (fun int (fun nat nat)), nat_aux ) 23.76/23.72 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.76/23.72 ( (fun int (list int)), quickc666637781d_zero ) 23.76/23.72 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.76/23.72 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.76/23.72 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.76/23.72 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.76/23.72 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.76/23.72 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.76/23.72 ( (fun code_code_numeral int), code_int_of ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (min_1 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)))) ) 23.76/23.72 ( rat ) 23.76/23.72 ( int ) 23.76/23.72 ( (fun int int) ) 23.76/23.72 ( nat ) 23.76/23.72 ( bool ) 23.76/23.72 ( real ) 23.76/23.72 ( (fun nat real) ) 23.76/23.72 ( (fun real real) ) 23.76/23.72 ( (filter nat) ) 23.76/23.72 ( complex ) 23.76/23.72 ( (fun int bool) ) 23.76/23.72 ( (product_prod int int) ) 23.76/23.72 ( (fun (product_prod int int) int) ) 23.76/23.72 ( (fun int (fun int bool)) ) 23.76/23.72 ( (fun nat bool) ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (product_prod _let_0 _let_0)) ) 23.76/23.72 ( (fun (product_prod int int) bool) ) 23.76/23.72 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.76/23.72 ( (fun real bool) ) 23.76/23.72 ( quickcheck_code_int ) 23.76/23.72 ( code_code_numeral ) 23.76/23.72 ( (product_prod real real) ) 23.76/23.72 ( (filter real) ) 23.76/23.72 ( (product_prod nat nat) ) 23.76/23.72 ( (fun nat rat) ) 23.76/23.72 ( (fun int (fun int (fun int bool))) ) 23.76/23.72 ( (let ((_let_0 (product_prod nat nat))) (product_prod _let_0 _let_0)) ) 23.76/23.72 ( (fun int real) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP _let_0 rat frct (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (one_one int)) (hAPP int int (number_number_of int) K_4))) (hAPP rat rat (hAPP rat (fun rat rat) (inverse_divide rat) (one_one rat)) (hAPP int rat (number_number_of rat) K_4)))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (hAPP int int bit1 pls) ) 23.76/23.72 ( min ) 23.76/23.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162177 $$unsorted)) (let ((_let_0 (norm_norm X_a))) (or (not (real_normed_vector X_a)) (= (hAPP X_a real _let_0 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_162177)) (hAPP X_a real _let_0 BOUND_VARIABLE_162177)))) ) 23.76/23.72 ( int, pls ) 23.76/23.72 ( int, (one_one int) ) 23.76/23.72 ( int, min ) 23.76/23.72 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( real, (one_one real) ) 23.76/23.72 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.76/23.72 ( complex, ii ) 23.76/23.72 ( complex, (one_one complex) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$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 P_1)))) (not (hBOOL (hAPP _let_1 bool _let_2 (hAPP _let_1 _let_1 _let_3 Q_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)))))))))) ) 23.76/23.72 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (fun real _let_1))) (hAPP real _let_1 (hAPP _let_2 _let_2 (combc real real bool) (hAPP _let_0 _let_2 (hAPP _let_2 (fun _let_0 _let_2) (combb real _let_1 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))))) ) 23.76/23.72 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun real bool))) (let ((_let_3 (fun real _let_2))) (let ((_let_4 (fun real _let_1))) (let ((_let_5 (combc real real bool))) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs real bool bool) (hAPP _let_2 _let_4 (hAPP (fun bool _let_1) (fun _let_2 _let_4) (combb bool _let_1 real) fconj) (hAPP real _let_2 (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_2 (hAPP _let_3 _let_3 _let_5 (hAPP _let_0 _let_3 (hAPP _let_3 (fun _let_0 _let_3) (combb real _let_2 real) (fequal real)) cos)) (zero_zero real))))))))), (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (real_1 int))) (= (hAPP real real (abs_abs real) (hAPP int real _let_0 X)) (hAPP int real _let_0 (hAPP int int (abs_abs int) X)))) ) 23.76/23.72 ( v ) 23.76/23.72 ( w ) 23.76/23.72 ( skv_14 ) 23.76/23.72 ( skv_20 ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((Na $$unsorted)) (let ((_let_0 (ord_less_eq int))) (let ((_let_1 (hAPP int (fun int bool) _let_0 (zero_zero int)))) (let ((_let_2 (fun bool bool))) (let ((_let_3 (fun int _let_2))) (let ((_let_4 (fun int (fun int bool)))) (or (not (hBOOL (hAPP int bool _let_1 Na))) (= (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_4 _let_4 (combc int int bool) _let_0) Na)))) (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) (hAPP int nat nat_1 Na)) (one_one nat))))))))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (one_one int) ) 23.76/23.72 ( min ) 23.76/23.72 ( (zero_zero int) ) 23.76/23.72 ( s ) 23.76/23.72 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.72 ( t ) 23.76/23.72 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.72 ( skv_4 ) 23.76/23.72 ( skv_5 ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((Va $$unsorted) (V_1 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (fun int bool))) (let ((_let_2 (ord_less int))) (let ((_let_3 (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 Va) V_1)))) (= (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (hAPP int nat _let_0 Va)) (hAPP int nat _let_0 V_1))) (and _let_3 (or (not _let_3) (hBOOL (hAPP int bool (hAPP int _let_1 _let_2 pls) V_1))))))))) ) 23.76/23.72 ( pls, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (one_one int), t ) 23.76/23.72 ( min, min ) 23.76/23.72 ( min, (zero_zero int) ) 23.76/23.72 ( (zero_zero int), pls ) 23.76/23.72 ( (zero_zero int), (one_one int) ) 23.76/23.72 ( (zero_zero int), min ) 23.76/23.72 ( (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))) ) 23.76/23.72 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.72 ( 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))) ) 23.76/23.72 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((Z_1 $$unsorted)) (= (ti int Z_1) (hAPP int int (hAPP int (fun int int) (plus_plus int) Z_1) (zero_zero int))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (one_one int) ) 23.76/23.72 ( min ) 23.76/23.72 ( s ) 23.76/23.72 ( (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)))) ) 23.76/23.72 ( s1 ) 23.76/23.72 ( m ) 23.76/23.72 ( (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) ) 23.76/23.72 ( t ) 23.76/23.72 ( v ) 23.76/23.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( w ) 23.76/23.72 ( y ) 23.76/23.72 ( sa ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.72 ( x ) 23.76/23.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.72 ( r ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.76/23.72 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.76/23.72 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.76/23.72 ( m1 ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.76/23.72 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.76/23.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( skv_14 ) 23.76/23.72 ( skv_20 ) 23.76/23.72 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_algebra X_a)) (not (forall ((K_2 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (times_times real))) (let ((_let_2 (norm_norm X_a))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP X_a real _let_2 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (times_times X_a) A_4) B_4))) (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real (hAPP real _let_0 _let_1 (hAPP X_a real _let_2 A_4)) (hAPP X_a real _let_2 B_4))) K_2)))))) )) ))) ) 23.76/23.72 ( real ) 23.76/23.72 ( complex ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (= (hAPP int int bit1 K_4) (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)))) ) 23.76/23.72 ( pls ) 23.76/23.72 ( (hAPP int int bit1 pls) ) 23.76/23.72 ( min ) 23.76/23.72 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.72 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.76/23.72 ( (hAPP nat int (semiring_1_of_nat int) n) ) 23.76/23.72 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.76/23.72 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls))))) ) 23.76/23.72 ( (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)))))) ) 23.76/23.72 ( (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))))))) ) 23.76/23.72 ) 23.76/23.72 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162394 $$unsorted) (BOUND_VARIABLE_162395 $$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_162394) BOUND_VARIABLE_162395)) (hAPP X_a real (hAPP X_a (fun X_a real) (dist_dist X_a) BOUND_VARIABLE_162394) BOUND_VARIABLE_162395))) ) 23.76/23.73 ( 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)))), (hAPP int int (number_number_of int) min) ) 23.76/23.73 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.73 ( int, y, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_13) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.73 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.73 ( int, x, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) skv_19) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) v) ) 23.76/23.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) v)))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.76/23.73 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.76/23.73 ( 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))) m1))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.76/23.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.73 ( nat, (hAPP int nat nat_1 t), (one_one nat) ) 23.76/23.73 ( real, (let ((_let_0 (number_number_of real))) (let ((_let_1 (fun real real))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP real real (hAPP real _let_1 (times_times real) (hAPP int real _let_0 (hAPP int int bit0 _let_2))) (hAPP real real arctan (hAPP real real (hAPP real _let_1 (inverse_divide real) (one_one real)) (hAPP int real _let_0 (hAPP int int bit1 _let_2)))))))), (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))))))))))) ) 23.76/23.73 ( code_code_numeral, (zero_zero code_code_numeral), (one_one code_code_numeral) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162454 $$unsorted) (BOUND_VARIABLE_162455 $$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_162454)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_162455)))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (zero_zero X_a)) BOUND_VARIABLE_162454))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_162455) BOUND_VARIABLE_162454)))))) ) 23.76/23.73 ( int, pls, (zero_zero int) ) 23.76/23.73 ( int, (one_one int), (zero_zero int) ) 23.76/23.73 ( int, min, min ) 23.76/23.73 ( int, min, (zero_zero int) ) 23.76/23.73 ( int, (zero_zero int), min ) 23.76/23.73 ( 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))), (zero_zero int) ) 23.76/23.73 ( 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 ) 23.76/23.73 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.73 ( 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 ) 23.76/23.73 ( 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 ) 23.76/23.73 ( 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_5 ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (zero_zero int) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.76/23.73 ( int, t, (one_one int) ) 23.76/23.73 ( nat, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 23.76/23.73 ( nat, n, (zero_zero nat) ) 23.76/23.73 ( nat, tn, (zero_zero nat) ) 23.76/23.73 ( real, pi, (zero_zero real) ) 23.76/23.73 ( 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)) ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( 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) ) 23.76/23.73 ( real, (zero_zero real), pi ) 23.76/23.73 ( real, (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( 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))))) ) 23.76/23.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 23.76/23.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.76/23.73 ( real, skv_2, (zero_zero real) ) 23.76/23.73 ( real, skv_9, (zero_zero real) ) 23.76/23.73 ( real, skv_12, (zero_zero real) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162477 $$unsorted) (BOUND_VARIABLE_162478 $$unsorted)) (or (not (archim1727834104eiling X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_162477)) BOUND_VARIABLE_162478)) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) (hAPP int int (number_number_of int) BOUND_VARIABLE_162477)) (hAPP X_a int (archimedean_ceiling X_a) BOUND_VARIABLE_162478))))) ) 23.76/23.73 ( int, pls, pls ) 23.76/23.73 ( int, pls, (one_one int) ) 23.76/23.73 ( int, pls, min ) 23.76/23.73 ( int, pls, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.73 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.73 ( int, (hAPP int int bit1 pls), t ) 23.76/23.73 ( nat, pls, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( nat, pls, n ) 23.76/23.73 ( nat, pls, tn ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162511 $$unsorted) (BOUND_VARIABLE_162512 $$unsorted) (BOUND_VARIABLE_162513 $$unsorted) (BOUND_VARIABLE_162525 $$unsorted) (BOUND_VARIABLE_162526 $$unsorted) (BOUND_VARIABLE_162527 $$unsorted)) (let ((_let_0 (div_div X_a))) (let ((_let_1 (zero_zero X_a))) (let ((_let_2 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_162513))) (let ((_let_3 (hAPP X_a (fun X_a X_a) (times_times X_a) BOUND_VARIABLE_162527))) (or (not (semiring_div X_a)) (and (or (= _let_1 (ti X_a BOUND_VARIABLE_162513)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) _let_0 (hAPP X_a X_a _let_2 BOUND_VARIABLE_162511)) (hAPP X_a X_a _let_2 BOUND_VARIABLE_162512)) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) _let_0 BOUND_VARIABLE_162511) BOUND_VARIABLE_162512))) (or (not (= _let_1 (ti X_a BOUND_VARIABLE_162527))) (= _let_1 (hAPP X_a X_a (hAPP X_a (fun X_a X_a) _let_0 (hAPP X_a X_a _let_3 BOUND_VARIABLE_162525)) (hAPP X_a X_a _let_3 BOUND_VARIABLE_162526)))))))))) ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, (hAPP int int (hAPP 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( int, w, w, sa, w, w, sa ) 23.76/23.73 ( int, w, w, x, w, w, x ) 23.76/23.73 ( int, w, w, r, w, w, r ) 23.76/23.73 ( int, w, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.76/23.73 ( int, w, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w, w, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (hAPP 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(hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v), (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.76/23.73 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( int, skv_3, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.73 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14), (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20), (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( int, skv_21, skv_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))), skv_21, skv_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))) ) 23.76/23.73 ( 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))) ) 23.76/23.73 ( 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))))) ) 23.76/23.73 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( complex, ii, ii, ii, ii, ii, ii ) 23.76/23.73 ( 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)) ) 23.76/23.73 ( 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))) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162559 $$unsorted) (BOUND_VARIABLE_162560 $$unsorted) (BOUND_VARIABLE_162561 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (let ((_let_2 (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_162559))) (or (not (linordered_semidom X_a)) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) BOUND_VARIABLE_162560) BOUND_VARIABLE_162561))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (one_one X_a)) BOUND_VARIABLE_162559))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP nat X_a _let_2 BOUND_VARIABLE_162560)) (hAPP nat X_a _let_2 BOUND_VARIABLE_162561))))))) ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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))) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162594 $$unsorted) (BOUND_VARIABLE_162595 $$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_162595))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less X_a) _let_1) BOUND_VARIABLE_162594))) (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_162595) BOUND_VARIABLE_162594))))))) ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (one_one real) ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( 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))) ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), pi ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls)))), pi ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), pi ) 23.76/23.73 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))), (one_one real) ) 23.76/23.73 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls)))), (one_one real) ) 23.76/23.73 ( 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) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X $$unsorted) (N $$unsorted) (M $$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))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) X))) (= (hAPP real real (hAPP nat _let_0 root (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) M) N)) X) (hAPP real real (hAPP nat _let_0 root M) (hAPP real real (hAPP nat _let_0 root N) X)))))) ) 23.76/23.73 ( (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))) ) 23.76/23.73 ( (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))) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162635 $$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_162635) (zero_zero X_a)))) (= (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_162635) (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_162635))) ) 23.76/23.73 ( int, pls ) 23.76/23.73 ( int, (one_one int) ) 23.76/23.73 ( int, min ) 23.76/23.73 ( int, (zero_zero int) ) 23.76/23.73 ( int, s ) 23.76/23.73 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.73 ( int, t ) 23.76/23.73 ( int, v ) 23.76/23.73 ( int, w ) 23.76/23.73 ( int, m1 ) 23.76/23.73 ( int, skv_4 ) 23.76/23.73 ( int, skv_5 ) 23.76/23.73 ( int, skv_14 ) 23.76/23.73 ( int, skv_20 ) 23.76/23.73 ( nat, (zero_zero nat) ) 23.76/23.73 ( real, pi ) 23.76/23.73 ( 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)))) ) 23.76/23.73 ( real, (one_one real) ) 23.76/23.73 ( real, (zero_zero real) ) 23.76/23.73 ( 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) ) 23.76/23.73 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( 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))))) ) 23.76/23.73 ( 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)) ) 23.76/23.73 ( complex, ii ) 23.76/23.73 ( complex, (one_one complex) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((I $$unsorted) (P_1 $$unsorted) (K $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 K))) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool P_1 (hAPP nat nat suc N_1)))) (hBOOL (hAPP nat bool P_1 N_1))) )) (hBOOL (hAPP nat bool P_1 (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) K) I)))) ) 23.76/23.73 ( (one_one nat), (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)), (hAPP int nat nat_1 t) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((Xa $$unsorted) (K $$unsorted)) (let ((_let_0 (fun int bool))) (or (not (= (ti int Xa) (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))) (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Xa) zEven)))) ) 23.76/23.73 ( s1, (hAPP int int (abs_abs int) w) ) 23.76/23.73 ( m, (hAPP int int (abs_abs int) skv_20) ) 23.76/23.73 ( v, (hAPP int int (abs_abs int) v) ) 23.76/23.73 ( r, (hAPP int int (abs_abs int) skv_14) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (hAPP int real (real_1 int) N))) (or (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less real) _let_1) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 (ord_less_eq real) X) (hAPP real real (hAPP real (fun real real) (plus_plus real) _let_1) (one_one real))))) (= (hAPP real int (archimedean_ceiling real) X) (hAPP int int (hAPP int (fun int int) (plus_plus int) N) (one_one int)))))) ) 23.76/23.73 ( (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( (zero_zero int), pi ) 23.76/23.73 ( (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)))) ) 23.76/23.73 ( (zero_zero int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( (zero_zero int), skv_2 ) 23.76/23.73 ( (zero_zero int), skv_9 ) 23.76/23.73 ( (zero_zero int), skv_12 ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162724 $$unsorted) (BOUND_VARIABLE_162725 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less_eq X_a))) (or (not (ordere142940540dd_abs X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (abs_abs X_a) BOUND_VARIABLE_162724)) BOUND_VARIABLE_162725))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_162724)) BOUND_VARIABLE_162725))))) ) 23.76/23.73 ( int, pls, pls ) 23.76/23.73 ( int, pls, (one_one int) ) 23.76/23.73 ( int, pls, min ) 23.76/23.73 ( int, pls, s ) 23.76/23.73 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( int, pls, (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.73 ( int, pls, skv_4 ) 23.76/23.73 ( int, pls, skv_5 ) 23.76/23.73 ( int, (one_one int), pls ) 23.76/23.73 ( int, (one_one int), min ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162768 $$unsorted) (BOUND_VARIABLE_162769 $$unsorted)) (let ((_let_0 (of_real X_a))) (or (not (real_algebra_1 X_a)) (= (= BOUND_VARIABLE_162768 BOUND_VARIABLE_162769) (= (hAPP real X_a _let_0 BOUND_VARIABLE_162768) (hAPP real X_a _let_0 BOUND_VARIABLE_162769))))) ) 23.76/23.73 ( complex, (hAPP int real (number_number_of real) min), (hAPP int real (number_number_of real) min) ) 23.76/23.73 ( complex, (hAPP int real (number_number_of real) min), pi ) 23.76/23.73 ( complex, pi, (hAPP int real (number_number_of real) min) ) 23.76/23.73 ( complex, pi, (hAPP real real (uminus_uminus real) (one_one real)) ) 23.76/23.73 ( complex, (hAPP real real (uminus_uminus real) (one_one real)), (hAPP int real (number_number_of real) min) ) 23.76/23.73 ) 23.76/23.73 (instantiation (forall ((Xa $$unsorted)) (= (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) Xa)) (= Xa (hAPP nat real (hAPP real (fun nat real) (power_power real) (hAPP real real sqrt Xa)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.76/23.73 ( pi ) 23.76/23.73 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.73 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( (one_one real) ) 23.76/23.73 ( (zero_zero real) ) 23.76/23.73 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.73 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.73 ( skv_10 ) 23.76/23.73 ( skv_11 ) 23.76/23.73 ( skv_15 ) 23.76/23.73 ( skv_18 ) 23.76/23.73 ) 23.76/23.74 (instantiation (forall ((X $$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))) (= (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)) (hAPP real real _let_0 X)))) ) 23.76/23.74 ( pi ) 23.76/23.74 ( (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)))) ) 23.76/23.74 ( (one_one real) ) 23.76/23.74 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( skv_2 ) 23.76/23.74 ( skv_9 ) 23.76/23.74 ( skv_12 ) 23.76/23.74 ) 23.76/23.74 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162852 $$unsorted)) (or (not (comm_monoid_add X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (plus_plus X_a) (zero_zero X_a)) BOUND_VARIABLE_162852) (ti X_a BOUND_VARIABLE_162852))) ) 23.76/23.74 ( int, pls ) 23.76/23.74 ( int, min ) 23.76/23.74 ( int, s ) 23.76/23.74 ( int, s1 ) 23.76/23.74 ( int, m ) 23.76/23.74 ( int, t ) 23.76/23.74 ( int, v ) 23.76/23.74 ( int, w ) 23.76/23.74 ( int, y ) 23.76/23.74 ( int, sa ) 23.76/23.74 ( int, x ) 23.76/23.74 ( int, r ) 23.76/23.74 ( int, m1 ) 23.76/23.74 ( int, skv_14 ) 23.76/23.74 ( int, skv_20 ) 23.76/23.74 ( (fun int int), bit1 ) 23.76/23.74 ( (fun int int), bit0 ) 23.76/23.74 ( (fun int int), succ ) 23.76/23.74 ( (fun int int), pred ) 23.76/23.74 ( (fun int int), (fact_fact int) ) 23.76/23.74 ( (fun int int), zfact ) 23.76/23.74 ( nat, n ) 23.76/23.74 ( nat, tn ) 23.76/23.74 ( bool, fTrue ) 23.76/23.74 ( bool, fFalse ) 23.76/23.74 ( real, pi ) 23.76/23.74 ( (fun nat real), (real_1 nat) ) 23.76/23.74 ( (fun nat real), cos_coeff ) 23.76/23.74 ( (fun nat real), sin_coeff ) 23.76/23.74 ( (fun real real), sin ) 23.76/23.74 ( (fun real real), cos ) 23.76/23.74 ( (fun real real), sqrt ) 23.76/23.74 ( (fun real real), tan ) 23.76/23.74 ( (fun real real), ln ) 23.76/23.74 ( (fun real real), arctan ) 23.76/23.74 ( (fun real real), arcsin ) 23.76/23.74 ( (fun real real), arccos ) 23.76/23.74 ( (fun nat nat), suc ) 23.76/23.74 ( (fun nat nat), (fact_fact nat) ) 23.76/23.74 ( (fun nat nat), nat_size ) 23.76/23.74 ( (fun nat nat), (size_size nat) ) 23.76/23.74 ( (fun nat nat), fact ) 23.76/23.74 ( (filter nat), sequentially ) 23.76/23.74 ( (fun int (fun int rat)), fract ) 23.76/23.74 ( complex, ii ) 23.76/23.74 ( (fun int bool), zOdd ) 23.76/23.74 ( (fun int bool), zprime ) 23.76/23.74 ( (fun int bool), zEven ) 23.76/23.74 ( (fun int bool), nat_neg ) 23.76/23.74 ( (fun int bool), nat_is_nat ) 23.76/23.74 ( (fun int bool), (even_odd_even int) ) 23.76/23.74 ( (fun int bool), twoSqu1091635170sum2sq ) 23.76/23.74 ( (fun int (fun int int)), legacy_zgcd ) 23.76/23.74 ( (fun int (fun int int)), (gcd_gcd int) ) 23.76/23.74 ( (fun int (fun int int)), inv ) 23.76/23.74 ( (fun int (fun int int)), multInv ) 23.76/23.74 ( (fun int (fun int int)), legendre ) 23.76/23.74 ( (fun int (fun int int)), standardRes ) 23.76/23.74 ( (fun int (fun int int)), nat_tsub ) 23.76/23.74 ( (fun int (fun int int)), z3div ) 23.76/23.74 ( (fun int (fun int int)), z3mod ) 23.76/23.74 ( (fun int (fun int int)), int_lcm ) 23.76/23.74 ( (fun int (fun int int)), int_gcd ) 23.76/23.74 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.76/23.74 ( (fun bool bool), fNot ) 23.76/23.74 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.76/23.74 ( (fun bool (fun bool bool)), fconj ) 23.76/23.74 ( (fun bool (fun bool bool)), fdisj ) 23.76/23.74 ( (fun bool (fun bool bool)), fimplies ) 23.76/23.74 ( (fun int (fun int bool)), quadRes ) 23.76/23.74 ( (fun int (fun int bool)), d22set ) 23.76/23.74 ( (fun int (fun int bool)), norRRset ) 23.76/23.74 ( (fun int (fun int bool)), sRStar ) 23.76/23.74 ( (fun int (fun int bool)), sr ) 23.76/23.74 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.76/23.74 ( (fun nat bool), (even_odd_even nat) ) 23.76/23.74 ( (fun nat bool), prime ) 23.76/23.74 ( (fun real complex), cis ) 23.76/23.74 ( (fun nat (fun nat bool)), coprime ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.76/23.74 ( (fun (product_prod int int) bool), frac_1 ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.76/23.74 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.76/23.74 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.76/23.74 ( (fun (fun int bool) bool), nat_nat_set ) 23.76/23.74 ( (fun nat (fun real real)), root ) 23.76/23.74 ( (fun real (fun real real)), log ) 23.76/23.74 ( (fun real (fun real real)), powr ) 23.76/23.74 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.76/23.74 ( (fun complex complex), cnj ) 23.76/23.74 ( (fun complex complex), expi ) 23.76/23.74 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.76/23.74 ( (fun nat (fun nat nat)), nat_gcd ) 23.76/23.74 ( (fun nat (fun nat nat)), nat_lcm ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.76/23.74 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.76/23.74 ( (fun int (fun (fun int bool) bool)), resSet ) 23.76/23.74 ( (fun int nat), nat_1 ) 23.76/23.74 ( (fun int nat), phi ) 23.76/23.74 ( (fun complex real), re ) 23.76/23.74 ( (fun complex real), im ) 23.76/23.74 ( (fun complex real), arg ) 23.76/23.74 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.76/23.74 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.76/23.74 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.76/23.74 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.76/23.74 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.76/23.74 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.76/23.74 ( (fun (product_prod nat nat) bool), pred_nat ) 23.76/23.74 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.76/23.74 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.76/23.74 ( (fun (fun int bool) int), (the int) ) 23.76/23.74 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.76/23.74 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.76/23.74 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.76/23.74 ( (fun real (fun real complex)), rcis ) 23.76/23.74 ( (fun real (fun real complex)), complex_1 ) 23.76/23.74 ( (fun int (fun int (fun int bool))), zcong ) 23.76/23.74 ( (fun int (fun int (fun int bool))), wset ) 23.76/23.74 ( (fun int (fun int (fun int bool))), noXRRset ) 23.76/23.74 ( (fun int (fun int (fun int bool))), bnorRset ) 23.76/23.74 ( (fun int (fun int (fun int bool))), zcongm ) 23.76/23.74 ( (fun real nat), natceiling ) 23.76/23.74 ( (fun real nat), natfloor ) 23.76/23.74 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.76/23.74 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.76/23.74 ( (fun int real), (real_1 int) ) 23.76/23.74 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.76/23.74 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.76/23.74 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.76/23.74 ( (fun complex nat), (size_size complex) ) 23.76/23.74 ( (fun complex nat), complex_size ) 23.76/23.74 ( (fun (fun nat rat) bool), vanishes ) 23.76/23.74 ( (fun (product_prod int int) rat), frct ) 23.76/23.74 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.76/23.74 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.76/23.74 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.76/23.74 ( (fun rat real), ratreal ) 23.76/23.74 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.76/23.74 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.76/23.74 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.76/23.74 ( (fun rat (product_prod int int)), quotient_of ) 23.76/23.74 ( (fun int (fun nat nat)), nat_aux ) 23.76/23.74 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.76/23.74 ( (fun int (list int)), quickc666637781d_zero ) 23.76/23.74 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.76/23.74 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.76/23.74 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.76/23.74 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.76/23.74 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.76/23.74 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.76/23.74 ( (fun code_code_numeral int), code_int_of ) 23.76/23.74 ) 23.76/23.74 (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)))) ) 23.76/23.74 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.76/23.74 ( 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))) ) 23.76/23.74 ( v, y ) 23.76/23.74 ( v, sa ) 23.76/23.74 ( v, x ) 23.76/23.74 ( v, r ) 23.76/23.74 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.76/23.74 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.76/23.74 ( w, y ) 23.76/23.74 ( w, sa ) 23.76/23.74 ( w, x ) 23.76/23.74 ( w, r ) 23.76/23.74 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.76/23.74 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.76/23.74 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.76/23.74 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.74 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.76/23.74 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.74 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.74 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.74 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.76/23.77 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.77 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.77 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.77 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.77 ( skv_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))) ) 23.76/23.77 ) 23.76/23.77 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162875 $$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_eq X_a) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_162875)) (one_one X_a))) (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) BOUND_VARIABLE_162875) (hAPP int int bit1 pls))))) ) 23.76/23.77 ( int, pls ) 23.76/23.77 ( int, (hAPP int int bit1 pls) ) 23.76/23.77 ( int, min ) 23.76/23.77 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.77 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.77 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.77 ( nat, pls ) 23.76/23.77 ( nat, (hAPP int int bit1 pls) ) 23.76/23.77 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.77 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.77 ( real, min ) 23.76/23.77 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.77 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.77 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.76/23.77 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.76/23.77 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.76/23.77 ( 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)))))))) ) 23.76/23.77 ( complex, min ) 23.76/23.77 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.76/23.77 ( quickcheck_code_int, pls ) 23.76/23.77 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 23.76/23.77 ( quickcheck_code_int, (one_one int) ) 23.76/23.77 ( code_code_numeral, pls ) 23.76/23.77 ( code_code_numeral, (hAPP int int bit1 pls) ) 23.76/23.77 ) 23.76/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162908 $$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_162908))) (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_162908))) (hAPP _let_0 real (suminf real) _let_3)))))))) ) 23.76/23.78 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat _let_1))) (let ((_let_3 (fun real _let_1))) (let ((_let_4 (fun _let_0 _let_2))) (let ((_let_5 (combb real _let_1 nat))) (let ((_let_6 (fun nat (fun nat nat)))) (let ((_let_7 (combc nat nat nat))) (hAPP _let_0 _let_0 (hAPP _let_2 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (inverse_divide real)) (hAPP real _let_0 (hAPP _let_2 (fun real _let_0) (combc nat real real) (hAPP _let_0 _let_2 (hAPP _let_3 _let_4 _let_5 (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) (one_one real)))) (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_6 _let_6 _let_7 (hAPP (fun nat nat) _let_6 (hAPP _let_6 (fun (fun nat nat) _let_6) (combb nat (fun nat nat) nat) (plus_plus nat)) (hAPP nat (fun nat nat) (hAPP _let_6 _let_6 _let_7 (times_times nat)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (one_one nat)))))))))))) ) 23.76/23.78 ) 23.76/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_162962 $$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_162962)) (one_one real)))) (hBOOL (hAPP _let_0 bool (summable X_a) (hAPP X_a _let_0 (power_power X_a) BOUND_VARIABLE_162962))))) ) 23.76/23.78 ( int, s ) 23.76/23.78 ( int, s1 ) 23.76/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.78 ( int, v ) 23.76/23.78 ( int, w ) 23.76/23.78 ( int, y ) 23.76/23.78 ( int, x ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.76/23.78 ( int, skv_6 ) 23.76/23.78 ( int, skv_7 ) 23.76/23.78 ( int, skv_16 ) 23.76/23.78 ( int, skv_23 ) 23.76/23.78 ( int, skv_24 ) 23.76/23.78 ( real, (hAPP int real (number_number_of real) min) ) 23.76/23.78 ( 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)))) ) 23.76/23.78 ( complex, ii ) 23.76/23.78 ) 23.76/23.78 (instantiation (forall ((K $$unsorted) (F $$unsorted) (Na $$unsorted) (Ma $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less_eq int))) (or (not (forall ((I_2 $$unsorted)) (let ((_let_2 (fun nat bool))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_2 (ord_less nat) I_2) Na))) (not (hBOOL (hAPP nat bool (hAPP nat _let_2 (ord_less_eq nat) Ma) I_2))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (abs_abs int) (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int F (hAPP nat nat (hAPP nat (fun nat nat) (plus_plus nat) I_2) (one_one nat)))) (hAPP nat int F I_2)))) (one_one int))))) )) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) Ma) Na))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP nat int F Ma)) K))) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 K) (hAPP nat int F Na)))) (not (forall ((I_2 $$unsorted)) (let ((_let_0 (fun nat bool))) (let ((_let_1 (ord_less_eq nat))) (or (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 I_2) Na))) (not (= (ti int K) (hAPP nat int F I_2))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 _let_1 Ma) I_2)))))) ))))) ) 23.76/23.78 ( pls, (semiring_1_of_nat int), tn, (zero_zero nat) ) 23.76/23.78 ( (one_one int), (semiring_1_of_nat int), n, (zero_zero nat) ) 23.76/23.78 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))), (semiring_1_of_nat int), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 23.76/23.78 ) 23.76/23.78 (instantiation (forall ((N $$unsorted) (M $$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))) (not (hBOOL (hAPP nat bool (hAPP nat _let_0 (dvd_dvd nat) N) M)))))) ) 23.76/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (zero_zero nat) ) 23.76/23.78 ( n, (zero_zero nat) ) 23.76/23.78 ( tn, (zero_zero nat) ) 23.76/23.78 ) 23.76/23.78 (instantiation (forall ((A_1 $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (hAPP real real (sgn_sgn real) A_1))) (let ((_let_2 (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1)))) (or (= (zero_zero real) A_1) (and (or _let_2 (= (hAPP real real (uminus_uminus real) _let_0) _let_1)) (or (not _let_2) (= _let_0 _let_1))))))) ) 23.76/23.78 ( pi ) 23.76/23.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.78 ( (zero_zero real) ) 23.76/23.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.76/23.78 ( skv_2 ) 23.76/23.78 ( skv_9 ) 23.76/23.78 ( skv_12 ) 23.76/23.78 ) 23.76/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163162 $$unsorted) (BOUND_VARIABLE_163163 $$unsorted) (BOUND_VARIABLE_163164 $$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_163164) BOUND_VARIABLE_163163) (hAPP nat X_a (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163162) BOUND_VARIABLE_163163))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_163162))) (not (hBOOL (hAPP X_a bool _let_2 BOUND_VARIABLE_163164))) (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) BOUND_VARIABLE_163163))) (= (ti X_a BOUND_VARIABLE_163162) (ti X_a BOUND_VARIABLE_163164)))))) ) 23.76/23.78 ( int, s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.76/23.78 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.76/23.78 ( int, s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.76/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.76/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.76/23.78 ( int, v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.76/23.78 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.76/23.78 ( int, w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.76/23.78 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.76/23.78 ( int, y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.76/23.78 ( int, x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.76/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.78 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.83/23.78 ( int, skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.83/23.78 ( int, skv_7, (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.83/23.78 ( int, skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.83/23.78 ( int, skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.83/23.78 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.83/23.78 ( int, skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.83/23.78 ( complex, ii, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_0 (even_odd_even int))) (or (hBOOL (hAPP int bool _let_0 X)) (not (hBOOL (hAPP int bool _let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) X) N)))))) ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.83/23.78 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.83/23.78 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.83/23.78 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.83/23.78 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.83/23.78 ( (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.83/23.78 ( (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.83/23.78 ( (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.83/23.78 ( (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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.83/23.78 ( (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163199 $$unsorted)) (let ((_let_0 (fun (filter nat) bool))) (let ((_let_1 (fun nat X_a))) (or (not (real_normed_field X_a)) (not (hBOOL (hAPP _let_1 bool (summable X_a) BOUND_VARIABLE_163199))) (hBOOL (hAPP (filter nat) bool (hAPP X_a _let_0 (hAPP _let_1 (fun X_a _let_0) (tendsto nat X_a) BOUND_VARIABLE_163199) (zero_zero X_a)) sequentially))))) ) 23.83/23.78 ( real, (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X $$unsorted)) (= (hAPP int int succ (hAPP int int pred X)) (ti int X)) ) 23.83/23.78 ( pls ) 23.83/23.78 ( min ) 23.83/23.78 ( s ) 23.83/23.78 ( s1 ) 23.83/23.78 ( m ) 23.83/23.78 ( t ) 23.83/23.78 ( v ) 23.83/23.78 ( w ) 23.83/23.78 ( y ) 23.83/23.78 ( sa ) 23.83/23.78 ( x ) 23.83/23.78 ( r ) 23.83/23.78 ( m1 ) 23.83/23.78 ( skv_14 ) 23.83/23.78 ( skv_20 ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X_a $$unsorted)) (or (not (real_normed_vector X_a)) (not (forall ((K_2 $$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 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)))))) )) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) K_2)))) ))) ) 23.83/23.78 ( real ) 23.83/23.78 ( complex ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X $$unsorted) (Y $$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))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Y) X))) (not (hBOOL (hAPP real bool (hAPP real _let_0 _let_2 X) (zero_zero real)))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real cos Y)) (hAPP real real cos X))))))) ) 23.83/23.78 ( skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((Y $$unsorted)) (let ((_let_0 (zero_zero real))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) _let_0) Y))) (= _let_0 (hAPP real real cos (hAPP complex real arg (hAPP real complex (hAPP real (fun real complex) complex_1 _let_0) Y)))))) ) 23.83/23.78 ( pi ) 23.83/23.78 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( (one_one real) ) 23.83/23.78 ( (zero_zero real) ) 23.83/23.78 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( skv_2 ) 23.83/23.78 ( skv_9 ) 23.83/23.78 ( skv_12 ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less_eq real))) (let ((_let_2 (hAPP nat (fun real real) root Na))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 Xa)) (hAPP real real _let_2 Ya))) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) Ya))))))) ) 23.83/23.78 ( (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))) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((Xa $$unsorted) (Na $$unsorted)) (let ((_let_0 (one_one real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 (hAPP real real (hAPP nat (fun real real) root Na) Xa)) _let_0)) (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Xa) _let_0))))))) ) 23.83/23.78 ( (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))) ) 23.83/23.78 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ( (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))) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163372 $$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_163372) (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_163372) BOUND_VARIABLE_163372)))) ) 23.83/23.78 ( int, (one_one int) ) 23.83/23.78 ( 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)))) ) 23.83/23.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( 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) ) 23.83/23.78 ( 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))) ) 23.83/23.78 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( int, y ) 23.83/23.78 ( int, sa ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.83/23.78 ( int, x ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.78 ( int, r ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.83/23.78 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))) ) 23.83/23.78 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.83/23.78 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))) ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.83/23.78 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( int, skv_13 ) 23.83/23.78 ( int, skv_19 ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( nat, (one_one nat) ) 23.83/23.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( 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))))) ) 23.83/23.78 ( complex, ii ) 23.83/23.78 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.78 ( 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)) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163388 $$unsorted) (BOUND_VARIABLE_163389 $$unsorted) (BOUND_VARIABLE_163390 $$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_163389))) (let ((_let_3 (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163388))) (or (not (comm_semiring_1 X_a)) (= (hAPP X_a X_a _let_2 (hAPP X_a X_a _let_3 BOUND_VARIABLE_163390)) (hAPP X_a X_a _let_3 (hAPP X_a X_a _let_2 BOUND_VARIABLE_163390)))))))) ) 23.83/23.78 ( 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))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), m1 ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, v ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa, w ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), skv_3 ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, v ) 23.83/23.78 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r, w ) 23.83/23.78 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 23.83/23.78 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 23.83/23.78 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.83/23.78 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.83/23.78 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), v ) 23.83/23.78 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), w ) 23.83/23.78 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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))), m1 ) 23.83/23.78 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.83/23.78 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.83/23.78 ( 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))))), (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.83/23.78 ) 23.83/23.78 (instantiation (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_0 (fun int rat))) (or (= (zero_zero int) (ti int N)) (= (hAPP rat rat (hAPP rat (fun rat rat) (plus_plus rat) (hAPP int rat (hAPP int _let_0 fract M) N)) (one_one rat)) (hAPP int rat (hAPP int _let_0 fract (hAPP int int (hAPP int (fun int int) (plus_plus int) M) N)) N)))) ) 23.83/23.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.83/23.78 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.83/23.78 ( (hAPP nat int (hAPP 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) ) 23.83/23.78 ( (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) ) 23.83/23.78 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.78 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.83/23.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.83/23.79 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.83/23.79 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1 ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.79 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.83/23.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((V $$unsorted)) (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V)))) (= (zero_zero real) (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V)))) ) 23.83/23.79 ( pls ) 23.83/23.79 ( (hAPP int int bit1 pls) ) 23.83/23.79 ( min ) 23.83/23.79 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.79 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((V $$unsorted)) (or (hBOOL (hAPP int bool nat_neg (hAPP int int (number_number_of int) V))) (= (hAPP nat real (real_1 nat) (hAPP int nat (number_number_of nat) V)) (hAPP int real (number_number_of real) V))) ) 23.83/23.79 ( pls ) 23.83/23.79 ( (hAPP int int bit1 pls) ) 23.83/23.79 ( min ) 23.83/23.79 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.79 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.79 ( (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (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)))))))) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_b $$unsorted)) (let ((_let_0 (uminus_uminus X_b))) (or (not (uminus X_b)) (= _let_0 (ti (fun X_b X_b) _let_0)))) ) 23.83/23.79 ( rat ) 23.83/23.79 ( int ) 23.83/23.79 ( (fun int int) ) 23.83/23.79 ( nat ) 23.83/23.79 ( bool ) 23.83/23.79 ( real ) 23.83/23.79 ( (fun nat real) ) 23.83/23.79 ( (fun real real) ) 23.83/23.79 ( complex ) 23.83/23.79 ( (fun int bool) ) 23.83/23.79 ( (product_prod int int) ) 23.83/23.79 ( (fun (product_prod int int) int) ) 23.83/23.79 ( (fun int (fun int bool)) ) 23.83/23.79 ( (fun nat bool) ) 23.83/23.79 ( (fun (product_prod int int) bool) ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))) ) 23.83/23.79 ( (fun real bool) ) 23.83/23.79 ( code_code_numeral ) 23.83/23.79 ( (fun int (fun int (fun int bool))) ) 23.83/23.79 ( (fun int real) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163525 $$unsorted)) (or (not (number_ring X_a)) (not (field_inverse_zero X_a)) (= (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (inverse_divide X_a) BOUND_VARIABLE_163525) (hAPP int X_a (number_number_of X_a) min)) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_163525))) ) 23.83/23.79 ( int, pls ) 23.83/23.79 ( int, (one_one int) ) 23.83/23.79 ( int, min ) 23.83/23.79 ( real, pi ) 23.83/23.79 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( real, (one_one real) ) 23.83/23.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.83/23.79 ( real, (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.79 ( real, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( complex, ii ) 23.83/23.79 ( complex, (one_one complex) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_b $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_163555 $$unsorted) (BOUND_VARIABLE_163556 $$unsorted) (BOUND_VARIABLE_163557 $$unsorted) (BOUND_VARIABLE_163558 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (or (not (order X_b)) (not (order X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_163556 BOUND_VARIABLE_163557)) BOUND_VARIABLE_163558))) (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) BOUND_VARIABLE_163555) BOUND_VARIABLE_163557))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_b bool (hAPP X_b (fun X_b bool) (ord_less_eq X_b) Y_1) X_1))) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 (ord_less_eq X_a) (hAPP X_b X_a BOUND_VARIABLE_163556 Y_1)) (hAPP X_b X_a BOUND_VARIABLE_163556 X_1)))) )) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_b X_a BOUND_VARIABLE_163556 BOUND_VARIABLE_163555)) BOUND_VARIABLE_163558))))) ) 23.83/23.79 ( int, int, (one_one int), bit0, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, int, min, bit1, min, min ) 23.83/23.79 ( int, int, (zero_zero int), bit0, 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))) ) 23.83/23.79 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) w)), bit0, pls, (one_one int) ) 23.83/23.79 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) v)), bit1, min, (zero_zero int) ) 23.83/23.79 ( int, 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 bit1 pls)))) (hAPP int int (abs_abs int) skv_14)), (fact_fact int), (zero_zero int), t ) 23.83/23.79 ( int, real, (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)))) (hAPP int int (abs_abs int) skv_20)), (real_1 int), (one_one int), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( real, nat, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), natfloor, (zero_zero real), n ) 23.83/23.79 ( 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)))), (hAPP 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))) ) 23.83/23.79 ( 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 real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( real, real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), cos, skv_10, pi ) 23.83/23.79 ( real, real, skv_10, cos, skv_10, (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163601 $$unsorted)) (let ((_let_0 (inverse_inverse X_a))) (let ((_let_1 (ti X_a BOUND_VARIABLE_163601))) (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_163601)))))) ) 23.83/23.79 ( int, pls ) 23.83/23.79 ( int, min ) 23.83/23.79 ( int, s ) 23.83/23.79 ( int, s1 ) 23.83/23.79 ( int, m ) 23.83/23.79 ( int, t ) 23.83/23.79 ( int, v ) 23.83/23.79 ( int, w ) 23.83/23.79 ( int, y ) 23.83/23.79 ( int, sa ) 23.83/23.79 ( int, x ) 23.83/23.79 ( int, r ) 23.83/23.79 ( int, m1 ) 23.83/23.79 ( int, skv_14 ) 23.83/23.79 ( int, skv_20 ) 23.83/23.79 ( (fun int int), bit1 ) 23.83/23.79 ( (fun int int), bit0 ) 23.83/23.79 ( (fun int int), succ ) 23.83/23.79 ( (fun int int), pred ) 23.83/23.79 ( (fun int int), (fact_fact int) ) 23.83/23.79 ( (fun int int), zfact ) 23.83/23.79 ( nat, n ) 23.83/23.79 ( nat, tn ) 23.83/23.79 ( bool, fTrue ) 23.83/23.79 ( bool, fFalse ) 23.83/23.79 ( real, pi ) 23.83/23.79 ( real, (zero_zero real) ) 23.83/23.79 ( (fun nat real), (real_1 nat) ) 23.83/23.79 ( (fun nat real), cos_coeff ) 23.83/23.79 ( (fun nat real), sin_coeff ) 23.83/23.79 ( (fun real real), sin ) 23.83/23.79 ( (fun real real), cos ) 23.83/23.79 ( (fun real real), sqrt ) 23.83/23.79 ( (fun real real), tan ) 23.83/23.79 ( (fun real real), ln ) 23.83/23.79 ( (fun real real), arctan ) 23.83/23.79 ( (fun real real), arcsin ) 23.83/23.79 ( (fun real real), arccos ) 23.83/23.79 ( (fun nat nat), suc ) 23.83/23.79 ( (fun nat nat), (fact_fact nat) ) 23.83/23.79 ( (fun nat nat), nat_size ) 23.83/23.79 ( (fun nat nat), (size_size nat) ) 23.83/23.79 ( (fun nat nat), fact ) 23.83/23.79 ( (filter nat), sequentially ) 23.83/23.79 ( (fun int (fun int rat)), fract ) 23.83/23.79 ( complex, ii ) 23.83/23.79 ( (fun int bool), zOdd ) 23.83/23.79 ( (fun int bool), zprime ) 23.83/23.79 ( (fun int bool), zEven ) 23.83/23.79 ( (fun int bool), nat_neg ) 23.83/23.79 ( (fun int bool), nat_is_nat ) 23.83/23.79 ( (fun int bool), (even_odd_even int) ) 23.83/23.79 ( (fun int bool), twoSqu1091635170sum2sq ) 23.83/23.79 ( (fun int (fun int int)), legacy_zgcd ) 23.83/23.79 ( (fun int (fun int int)), (gcd_gcd int) ) 23.83/23.79 ( (fun int (fun int int)), inv ) 23.83/23.79 ( (fun int (fun int int)), multInv ) 23.83/23.79 ( (fun int (fun int int)), legendre ) 23.83/23.79 ( (fun int (fun int int)), standardRes ) 23.83/23.79 ( (fun int (fun int int)), nat_tsub ) 23.83/23.79 ( (fun int (fun int int)), z3div ) 23.83/23.79 ( (fun int (fun int int)), z3mod ) 23.83/23.79 ( (fun int (fun int int)), int_lcm ) 23.83/23.79 ( (fun int (fun int int)), int_gcd ) 23.83/23.79 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.83/23.79 ( (fun bool bool), fNot ) 23.83/23.79 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.83/23.79 ( (fun bool (fun bool bool)), fconj ) 23.83/23.79 ( (fun bool (fun bool bool)), fdisj ) 23.83/23.79 ( (fun bool (fun bool bool)), fimplies ) 23.83/23.79 ( (fun int (fun int bool)), quadRes ) 23.83/23.79 ( (fun int (fun int bool)), d22set ) 23.83/23.79 ( (fun int (fun int bool)), norRRset ) 23.83/23.79 ( (fun int (fun int bool)), sRStar ) 23.83/23.79 ( (fun int (fun int bool)), sr ) 23.83/23.79 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.83/23.79 ( (fun nat bool), (even_odd_even nat) ) 23.83/23.79 ( (fun nat bool), prime ) 23.83/23.79 ( (fun real complex), cis ) 23.83/23.79 ( (fun nat (fun nat bool)), coprime ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.83/23.79 ( (fun (product_prod int int) bool), frac_1 ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.83/23.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.83/23.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.83/23.79 ( (fun (fun int bool) bool), nat_nat_set ) 23.83/23.79 ( (fun nat (fun real real)), root ) 23.83/23.79 ( (fun real (fun real real)), log ) 23.83/23.79 ( (fun real (fun real real)), powr ) 23.83/23.79 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.83/23.79 ( (fun complex complex), cnj ) 23.83/23.79 ( (fun complex complex), expi ) 23.83/23.79 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.83/23.79 ( (fun nat (fun nat nat)), nat_gcd ) 23.83/23.79 ( (fun nat (fun nat nat)), nat_lcm ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.83/23.79 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.83/23.79 ( (fun int (fun (fun int bool) bool)), resSet ) 23.83/23.79 ( (fun int nat), nat_1 ) 23.83/23.79 ( (fun int nat), phi ) 23.83/23.79 ( (fun complex real), re ) 23.83/23.79 ( (fun complex real), im ) 23.83/23.79 ( (fun complex real), arg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.83/23.79 ( (fun (product_prod nat nat) bool), pred_nat ) 23.83/23.79 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.83/23.79 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.83/23.79 ( (fun (fun int bool) int), (the int) ) 23.83/23.79 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.83/23.79 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.83/23.79 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.83/23.79 ( (fun real (fun real complex)), rcis ) 23.83/23.79 ( (fun real (fun real complex)), complex_1 ) 23.83/23.79 ( (fun int (fun int (fun int bool))), zcong ) 23.83/23.79 ( (fun int (fun int (fun int bool))), wset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), noXRRset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), bnorRset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), zcongm ) 23.83/23.79 ( (fun real nat), natceiling ) 23.83/23.79 ( (fun real nat), natfloor ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.83/23.79 ( (fun int real), (real_1 int) ) 23.83/23.79 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.83/23.79 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.83/23.79 ( (fun complex nat), (size_size complex) ) 23.83/23.79 ( (fun complex nat), complex_size ) 23.83/23.79 ( (fun (fun nat rat) bool), vanishes ) 23.83/23.79 ( (fun (product_prod int int) rat), frct ) 23.83/23.79 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.83/23.79 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.83/23.79 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.83/23.79 ( (fun rat real), ratreal ) 23.83/23.79 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.83/23.79 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.83/23.79 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.83/23.79 ( (fun rat (product_prod int int)), quotient_of ) 23.83/23.79 ( (fun int (fun nat nat)), nat_aux ) 23.83/23.79 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.83/23.79 ( (fun int (list int)), quickc666637781d_zero ) 23.83/23.79 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.83/23.79 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.83/23.79 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.83/23.79 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.83/23.79 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.83/23.79 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.83/23.79 ( (fun code_code_numeral int), code_int_of ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163623 $$unsorted)) (or (not (semiring_1 X_a)) (= (= (zero_zero X_a) (ti X_a BOUND_VARIABLE_163623)) (hBOOL (hAPP X_a bool (iszero X_a) BOUND_VARIABLE_163623)))) ) 23.83/23.79 ( int, pls ) 23.83/23.79 ( int, min ) 23.83/23.79 ( int, s ) 23.83/23.79 ( int, s1 ) 23.83/23.79 ( int, m ) 23.83/23.79 ( int, t ) 23.83/23.79 ( int, v ) 23.83/23.79 ( int, w ) 23.83/23.79 ( int, y ) 23.83/23.79 ( int, sa ) 23.83/23.79 ( int, x ) 23.83/23.79 ( int, r ) 23.83/23.79 ( int, m1 ) 23.83/23.79 ( int, skv_14 ) 23.83/23.79 ( int, skv_20 ) 23.83/23.79 ( (fun int int), bit1 ) 23.83/23.79 ( (fun int int), bit0 ) 23.83/23.79 ( (fun int int), succ ) 23.83/23.79 ( (fun int int), pred ) 23.83/23.79 ( (fun int int), (fact_fact int) ) 23.83/23.79 ( (fun int int), zfact ) 23.83/23.79 ( nat, n ) 23.83/23.79 ( nat, tn ) 23.83/23.79 ( bool, fTrue ) 23.83/23.79 ( bool, fFalse ) 23.83/23.79 ( real, pi ) 23.83/23.79 ( (fun nat real), (real_1 nat) ) 23.83/23.79 ( (fun nat real), cos_coeff ) 23.83/23.79 ( (fun nat real), sin_coeff ) 23.83/23.79 ( (fun real real), sin ) 23.83/23.79 ( (fun real real), cos ) 23.83/23.79 ( (fun real real), sqrt ) 23.83/23.79 ( (fun real real), tan ) 23.83/23.79 ( (fun real real), ln ) 23.83/23.79 ( (fun real real), arctan ) 23.83/23.79 ( (fun real real), arcsin ) 23.83/23.79 ( (fun real real), arccos ) 23.83/23.79 ( (fun nat nat), suc ) 23.83/23.79 ( (fun nat nat), (fact_fact nat) ) 23.83/23.79 ( (fun nat nat), nat_size ) 23.83/23.79 ( (fun nat nat), (size_size nat) ) 23.83/23.79 ( (fun nat nat), fact ) 23.83/23.79 ( (filter nat), sequentially ) 23.83/23.79 ( (fun int (fun int rat)), fract ) 23.83/23.79 ( complex, ii ) 23.83/23.79 ( (fun int bool), zOdd ) 23.83/23.79 ( (fun int bool), zprime ) 23.83/23.79 ( (fun int bool), zEven ) 23.83/23.79 ( (fun int bool), nat_neg ) 23.83/23.79 ( (fun int bool), nat_is_nat ) 23.83/23.79 ( (fun int bool), (even_odd_even int) ) 23.83/23.79 ( (fun int bool), twoSqu1091635170sum2sq ) 23.83/23.79 ( (fun int (fun int int)), legacy_zgcd ) 23.83/23.79 ( (fun int (fun int int)), (gcd_gcd int) ) 23.83/23.79 ( (fun int (fun int int)), inv ) 23.83/23.79 ( (fun int (fun int int)), multInv ) 23.83/23.79 ( (fun int (fun int int)), legendre ) 23.83/23.79 ( (fun int (fun int int)), standardRes ) 23.83/23.79 ( (fun int (fun int int)), nat_tsub ) 23.83/23.79 ( (fun int (fun int int)), z3div ) 23.83/23.79 ( (fun int (fun int int)), z3mod ) 23.83/23.79 ( (fun int (fun int int)), int_lcm ) 23.83/23.79 ( (fun int (fun int int)), int_gcd ) 23.83/23.79 ( (fun (product_prod int int) int), twoSqu1094008024sum2sq ) 23.83/23.79 ( (fun bool bool), fNot ) 23.83/23.79 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)), is_RRset ) 23.83/23.79 ( (fun bool (fun bool bool)), fconj ) 23.83/23.79 ( (fun bool (fun bool bool)), fdisj ) 23.83/23.79 ( (fun bool (fun bool bool)), fimplies ) 23.83/23.79 ( (fun int (fun int bool)), quadRes ) 23.83/23.79 ( (fun int (fun int bool)), d22set ) 23.83/23.79 ( (fun int (fun int bool)), norRRset ) 23.83/23.79 ( (fun int (fun int bool)), sRStar ) 23.83/23.79 ( (fun int (fun int bool)), sr ) 23.83/23.79 ( (fun int (fun int bool)), quickc1265749348ro_rel ) 23.83/23.79 ( (fun nat bool), (even_odd_even nat) ) 23.83/23.79 ( (fun nat bool), prime ) 23.83/23.79 ( (fun real complex), cis ) 23.83/23.79 ( (fun nat (fun nat bool)), coprime ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun (product_prod _let_0 _let_0) bool)), ratrel ) 23.83/23.79 ( (fun (product_prod int int) bool), frac_1 ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), upto_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), posDivAlg_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), negDivAlg_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), lazy_small_lazy_rel ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), norm_frac_rel ) 23.83/23.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than2 ) 23.83/23.79 ( (fun int (fun (product_prod int int) bool)), int_ge_less_than ) 23.83/23.79 ( (fun (fun int bool) bool), nat_nat_set ) 23.83/23.79 ( (fun nat (fun real real)), root ) 23.83/23.79 ( (fun real (fun real real)), log ) 23.83/23.79 ( (fun real (fun real real)), powr ) 23.83/23.79 ( (fun int (fun int (product_prod int (product_prod int int)))), xzgcd ) 23.83/23.79 ( (fun complex complex), cnj ) 23.83/23.79 ( (fun complex complex), expi ) 23.83/23.79 ( (fun nat (fun nat nat)), (gcd_gcd nat) ) 23.83/23.79 ( (fun nat (fun nat nat)), nat_gcd ) 23.83/23.79 ( (fun nat (fun nat nat)), nat_lcm ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), normalize ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)), negateSnd ) 23.83/23.79 ( (fun int (fun (fun int bool) bool)), rsetR ) 23.83/23.79 ( (fun int (fun (fun int bool) bool)), resSet ) 23.83/23.79 ( (fun int nat), nat_1 ) 23.83/23.79 ( (fun int nat), phi ) 23.83/23.79 ( (fun complex real), re ) 23.83/23.79 ( (fun complex real), im ) 23.83/23.79 ( (fun complex real), arg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), divmod_int ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), posDivAlg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), negDivAlg ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), pdivmod ) 23.83/23.79 ( (fun int (fun int (product_prod int int))), norm_frac ) 23.83/23.79 ( (let ((_let_0 (product_prod int int))) (fun int (fun _let_0 _let_0))), adjust ) 23.83/23.79 ( (fun (product_prod nat nat) bool), pred_nat ) 23.83/23.79 ( (fun code_code_numeral (fun nat nat)), code_nat_of_aux ) 23.83/23.79 ( (fun code_code_numeral code_code_numeral), code_S1047413653umeral ) 23.83/23.79 ( (fun (fun int bool) int), (the int) ) 23.83/23.79 ( (fun int quickcheck_code_int), quickcheck_of_int ) 23.83/23.79 ( (fun nat (fun nat (product_prod nat nat))), divmod_nat ) 23.83/23.79 ( (fun code_code_numeral (fun code_code_numeral (product_prod code_code_numeral code_code_numeral))), code_d418564891umeral ) 23.83/23.79 ( (fun real (fun real complex)), rcis ) 23.83/23.79 ( (fun real (fun real complex)), complex_1 ) 23.83/23.79 ( (fun int (fun int (fun int bool))), zcong ) 23.83/23.79 ( (fun int (fun int (fun int bool))), wset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), noXRRset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), bnorRset ) 23.83/23.79 ( (fun int (fun int (fun int bool))), zcongm ) 23.83/23.79 ( (fun real nat), natceiling ) 23.83/23.79 ( (fun real nat), natfloor ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_less ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun (product_prod _let_0 _let_0) bool)), pair_leq ) 23.83/23.79 ( (fun int real), (real_1 int) ) 23.83/23.79 ( (fun quickcheck_code_int int), quickcheck_int_of ) 23.83/23.79 ( (fun quickcheck_code_int (fun quickcheck_code_int (product_prod quickcheck_code_int quickcheck_code_int))), quickc495462417de_int ) 23.83/23.79 ( (let ((_let_0 (product_prod nat nat))) (fun _let_0 (fun _let_0 bool))), nat_gcd_rel ) 23.83/23.79 ( (fun complex nat), (size_size complex) ) 23.83/23.79 ( (fun complex nat), complex_size ) 23.83/23.79 ( (fun (fun nat rat) bool), vanishes ) 23.83/23.79 ( (fun (product_prod int int) rat), frct ) 23.83/23.79 ( (fun int (fun int (fun (fun int bool) bool))), setS ) 23.83/23.79 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))))), xzgcda ) 23.83/23.79 ( (fun nat (fun nat (fun nat bool))), (ord_gr676655987ssThan nat) ) 23.83/23.79 ( (fun rat real), ratreal ) 23.83/23.79 ( (fun int (fun int (fun int (fun int bool)))), multInvPair ) 23.83/23.79 ( (fun (fun int bool) (fun int (fun int int))), rRset2norRR ) 23.83/23.79 ( (let ((_let_0 (product_prod real real))) (fun (fun _let_0 bool) (fun real (fun real (fun nat _let_0))))), bolzano_bisect ) 23.83/23.79 ( (fun rat (product_prod int int)), quotient_of ) 23.83/23.79 ( (fun int (fun nat nat)), nat_aux ) 23.83/23.79 ( (fun nat (fun nat (product_prod int int))), bezw ) 23.83/23.79 ( (fun int (list int)), quickc666637781d_zero ) 23.83/23.79 ( (fun quickcheck_code_int nat), quickcheck_nat_of ) 23.83/23.79 ( (fun (fun real bool) real), (complete_Sup_Sup real) ) 23.83/23.79 ( (fun int (fun int (fun (product_prod int int) bool))), divmod_int_rel ) 23.83/23.79 ( (fun code_code_numeral nat), code_c271388182l_size ) 23.83/23.79 ( (fun code_code_numeral nat), (size_size code_code_numeral) ) 23.83/23.79 ( (fun nat (fun nat (fun (product_prod nat nat) bool))), divmod_nat_rel ) 23.83/23.79 ( (fun code_code_numeral int), code_int_of ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163648 $$unsorted) (BOUND_VARIABLE_163656 $$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 (abs_abs X_a))) (or (not (abs_if X_a)) (and (or (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163648) _let_2)) (= (ti X_a BOUND_VARIABLE_163648) (hAPP X_a X_a _let_3 BOUND_VARIABLE_163648))) (or (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_163656) _let_2))) (= (hAPP X_a X_a _let_3 BOUND_VARIABLE_163656) (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_163656))))))))) ) 23.83/23.79 ( int, (one_one int), (one_one int) ) 23.83/23.79 ( int, min, min ) 23.83/23.79 ( int, (zero_zero int), (zero_zero int) ) 23.83/23.79 ( int, s, s ) 23.83/23.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, t, t ) 23.83/23.79 ( int, m1, m1 ) 23.83/23.79 ( int, skv_4, skv_4 ) 23.83/23.79 ( int, skv_5, skv_5 ) 23.83/23.79 ( nat, (zero_zero nat), (zero_zero nat) ) 23.83/23.79 ( real, pi, pi ) 23.83/23.79 ( 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 real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( real, (one_one real), (one_one real) ) 23.83/23.79 ( real, (zero_zero real), (zero_zero real) ) 23.83/23.79 ( 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)))) ) 23.83/23.79 ( 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))))), (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))))) ) 23.83/23.79 ( 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)), (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)) ) 23.83/23.79 ) 23.83/23.79 (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)))) ) 23.83/23.79 ( (one_one int), t ) 23.83/23.79 ( min, min ) 23.83/23.79 ( min, (zero_zero int) ) 23.83/23.79 ( (zero_zero int), pls ) 23.83/23.79 ( (zero_zero int), (one_one int) ) 23.83/23.79 ( (zero_zero int), min ) 23.83/23.79 ( (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))) ) 23.83/23.79 ( (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( 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))) ) 23.83/23.79 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.79 ( 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))) ) 23.83/23.79 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( 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))) ) 23.83/23.79 ( skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163686 $$unsorted) (BOUND_VARIABLE_163687 $$unsorted)) (or (not (semiring_div X_a)) (= (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_163686) BOUND_VARIABLE_163687)) (= (zero_zero X_a) (hAPP X_a X_a (hAPP X_a (fun X_a X_a) (div_mod X_a) BOUND_VARIABLE_163687) BOUND_VARIABLE_163686)))) ) 23.83/23.79 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (minus_minus int) (hAPP nat int (hAPP int (fun nat int) (power_power int) s) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (hAPP int int (number_number_of int) min)) ) 23.83/23.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((Ta $$unsorted) (A_2 $$unsorted) (D $$unsorted) (BOUND_VARIABLE_163740 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (zero_zero int)) D))) (not (hBOOL (hAPP _let_0 bool (hAPP int (fun _let_0 bool) (member int) Ta) A_2))) (not (forall ((Xa_1 $$unsorted) (BOUND_VARIABLE_163710 $$unsorted)) (let ((_let_1 (member int))) (let ((_let_2 (fun _let_0 bool))) (or (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 Xa_1) (hAPP int _let_0 (hAPP int (fun int _let_0) (ord_atLeastAtMost int) (one_one int)) D)))) (not (hBOOL (hAPP _let_0 bool (hAPP int _let_2 _let_1 BOUND_VARIABLE_163710) A_2))) (not (= (hAPP int int (hAPP int (fun int int) (minus_minus int) BOUND_VARIABLE_163710) Xa_1) (ti int BOUND_VARIABLE_163740)))))) )) (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 BOUND_VARIABLE_163740) Ta))) (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 (hAPP int int (hAPP int (fun int int) (plus_plus int) BOUND_VARIABLE_163740) D)) Ta))))) ) 23.83/23.79 ( (one_one int), zEven, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))), (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_163776 $$unsorted) (BOUND_VARIABLE_163777 $$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_163777))) (hBOOL (hAPP X_a bool _let_0 (hAPP nat X_a (hAPP X_a (fun nat X_a) (power_power X_a) BOUND_VARIABLE_163777) BOUND_VARIABLE_163776))))) ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), s1 ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), v ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), w ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), y ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), x ) 23.83/23.79 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.83/23.79 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.83/23.79 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.83/23.79 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.83/23.79 ( 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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.83/23.79 ( 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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.83/23.79 ( 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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.83/23.79 ( 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 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_6 ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_7 ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_16 ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_23 ) 23.83/23.79 ( int, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), skv_24 ) 23.83/23.79 ( complex, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))), ii ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (one_one real))) (let ((_let_2 (hAPP real real (hAPP real _let_0 (minus_minus real) _let_1) X))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) X) _let_1))) (= (hAPP real real ln _let_2) (hAPP real real (uminus_uminus real) (hAPP real real ln (hAPP real real (hAPP real _let_0 (plus_plus real) _let_1) (hAPP real real (hAPP real _let_0 (inverse_divide real) X) _let_2))))))))) ) 23.83/23.79 ( pi ) 23.83/23.79 ( (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (one_one real) ) 23.83/23.79 ( (zero_zero real) ) 23.83/23.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))))) ) 23.83/23.79 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls)))) ) 23.83/23.79 ( (hAPP real real (uminus_uminus real) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi)) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((A_1 $$unsorted) (N $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) A_1))) (not (forall ((R_1 $$unsorted)) (or (not (= A_1 (hAPP nat real (hAPP real (fun nat real) (power_power real) R_1) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) (zero_zero real)) R_1)))) ))) ) 23.83/23.79 ( pi, n ) 23.83/23.79 ( (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)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), tn ) 23.83/23.79 ) 23.83/23.79 (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 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) I_1) J_1))) (not (= K_4 (hAPP nat nat suc J_1)))) ))) ) 23.83/23.79 ( (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.79 ( (zero_zero nat), n ) 23.83/23.79 ( (zero_zero nat), tn ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((N $$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))) (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) (one_one nat))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))))) ) 23.83/23.79 ( (one_one nat) ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164018 $$unsorted) (BOUND_VARIABLE_164019 $$unsorted) (BOUND_VARIABLE_164020 $$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_164019) BOUND_VARIABLE_164020) (ti X_a BOUND_VARIABLE_164018))) (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (dvd_dvd X_a) BOUND_VARIABLE_164019) BOUND_VARIABLE_164018))) ) 23.83/23.79 ( int, pls, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, min, y, v ) 23.83/23.79 ( int, s, x, w ) 23.83/23.79 ( int, s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.83/23.79 ( int, m, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.79 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, v, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.83/23.79 ( int, y, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.83/23.79 ( int, sa, x, v ) 23.83/23.79 ( int, x, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.83/23.79 ( int, r, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.83/23.79 ( int, m1, y, w ) 23.83/23.79 ( int, skv_14, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.83/23.79 ( int, skv_20, sa, v ) 23.83/23.79 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.83/23.79 ( complex, ii, ii, ii ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted)) (or (not (semiring_1 X_a)) (= (one_one X_a) (hAPP nat X_a (semiring_1_of_nat X_a) (one_one nat)))) ) 23.83/23.79 ( rat ) 23.83/23.79 ( int ) 23.83/23.79 ( nat ) 23.83/23.79 ( real ) 23.83/23.79 ( complex ) 23.83/23.79 ( quickcheck_code_int ) 23.83/23.79 ( code_code_numeral ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X $$unsorted)) (= (hAPP int int (abs_abs int) X) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) (zero_zero int))) ) 23.83/23.79 ( v ) 23.83/23.79 ( w ) 23.83/23.79 ( skv_14 ) 23.83/23.79 ( skv_20 ) 23.83/23.79 ) 23.83/23.79 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164086 $$unsorted) (BOUND_VARIABLE_164087 $$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_164086) BOUND_VARIABLE_164087))) (= (hAPP X_a X_a (inverse_inverse X_a) BOUND_VARIABLE_164086) (ti X_a BOUND_VARIABLE_164087))) ) 23.83/23.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))), m ) 23.83/23.79 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.79 ( 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 ) 23.83/23.79 ( 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))), m1 ) 23.83/23.79 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (zero_zero nat))) ) 23.83/23.79 ( 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_21 ) 23.83/23.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) w) ) 23.83/23.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) v) ) 23.83/23.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_14) ) 23.83/23.79 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int (abs_abs int) skv_20) ) 23.83/23.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) v) ) 23.83/23.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.83/23.79 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (hAPP int (fun int int) (times_times int) sa) v) ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), m1 ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_3 ) 23.83/23.80 ( int, y, v ) 23.83/23.80 ( int, y, w ) 23.83/23.80 ( int, sa, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( int, sa, v ) 23.83/23.80 ( int, sa, w ) 23.83/23.80 ( int, x, v ) 23.83/23.80 ( int, x, w ) 23.83/23.80 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.80 ( int, r, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( int, r, v ) 23.83/23.80 ( int, r, w ) 23.83/23.80 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), v ) 23.83/23.80 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))), w ) 23.83/23.80 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), v ) 23.83/23.80 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))), w ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (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))) m1))) ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))) ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))) ) 23.83/23.80 ( int, skv_13, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( int, skv_19, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.83/23.80 ( real, (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.83/23.80 ( 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)))))) ) 23.83/23.80 ( 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 ) 23.83/23.80 ( complex, ii, ii ) 23.83/23.80 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP real complex (of_real complex) pi) ) 23.83/23.80 ( 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 ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164156 $$unsorted) (BOUND_VARIABLE_164157 $$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 (comm_monoid_add X_a)) (not (topological_space X_a)) (not (= (zero_zero X_a) (hAPP nat X_a BOUND_VARIABLE_164157 (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_164157) suc)) BOUND_VARIABLE_164156))) (hBOOL (hAPP X_a bool (hAPP _let_1 _let_2 _let_3 BOUND_VARIABLE_164157) BOUND_VARIABLE_164156))))))) ) 23.83/23.80 ( 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))))) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((D_1 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (fun int _let_1))) (let ((_let_3 (fun _let_0 _let_0))) (let ((_let_4 (fun int _let_0))) (let ((_let_5 (fun (product_prod int int) bool))) (let ((_let_6 (fun int _let_3))) (= (hAPP _let_5 _let_5 (collect (product_prod int int)) (hAPP _let_4 _let_5 (product_prod_case int int bool) (hAPP _let_4 _let_4 (hAPP _let_6 (fun _let_4 _let_4) (combs int _let_0 _let_0) (hAPP _let_2 _let_6 (hAPP (fun _let_1 _let_3) (fun _let_2 _let_6) (combb _let_1 _let_3 int) (combb bool bool int)) (hAPP _let_0 _let_2 (hAPP (fun bool _let_1) (fun _let_0 _let_2) (combb bool _let_1 int) fconj) (hAPP int _let_0 (ord_less_eq int) D_1)))) (ord_less int)))) (hAPP int _let_5 int_ge_less_than D_1))))))))) ) 23.83/23.80 ( (one_one int) ) 23.83/23.80 ( min ) 23.83/23.80 ( (zero_zero int) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_0 (inverse_inverse real))) (let ((_let_1 (hAPP nat (fun real real) root N))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) N))) (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (zero_zero real)) X))) (= (hAPP real real _let_0 (hAPP real real _let_1 X)) (hAPP real real _let_1 (hAPP real real _let_0 X)))))) ) 23.83/23.80 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164223 $$unsorted)) (let ((_let_0 (abs_abs X_a))) (let ((_let_1 (hAPP X_a X_a _let_0 BOUND_VARIABLE_164223))) (or (not (ordere142940540dd_abs X_a)) (= _let_1 (hAPP X_a X_a _let_0 _let_1))))) ) 23.83/23.80 ( int, v ) 23.83/23.80 ( int, w ) 23.83/23.80 ( int, skv_14 ) 23.83/23.80 ( int, skv_20 ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((N $$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) 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) M))))) ) 23.83/23.80 ( (one_one int), t ) 23.83/23.80 ( min, pls ) 23.83/23.80 ( min, min ) 23.83/23.80 ( (zero_zero int), pls ) 23.83/23.80 ( (zero_zero int), (one_one int) ) 23.83/23.80 ( (zero_zero int), min ) 23.83/23.80 ( (zero_zero int), s ) 23.83/23.80 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (zero_zero int), skv_4 ) 23.83/23.80 ( (zero_zero int), skv_5 ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (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)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.80 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_0 (fun int rat))) (= (hAPP int rat (hAPP int _let_0 fract (hAPP int int (uminus_uminus int) A_1)) B) (hAPP rat rat (uminus_uminus rat) (hAPP int rat (hAPP int _let_0 fract A_1) B)))) ) 23.83/23.80 ( pls, (one_one int) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164248 $$unsorted)) (or (not (number_ring X_a)) (= (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_164248) (hAPP int X_a (ring_1_of_int X_a) (hAPP int int (number_number_of int) BOUND_VARIABLE_164248)))) ) 23.83/23.80 ( int, pls ) 23.83/23.80 ( int, (hAPP int int bit1 pls) ) 23.83/23.80 ( int, min ) 23.83/23.80 ( int, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( int, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.80 ( nat, pls ) 23.83/23.80 ( nat, (hAPP int int bit1 pls) ) 23.83/23.80 ( nat, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( nat, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.80 ( real, pls ) 23.83/23.80 ( real, (hAPP int int bit1 pls) ) 23.83/23.80 ( real, min ) 23.83/23.80 ( real, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( real, (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.80 ( real, (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( real, (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.80 ( real, (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit0 (hAPP int int bit1 (hAPP int int bit1 (hAPP int int bit1 pls)))))))) ) 23.83/23.80 ( complex, min ) 23.83/23.80 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( quickcheck_code_int, pls ) 23.83/23.80 ( quickcheck_code_int, (hAPP int int bit1 pls) ) 23.83/23.80 ( quickcheck_code_int, (one_one int) ) 23.83/23.80 ( code_code_numeral, pls ) 23.83/23.80 ( code_code_numeral, (hAPP int int bit1 pls) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((A_3 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun real real))) (let ((_let_2 (fun nat nat))) (let ((_let_3 (fun (filter nat) bool))) (let ((_let_4 (fun real _let_3))) (let ((_let_5 (tendsto nat real))) (let ((_let_6 (fun nat bool))) (let ((_let_7 (fun nat _let_6))) (let ((_let_8 (fun _let_6 real))) (let ((_let_9 (fun nat _let_1))) (let ((_let_10 (hAPP _let_0 _let_0 (hAPP _let_9 (fun _let_0 _let_0) (combs nat real real) (hAPP _let_0 _let_9 (hAPP (fun real _let_1) (fun _let_0 _let_9) (combb real _let_1 nat) (times_times real)) (hAPP real _let_0 (power_power real) (hAPP int real (number_number_of real) min)))) A_3))) (or (not (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 A_3) (zero_zero real)) sequentially))) (not (hBOOL (hAPP _let_0 bool (monoseq real) A_3))) (hBOOL (hAPP (filter nat) bool (hAPP real _let_3 (hAPP _let_0 _let_4 _let_5 (hAPP _let_7 _let_0 (hAPP _let_8 (fun _let_7 _let_0) (combb _let_6 real nat) (hAPP _let_0 _let_8 (big_co1399186613setsum nat real) _let_10)) (hAPP _let_2 _let_7 (hAPP _let_7 (fun _let_2 _let_7) (combb nat _let_6 nat) (hAPP nat _let_7 (ord_atLeastLessThan nat) (zero_zero nat))) (hAPP nat _let_2 (times_times nat) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) (hAPP _let_0 real (suminf real) _let_10)) sequentially)))))))))))))) ) 23.83/23.80 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc)))) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164364 $$unsorted) (BOUND_VARIABLE_164365 $$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 (hBOOL (hAPP nat bool (even_odd_even nat) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_164365))))) (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_164364) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_164365))) _let_2)) (and (not (= (zero_zero nat) (hAPP int nat (number_number_of nat) BOUND_VARIABLE_164365))) (or (and _let_3 (= _let_2 (ti X_a BOUND_VARIABLE_164364))) (and (not _let_3) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164364) _let_2))))))))))) ) 23.83/23.80 ( int, s, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, s1, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, v, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, w, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, y, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, x, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, skv_6, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, skv_7, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, skv_16, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, skv_23, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( int, skv_24, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ( complex, ii, (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.80 ) 23.83/23.80 (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))) ) 23.83/23.80 ( int, int, rat ) 23.83/23.80 ( int, int, int ) 23.83/23.80 ( int, int, bool ) 23.83/23.80 ( int, int, real ) 23.83/23.80 ( int, int, (fun int bool) ) 23.83/23.80 ( int, int, (product_prod int int) ) 23.83/23.80 ( int, int, (fun bool bool) ) 23.83/23.80 ( int, int, (fun int (fun int bool)) ) 23.83/23.80 ( int, int, (fun (product_prod int int) bool) ) 23.83/23.80 ( int, int, (fun (fun int bool) bool) ) 23.83/23.80 ( int, int, (product_prod int (product_prod int int)) ) 23.83/23.80 ( int, int, (fun int (product_prod int (product_prod int int))) ) 23.83/23.80 ( int, int, (fun int (fun int (product_prod int (product_prod int int)))) ) 23.83/23.80 ( int, int, (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 23.83/23.80 ( int, int, (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 23.83/23.80 ( int, int, (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 23.83/23.80 ( int, int, (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 23.83/23.80 ( int, (fun int int), int ) 23.83/23.80 ( int, (fun int int), (fun int int) ) 23.83/23.80 ( int, (fun int int), bool ) 23.83/23.80 ( int, (fun int int), (fun int bool) ) 23.83/23.80 ( int, nat, int ) 23.83/23.80 ( int, real, bool ) 23.83/23.80 ( int, real, (fun int bool) ) 23.83/23.80 ( int, real, (fun int (fun bool bool)) ) 23.83/23.80 ( int, real, (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 23.83/23.80 ( int, real, (fun nat bool) ) 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int bool) ) 23.83/23.80 ( (fun int int), (fun int int), (fun int int) ) 23.83/23.80 ( (fun int int), (fun int bool), (fun int bool) ) 23.83/23.80 ( nat, int, int ) 23.83/23.80 ( nat, int, nat ) 23.83/23.80 ( nat, int, bool ) 23.83/23.80 ( nat, int, real ) 23.83/23.80 ( nat, int, (fun bool bool) ) 23.83/23.80 ( nat, nat, nat ) 23.83/23.80 ( nat, nat, bool ) 23.83/23.80 ( nat, nat, (product_prod int int) ) 23.83/23.80 ( nat, nat, (fun nat bool) ) 23.83/23.80 ( nat, nat, (product_prod nat nat) ) 23.83/23.80 ( nat, nat, (fun (product_prod nat nat) bool) ) 23.83/23.80 ( nat, real, real ) 23.83/23.80 ( nat, real, (product_prod real real) ) 23.83/23.80 ( nat, (fun nat real), bool ) 23.83/23.80 ( nat, (fun nat real), real ) 23.83/23.80 ( nat, (fun nat real), (fun real real) ) 23.83/23.80 ( nat, (fun nat nat), real ) 23.83/23.80 ( nat, (fun nat nat), (fun nat nat) ) 23.83/23.80 ( nat, (fun nat nat), (fun nat bool) ) 23.83/23.80 ( nat, (fun nat bool), bool ) 23.83/23.80 ( nat, (fun nat bool), (fun bool bool) ) 23.83/23.80 ( nat, code_code_numeral, nat ) 23.83/23.80 ( bool, int, bool ) 23.83/23.80 ( bool, nat, bool ) 23.83/23.80 ( bool, bool, bool ) 23.83/23.80 ( bool, real, bool ) 23.83/23.80 ( bool, (product_prod int int), bool ) 23.83/23.80 ( real, int, real ) 23.83/23.80 ( real, nat, real ) 23.83/23.80 ( real, real, bool ) 23.83/23.80 ( real, real, real ) 23.83/23.80 ( real, real, complex ) 23.83/23.80 ( real, real, (fun nat (product_prod real real)) ) 23.83/23.80 ( real, (fun real real), real ) 23.83/23.80 ( real, (fun real real), (fun real real) ) 23.83/23.80 ( real, (fun real real), (fun real bool) ) 23.83/23.80 ( real, (fun int bool), (fun int (fun int bool)) ) 23.83/23.80 ( real, (fun nat bool), (fun int (fun nat bool)) ) 23.83/23.80 ( real, (fun real bool), bool ) 23.83/23.80 ( real, (fun real bool), (fun bool bool) ) 23.83/23.80 ( real, (fun real (fun real bool)), (fun (fun nat real) (fun nat bool)) ) 23.83/23.80 ( real, (fun real (fun real bool)), (fun (fun int real) (fun int bool)) ) 23.83/23.80 ( real, (fun (product_prod real real) bool), (fun real (fun nat (product_prod real real))) ) 23.83/23.80 ( real, (fun real (fun int bool)), bool ) 23.83/23.80 ( real, (fun real (fun int (fun nat bool))), (fun int bool) ) 23.83/23.80 ( real, (fun real (fun int (fun nat bool))), (fun int (fun nat (fun bool bool))) ) 23.83/23.80 ( 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))) ) 23.83/23.80 ( real, (fun real (fun int (fun nat (fun bool bool)))), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))) ) 23.83/23.80 ( real, (fun int (fun nat real)), (fun int (fun nat bool)) ) 23.83/23.80 ( real, (fun real (fun (fun nat real) (fun nat bool))), (fun (fun int (fun nat real)) (fun int (fun nat bool))) ) 23.83/23.80 ( real, (fun real (fun int (fun int bool))), (fun int bool) ) 23.83/23.80 ( real, (fun real (fun int (fun int bool))), (fun int (fun int (fun bool bool))) ) 23.83/23.80 ( 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))) ) 23.83/23.80 ( real, (fun real (fun int (fun int (fun bool bool)))), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))) ) 23.83/23.80 ( real, (fun int (fun int real)), (fun int (fun int bool)) ) 23.83/23.80 ( real, (fun real (fun (fun int real) (fun int bool))), (fun (fun int (fun int real)) (fun int (fun int bool))) ) 23.83/23.80 ( (fun nat real), int, (fun nat real) ) 23.83/23.80 ( (fun nat real), real, (fun nat bool) ) 23.83/23.80 ( (fun nat real), (fun real real), (fun nat real) ) 23.83/23.80 ( (fun nat real), (fun real bool), (fun nat bool) ) 23.83/23.80 ( (filter nat), real, bool ) 23.83/23.80 ( (fun int bool), int, bool ) 23.83/23.80 ( (fun int bool), int, (fun int bool) ) 23.83/23.80 ( (fun int bool), real, (fun int (fun int bool)) ) 23.83/23.80 ( (fun int bool), (fun int (fun bool bool)), (fun int bool) ) 23.83/23.80 ( (fun int bool), (let ((_let_0 (fun int bool))) (fun int (fun _let_0 _let_0))), (fun int (fun int bool)) ) 23.83/23.80 ( (product_prod int int), int, int ) 23.83/23.80 ( (product_prod int int), int, bool ) 23.83/23.80 ( (product_prod int int), int, (product_prod int int) ) 23.83/23.80 ( (product_prod int int), (product_prod int int), int ) 23.83/23.80 ( (product_prod int int), (product_prod int int), bool ) 23.83/23.80 ( (product_prod int int), (product_prod int int), (fun int bool) ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) int), int ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) int), (fun int int) ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) int), bool ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) int), (fun int bool) ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) int), (fun (product_prod int int) int) ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) bool), bool ) 23.83/23.80 ( (product_prod int int), (fun (product_prod int int) bool), (fun bool bool) ) 23.83/23.80 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 bool))), (fun (product_prod int int) bool) ) 23.83/23.80 ( (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)) ) 23.83/23.80 ( (product_prod int int), (let ((_let_0 (product_prod int int))) (fun _let_0 (fun _let_0 int))), (fun (product_prod int int) bool) ) 23.83/23.80 ( (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)) ) 23.83/23.80 ( (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))) ) 23.83/23.80 ( (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)) ) 23.83/23.80 ( (fun (product_prod int int) int), (fun int int), (fun (product_prod int int) int) ) 23.83/23.80 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) int) ) 23.83/23.80 ( (fun (product_prod int int) int), (product_prod int int), (fun (product_prod int int) bool) ) 23.83/23.80 ( (fun (product_prod int int) int), (fun (product_prod int int) (fun int bool)), (fun (product_prod int int) bool) ) 23.83/23.80 ( (fun nat bool), int, (fun nat bool) ) 23.83/23.80 ( (fun nat bool), real, (fun int (fun nat bool)) ) 23.83/23.80 ( (fun nat bool), (fun nat (fun bool bool)), (fun nat bool) ) 23.83/23.80 ( (fun nat bool), (let ((_let_0 (fun nat bool))) (fun int (fun _let_0 _let_0))), (fun int (fun nat bool)) ) 23.83/23.80 ( (fun (product_prod int int) bool), (product_prod int int), (fun (product_prod int int) bool) ) 23.83/23.80 ( (fun (product_prod int int) bool), (fun bool bool), (fun (product_prod int int) bool) ) 23.83/23.80 ( quickcheck_code_int, quickcheck_code_int, (product_prod quickcheck_code_int quickcheck_code_int) ) 23.83/23.80 ( code_code_numeral, code_code_numeral, (product_prod code_code_numeral code_code_numeral) ) 23.83/23.80 ( (filter real), real, bool ) 23.83/23.80 ( (product_prod nat nat), nat, bool ) 23.83/23.80 ( (product_prod nat nat), (product_prod nat nat), bool ) 23.83/23.80 ( (fun int real), int, (fun int real) ) 23.83/23.80 ( (fun int real), real, (fun int bool) ) 23.83/23.80 ( (fun int real), (fun real real), (fun int real) ) 23.83/23.80 ( (fun int real), (fun real bool), (fun int bool) ) 23.83/23.80 ( (fun int (fun nat real)), real, (fun int (fun nat bool)) ) 23.83/23.80 ( (fun int (fun nat real)), (fun (fun nat real) (fun nat bool)), (fun int (fun nat bool)) ) 23.83/23.80 ( (fun int (fun int real)), real, (fun int (fun int bool)) ) 23.83/23.80 ( (fun int (fun int real)), (fun (fun int real) (fun int bool)), (fun int (fun int bool)) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((Z_1 $$unsorted)) (or (not (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Z_1) (zero_zero int)))) (= (zero_zero nat) (hAPP int nat nat_1 Z_1))) ) 23.83/23.80 ( (one_one int) ) 23.83/23.80 ( min ) 23.83/23.80 ( (zero_zero int) ) 23.83/23.80 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( t ) 23.83/23.80 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) w)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) v)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_14)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls)))) (hAPP int int (abs_abs int) skv_20)) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164499 $$unsorted) (BOUND_VARIABLE_164500 $$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_164499) BOUND_VARIABLE_164500))) (= (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_164500) BOUND_VARIABLE_164499)) BOUND_VARIABLE_164499) (ti X_a BOUND_VARIABLE_164500)))) ) 23.83/23.80 ( 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))), (hAPP 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)) ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((V_2 $$unsorted) (V $$unsorted)) (let ((_let_0 (number_number_of nat))) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less int) V) pls)) (= (hAPP int nat _let_0 (hAPP int int (hAPP int (fun int int) (times_times int) V) V_2)) (hAPP nat nat (hAPP nat (fun nat nat) (times_times nat) (hAPP int nat _let_0 V)) (hAPP int nat _let_0 V_2))))) ) 23.83/23.80 ( m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.83/23.80 ( 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))) ) 23.83/23.80 ( v, y ) 23.83/23.80 ( v, sa ) 23.83/23.80 ( v, x ) 23.83/23.80 ( v, r ) 23.83/23.80 ( v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.80 ( v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.80 ( w, y ) 23.83/23.80 ( w, sa ) 23.83/23.80 ( w, x ) 23.83/23.80 ( w, r ) 23.83/23.80 ( w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.80 ( w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.80 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.83/23.80 ( (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.80 ( m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( skv_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))) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164566 $$unsorted) (BOUND_VARIABLE_164575 $$unsorted)) (let ((_let_0 (fun int bool))) (let ((_let_1 (ord_less int))) (let ((_let_2 (zero_zero int))) (let ((_let_3 (ring_1_of_int X_a))) (let ((_let_4 (semiring_1_of_nat X_a))) (or (not (ring_1 X_a)) (and (or (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 BOUND_VARIABLE_164566) _let_2)) (= (hAPP nat X_a _let_4 (hAPP int nat nat_1 BOUND_VARIABLE_164566)) (hAPP int X_a _let_3 BOUND_VARIABLE_164566))) (or (not (hBOOL (hAPP int bool (hAPP int _let_0 _let_1 BOUND_VARIABLE_164575) _let_2))) (= (hAPP int X_a _let_3 BOUND_VARIABLE_164575) (hAPP X_a X_a (uminus_uminus X_a) (hAPP nat X_a _let_4 (hAPP int nat nat_1 (hAPP int int (uminus_uminus int) BOUND_VARIABLE_164575))))))))))))) ) 23.83/23.80 ( rat, (zero_zero int), (zero_zero int) ) 23.83/23.80 ( int, (one_one int), (one_one int) ) 23.83/23.80 ( real, min, min ) 23.83/23.80 ( complex, t, t ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164618 $$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_164618) BOUND_VARIABLE_164618)))) ) 23.83/23.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( 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))) ) 23.83/23.80 ( int, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.80 ( int, y ) 23.83/23.80 ( int, sa ) 23.83/23.80 ( int, x ) 23.83/23.80 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.83/23.80 ( int, r ) 23.83/23.80 ( int, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.80 ( int, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.80 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( int, skv_13 ) 23.83/23.80 ( int, skv_19 ) 23.83/23.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( real, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( 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))))) ) 23.83/23.80 ( complex, ii ) 23.83/23.80 ( complex, (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( 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)) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164707 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (member X_a))) (let ((_let_3 (field_char_0_Rats X_a))) (or (not (field_char_0 X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 BOUND_VARIABLE_164707) _let_3))) (hBOOL (hAPP _let_0 bool (hAPP X_a _let_1 _let_2 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_164707)) _let_3))))))) ) 23.83/23.80 ( int, pls ) 23.83/23.80 ( int, (one_one int) ) 23.83/23.80 ( int, min ) 23.83/23.80 ( real, (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.80 ( real, (one_one real) ) 23.83/23.80 ( real, (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) pi) ) 23.83/23.80 ( complex, ii ) 23.83/23.80 ( complex, (one_one complex) ) 23.83/23.80 ) 23.83/23.80 (instantiation (forall ((Z_1 $$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))))))) ) 23.83/23.80 ( (zero_zero complex) ) 23.83/23.80 ( ii ) 23.83/23.80 ( (one_one complex) ) 23.83/23.80 ( (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (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)) ) 23.83/23.80 ) 23.83/23.80 (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)))) ) 23.83/23.80 ( rat ) 23.83/23.80 ( int ) 23.83/23.80 ( (fun int int) ) 23.83/23.80 ( nat ) 23.83/23.80 ( bool ) 23.83/23.80 ( real ) 23.83/23.80 ( (fun nat real) ) 23.83/23.80 ( (fun real real) ) 23.83/23.80 ( (fun nat nat) ) 23.83/23.80 ( (fun int rat) ) 23.83/23.80 ( complex ) 23.83/23.80 ( (fun int bool) ) 23.83/23.80 ( (product_prod int int) ) 23.83/23.80 ( (fun (product_prod int int) int) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (fun _let_0 _let_0)) ) 23.83/23.80 ( (fun nat int) ) 23.83/23.80 ( (fun bool bool) ) 23.83/23.80 ( (fun int (fun bool bool)) ) 23.83/23.80 ( (let ((_let_0 (fun int bool))) (fun _let_0 _let_0)) ) 23.83/23.80 ( (fun int (fun int bool)) ) 23.83/23.80 ( (fun nat bool) ) 23.83/23.80 ( (fun (product_prod int int) bool) ) 23.83/23.80 ( (fun int (fun (product_prod int int) bool)) ) 23.83/23.80 ( quickcheck_code_int ) 23.83/23.80 ( (fun (fun int bool) bool) ) 23.83/23.80 ( (let ((_let_0 (fun nat real))) (fun _let_0 _let_0)) ) 23.83/23.80 ( code_code_numeral ) 23.83/23.80 ( (product_prod int (product_prod int int)) ) 23.83/23.80 ( (fun int (product_prod int (product_prod int int))) ) 23.83/23.80 ( (fun int (fun int (product_prod int (product_prod int int)))) ) 23.83/23.80 ( (fun int (fun int (fun int (product_prod int (product_prod int int))))) ) 23.83/23.80 ( (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))) ) 23.83/23.80 ( (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))) ) 23.83/23.80 ( (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int)))))))) ) 23.83/23.80 ( (fun int (fun int (fun int (fun int (fun int (fun int (fun int (product_prod int (product_prod int int))))))))) ) 23.83/23.80 ( (fun nat (fun bool bool)) ) 23.83/23.80 ( (let ((_let_0 (fun nat bool))) (fun _let_0 _let_0)) ) 23.83/23.80 ( (fun int (product_prod int int)) ) 23.83/23.80 ( (let ((_let_0 (product_prod int int))) (fun _let_0 _let_0)) ) 23.83/23.80 ( (fun int (fun (fun int bool) bool)) ) 23.83/23.80 ( (fun (fun int int) (fun int bool)) ) 23.83/23.80 ( (list int) ) 23.83/23.80 ( (fun int (fun int (fun int bool))) ) 23.83/23.80 ( (fun int real) ) 23.83/23.80 ( (let ((_let_0 (fun int real))) (fun _let_0 _let_0)) ) 23.83/23.80 ) 23.83/23.80 (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 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)))) (hAPP nat int _let_0 _let_1))))) ) 23.83/23.80 ( s, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( s1, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( v, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( w, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( y, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( x, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.80 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.81 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.81 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.81 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.81 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.81 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_6, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_7, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_16, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_23, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_24, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (hAPP real (fun real bool) (ord_less real) (one_one real)))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool _let_0 (hAPP real real (hAPP nat (fun real real) root Na) Ya))) (hBOOL (hAPP real bool _let_0 Ya))))) ) 23.83/23.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (one_one real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (zero_zero real), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (hAPP int real (number_number_of real) (hAPP int int bit1 (hAPP int int bit1 pls))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((R_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_0 (fun real real))) (let ((_let_1 (inverse_divide real))) (let ((_let_2 (hAPP real _let_0 (times_times real) R_3))) (= (hAPP real real (hAPP real _let_0 _let_1 (hAPP real real _let_2 A_1)) (hAPP real real _let_2 R_3)) (hAPP real real (hAPP real _let_0 _let_1 A_1) R_3))))) ) 23.83/23.84 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))), pi ) 23.83/23.84 ( (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 bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))) ) 23.83/23.84 ( (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)))))) ) 23.83/23.84 ( (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 ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((Xa $$unsorted) (Ya $$unsorted) (Na $$unsorted)) (let ((_let_0 (fun real bool))) (let ((_let_1 (ord_less real))) (let ((_let_2 (hAPP nat (fun real real) root Na))) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less nat) (zero_zero nat)) Na))) (= (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 Xa) Ya)) (hBOOL (hAPP real bool (hAPP real _let_0 _let_1 (hAPP real real _let_2 Xa)) (hAPP real real _let_2 Ya)))))))) ) 23.83/23.84 ( (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))) ) 23.83/23.84 ( (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))) ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((X $$unsorted)) (= (hAPP real real (uminus_uminus real) (hAPP complex real im X)) (hAPP complex real im (hAPP complex complex (uminus_uminus complex) X))) ) 23.83/23.84 ( ii ) 23.83/23.84 ( (one_one complex) ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((Xa $$unsorted) (Na $$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)) Na))) (= (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 (hAPP nat int (hAPP int (fun nat int) (power_power int) Xa) Na)) zOdd)) (hBOOL (hAPP _let_0 bool (hAPP int _let_1 _let_2 Xa) zOdd))))))) ) 23.83/23.84 ( s, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( s1, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( v, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( w, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( y, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( x, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_6, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_7, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_16, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_23, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ( skv_24, (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_0 (hAPP nat real (real_1 nat) A_1))) (or (not (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) _let_0) X))) (= (hAPP nat nat (hAPP nat (fun nat nat) (minus_minus nat) (hAPP real nat natceiling X)) A_1) (hAPP real nat natceiling (hAPP real real (hAPP real (fun real real) (minus_minus real) X) _let_0))))) ) 23.83/23.84 ( (zero_zero nat), pi ) 23.83/23.84 ( (zero_zero nat), (hAPP real real (hAPP real (fun real real) (inverse_divide real) pi) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.84 ( (zero_zero nat), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.84 ( (zero_zero nat), skv_10 ) 23.83/23.84 ( (zero_zero nat), skv_11 ) 23.83/23.84 ( (zero_zero nat), skv_15 ) 23.83/23.84 ( (zero_zero nat), skv_18 ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164865 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (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_0 bool (summable 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)) (hAPP _let_2 _let_2 (hAPP _let_4 (fun _let_2 _let_2) (combs nat X_a X_a) (hAPP _let_0 _let_4 (hAPP (fun real _let_3) (fun _let_0 _let_4) (combb real _let_3 nat) (scaleR_scaleR X_a)) (hAPP _let_0 _let_0 (hAPP (fun real real) (fun _let_0 _let_0) (combb real real nat) (inverse_inverse real)) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) (fact_fact nat))))) (hAPP X_a _let_2 (power_power X_a) BOUND_VARIABLE_164865))))))))))) ) 23.83/23.84 ( int, s ) 23.83/23.84 ( int, s1 ) 23.83/23.84 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.84 ( int, v ) 23.83/23.84 ( int, w ) 23.83/23.84 ( int, y ) 23.83/23.84 ( int, x ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w)))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v)))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w)))))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v)))))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))))))))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)))) ) 23.83/23.84 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) ) 23.83/23.84 ( int, skv_6 ) 23.83/23.84 ( int, skv_7 ) 23.83/23.84 ( int, skv_16 ) 23.83/23.84 ( int, skv_23 ) 23.83/23.84 ( int, skv_24 ) 23.83/23.84 ( real, (hAPP int real (number_number_of real) min) ) 23.83/23.84 ( 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)))) ) 23.83/23.84 ( complex, ii ) 23.83/23.84 ) 23.83/23.84 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_164903 $$unsorted) (BOUND_VARIABLE_164904 $$unsorted) (BOUND_VARIABLE_164905 $$unsorted) (BOUND_VARIABLE_164906 $$unsorted)) (let ((_let_0 (fun X_a bool))) (let ((_let_1 (ord_less X_a))) (let ((_let_2 (fun X_a _let_0))) (let ((_let_3 (ord_atLeastLessThan X_a))) (or (not (linorder X_a)) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164905) BOUND_VARIABLE_164906))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_164903) BOUND_VARIABLE_164904))) (= (= (hAPP X_a _let_0 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_164905) BOUND_VARIABLE_164906) (hAPP X_a _let_0 (hAPP X_a _let_2 _let_3 BOUND_VARIABLE_164903) BOUND_VARIABLE_164904)) (and (= (ti X_a BOUND_VARIABLE_164906) (ti X_a BOUND_VARIABLE_164904)) (= (ti X_a BOUND_VARIABLE_164903) (ti X_a BOUND_VARIABLE_164905))))))))) ) 23.83/23.84 ( int, (one_one int), t, (one_one int), t ) 23.83/23.84 ( int, (one_one int), t, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.84 ( int, min, min, min, min ) 23.83/23.84 ( int, min, min, min, (zero_zero int) ) 23.83/23.84 ( int, min, (zero_zero int), min, min ) 23.83/23.84 ( int, (zero_zero int), pls, (zero_zero int), pls ) 23.83/23.84 ( int, (zero_zero int), pls, (zero_zero int), min ) 23.83/23.84 ( int, (zero_zero int), (one_one int), (zero_zero int), (one_one int) ) 23.83/23.84 ( int, (zero_zero int), (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))) ) 23.83/23.84 ( int, (zero_zero int), min, (zero_zero int), pls ) 23.83/23.84 ( 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))), (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))) ) 23.83/23.84 ( 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))), (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.84 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (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))) ) 23.83/23.85 ( 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))), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( 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))), (zero_zero int), (one_one int) ) 23.83/23.85 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (one_one int), t ) 23.83/23.85 ( 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))), 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))) ) 23.83/23.85 ( 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))), skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( nat, (zero_zero nat), n, (zero_zero nat), n ) 23.83/23.85 ( nat, (zero_zero nat), n, (zero_zero nat), tn ) 23.83/23.85 ( nat, (zero_zero nat), tn, (zero_zero nat), n ) 23.83/23.85 ( real, pi, (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) ) 23.83/23.85 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (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)))) ) 23.83/23.85 ( 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 pls)))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.85 ( 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))), pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (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) ) 23.83/23.85 ( real, (zero_zero real), pi, (zero_zero real), pi ) 23.83/23.85 ( real, (zero_zero real), pi, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( 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)))), (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 ) 23.83/23.85 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi ) 23.83/23.85 ( real, (zero_zero real), skv_2, (zero_zero real), skv_2 ) 23.83/23.85 ( real, (zero_zero real), skv_2, (zero_zero real), skv_9 ) 23.83/23.85 ( real, (zero_zero real), skv_9, (zero_zero real), skv_2 ) 23.83/23.85 ( real, (zero_zero real), skv_12, (zero_zero real), skv_12 ) 23.83/23.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), pi, (zero_zero real) ) 23.83/23.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real), (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.83/23.85 ( 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), (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( 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), (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) ) 23.83/23.85 ( 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, (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)))) ) 23.83/23.85 ( 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, (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 ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((A_3 $$unsorted) (B_2 $$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_2))) (= (hBOOL (hAPP int bool (hAPP int _let_0 (ord_less_eq int) A_3) _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_3) B_2)) (zero_zero rat))))))) ) 23.83/23.85 ( (one_one int), (one_one int) ) 23.83/23.85 ( (zero_zero int), (one_one int) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_a $$unsorted)) (let ((_let_0 (at X_a))) (or (not (topological_space X_a)) (= _let_0 (ti (fun X_a (filter X_a)) _let_0)))) ) 23.83/23.85 ( nat ) 23.83/23.85 ( real ) 23.83/23.85 ( complex ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165040 $$unsorted) (BOUND_VARIABLE_165041 $$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_165040)) BOUND_VARIABLE_165041)) (and (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165040) BOUND_VARIABLE_165041)) (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 (hAPP X_a X_a (uminus_uminus X_a) BOUND_VARIABLE_165040)) BOUND_VARIABLE_165041))))))) ) 23.83/23.85 ( int, pls, pls ) 23.83/23.85 ( int, pls, (one_one int) ) 23.83/23.85 ( int, pls, min ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( int, pls, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( int, (one_one int), min ) 23.83/23.85 ( int, (one_one int), (zero_zero int) ) 23.83/23.85 ( int, (one_one int), t ) 23.83/23.85 ( int, min, min ) 23.83/23.85 ( int, min, (zero_zero int) ) 23.83/23.85 ( int, (zero_zero int), pls ) 23.83/23.85 ( int, (zero_zero int), (one_one int) ) 23.83/23.85 ( int, (zero_zero int), min ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( int, (zero_zero int), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( int, skv_5, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( nat, (zero_zero nat), (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.85 ( nat, (zero_zero nat), n ) 23.83/23.85 ( nat, (zero_zero nat), tn ) 23.83/23.85 ( real, pi, (zero_zero real) ) 23.83/23.85 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( 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))) ) 23.83/23.85 ( 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) ) 23.83/23.85 ( real, (one_one real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( real, (zero_zero real), pi ) 23.83/23.85 ( 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)))) ) 23.83/23.85 ( real, (zero_zero real), (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( real, (zero_zero real), skv_2 ) 23.83/23.85 ( real, (zero_zero real), skv_9 ) 23.83/23.85 ( real, (zero_zero real), skv_12 ) 23.83/23.85 ( 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 ) 23.83/23.85 ( real, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.83/23.85 ( 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) ) 23.83/23.85 ( 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 ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((K_4 $$unsorted)) (let ((_let_0 (product_prod int int))) (= (hAPP rat _let_0 quotient_of (hAPP int rat (number_number_of rat) K_4)) (hAPP int _let_0 (hAPP int (fun int _let_0) (product_Pair int int) (hAPP int int (number_number_of int) K_4)) (one_one int)))) ) 23.83/23.85 ( pls ) 23.83/23.85 ( (hAPP int int bit1 pls) ) 23.83/23.85 ( min ) 23.83/23.85 ( (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.85 ( (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.85 ( (hAPP int int bit1 (hAPP int int bit1 pls)) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((B $$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 (minus_minus int) B) (one_one int)) (hAPP int int (hAPP int _let_0 (div_mod int) (hAPP int int (number_number_of int) min)) B)))) ) 23.83/23.85 ( pls ) 23.83/23.85 ( (one_one int) ) 23.83/23.85 ( min ) 23.83/23.85 ( (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)))) ) 23.83/23.85 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.85 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( y ) 23.83/23.85 ( x ) 23.83/23.85 ( (hAPP int int (hAPP int (fun int int) (times_times int) x) w) ) 23.83/23.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) w)))) ) 23.83/23.85 ( (hAPP int int (hAPP int (fun int int) (times_times int) r) w) ) 23.83/23.85 ( (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) w)))) ) 23.83/23.85 ( (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))) m1))) ) 23.83/23.85 ( (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int int bit0 (hAPP int int bit1 pls)))) (let ((_let_3 (times_times int))) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 _let_2))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) (hAPP int nat (number_number_of nat) _let_2))))))) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165185 $$unsorted) (BOUND_VARIABLE_165194 $$unsorted)) (let ((_let_0 (number_number_of nat))) (let ((_let_1 (number_number_of int))) (let ((_let_2 (semiring_1_of_nat X_a))) (or (not (number_ring X_a)) (and (or (not (hBOOL (hAPP int bool nat_neg (hAPP int int _let_1 BOUND_VARIABLE_165185)))) (= (zero_zero X_a) (hAPP nat X_a _let_2 (hAPP int nat _let_0 BOUND_VARIABLE_165185)))) (or (hBOOL (hAPP int bool nat_neg (hAPP int int _let_1 BOUND_VARIABLE_165194))) (= (hAPP nat X_a _let_2 (hAPP int nat _let_0 BOUND_VARIABLE_165194)) (hAPP int X_a (number_number_of X_a) BOUND_VARIABLE_165194)))))))) ) 23.83/23.85 ( rat, (hAPP int int bit1 pls), (hAPP int int bit1 pls) ) 23.83/23.85 ( int, min, min ) 23.83/23.85 ( real, (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))), (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.85 ( complex, (hAPP int int bit0 (hAPP int int bit1 pls)), (hAPP int int bit0 (hAPP int int bit1 pls)) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (BOUND_VARIABLE_165235 $$unsorted) (BOUND_VARIABLE_165236 $$unsorted) (BOUND_VARIABLE_165237 $$unsorted) (BOUND_VARIABLE_165238 $$unsorted) (BOUND_VARIABLE_165239 $$unsorted)) (let ((_let_0 (filter X_a))) (let ((_let_1 (fun _let_0 bool))) (let ((_let_2 (hAPP X_a _let_0 (at X_a) BOUND_VARIABLE_165239))) (or (not (real_normed_vector X_b)) (not (real_normed_vector X_c)) (not (topological_space X_a)) (not (hBOOL (hAPP _let_0 bool (hAPP X_b _let_1 (hAPP (fun X_a X_b) (fun X_b _let_1) (tendsto X_a X_b) BOUND_VARIABLE_165237) BOUND_VARIABLE_165238) _let_2))) (not (forall ((X_1 $$unsorted)) (or (= (ti X_a X_1) (ti X_a BOUND_VARIABLE_165239)) (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_165235 X_1)) BOUND_VARIABLE_165236))) (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_165237 X_1)) BOUND_VARIABLE_165238))))) )) (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_165235) BOUND_VARIABLE_165236) _let_2)))))) ) 23.83/23.85 ( 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)))) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((Y $$unsorted) (X $$unsorted)) (or (hBOOL (hAPP int bool (hAPP int (fun int bool) (ord_less_eq int) Y) X)) (= (zero_zero int) (hAPP int int (hAPP int (fun int int) nat_tsub X) Y))) ) 23.83/23.85 ( (one_one int), t ) 23.83/23.85 ( min, pls ) 23.83/23.85 ( min, min ) 23.83/23.85 ( (zero_zero int), pls ) 23.83/23.85 ( (zero_zero int), (one_one int) ) 23.83/23.85 ( (zero_zero int), min ) 23.83/23.85 ( (zero_zero int), s ) 23.83/23.85 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.85 ( (zero_zero int), (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.85 ( (zero_zero int), skv_4 ) 23.83/23.85 ( (zero_zero int), skv_5 ) 23.83/23.85 ( (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)))) (hAPP int int (abs_abs int) w)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( (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)))) (hAPP int int (abs_abs int) v)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( (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)))) (hAPP int int (abs_abs int) skv_14)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ( (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)))) (hAPP int int (abs_abs int) skv_20)), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165319 $$unsorted) (BOUND_VARIABLE_165320 $$unsorted) (BOUND_VARIABLE_165321 $$unsorted)) (let ((_let_0 (hAPP X_a (fun X_a X_a) (plus_plus X_a) BOUND_VARIABLE_165319))) (or (not (cancel146912293up_add X_a)) (not (= (hAPP X_a X_a _let_0 BOUND_VARIABLE_165320) (hAPP X_a X_a _let_0 BOUND_VARIABLE_165321))) (= (ti X_a BOUND_VARIABLE_165320) (ti X_a BOUND_VARIABLE_165321)))) ) 23.83/23.85 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (hAPP nat int (semiring_1_of_nat int) n) ) 23.83/23.85 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.83/23.85 ( int, (one_one int), (hAPP nat int (semiring_1_of_nat int) n), (hAPP nat int (semiring_1_of_nat int) n) ) 23.83/23.85 ( 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), (one_one int) ) 23.83/23.85 ( 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), (one_one int) ) 23.83/23.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w, w ) 23.83/23.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (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) y) (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) y) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) x) v), (hAPP int int (hAPP int (fun int int) (times_times int) y) w), (hAPP int int (hAPP int (fun int int) (times_times int) y) w) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 x) v)) (hAPP int int (hAPP int _let_0 _let_1 y) w))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 x) w)) (hAPP int int (hAPP int _let_0 _let_1 y) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), v, v ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v)) v)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w)) w)))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) v)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) w))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (let ((_let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) _let_3)) v)) w)) (hAPP int int (hAPP int _let_0 _let_2 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 sa) _let_3)) w)) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))))) ) 23.83/23.85 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (times_times int) sa) w) ) 23.83/23.85 ( 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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 r) v)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), (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) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 v) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 w) _let_2)))) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 _let_1 r) v)) (hAPP int int (hAPP int _let_0 _let_1 sa) w)))), m1, m1 ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.85 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_2 (times_times int))) (let ((_let_3 (fun nat int))) (let ((_let_4 (power_power int))) (hAPP int int (hAPP int _let_0 _let_2 (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_1)) (hAPP nat int (hAPP int _let_3 _let_4 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_2 r) w)) (hAPP int int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))) ) 23.83/23.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( int, (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( nat, (one_one nat), (one_one nat), (one_one nat) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X_2 $$unsorted)) (let ((_let_0 (fun nat real))) (let ((_let_1 (fun (filter nat) bool))) (or (not (forall ((R_1 $$unsorted)) (not (forall ((N_2 $$unsorted)) (not (forall ((N_1 $$unsorted)) (or (not (hBOOL (hAPP nat bool (hAPP nat (fun nat bool) (ord_less_eq nat) N_2) N_1))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less real) R_1) (hAPP nat real X_2 N_1)))) )) )) )) (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_2)) (zero_zero real)) sequentially))))) ) 23.83/23.85 ( (let ((_let_0 (fun nat real))) (let ((_let_1 (fun nat nat))) (hAPP _let_1 _let_0 (hAPP _let_0 (fun _let_1 _let_0) (combb nat real nat) (real_1 nat)) suc))) ) 23.83/23.85 ) 23.83/23.85 (instantiation (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_2 (div_mod int))) (or (not (= (hAPP int int (hAPP int _let_0 _let_2 X) M) (hAPP int int (hAPP int _let_0 _let_2 Y) M))) (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong X) Y) M)))))) ) 23.83/23.85 ( (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)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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)))) ) 23.83/23.85 ( (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)))), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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) ) 23.83/23.85 ( 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 ) 23.83/23.85 ( 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 ) 23.83/23.85 ( 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_5 ) 23.83/23.85 ( (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) ) 23.83/23.85 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_16) (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) ) 23.83/23.85 ) 23.83/23.85 (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 Z_1) W) (hAPP int int (hAPP int _let_0 _let_1 W) Z_1)))) ) 23.83/23.85 ( (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)))) ) 23.83/23.85 ( (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) ) 23.83/23.85 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)) ) 23.83/23.85 ( (one_one int), (hAPP nat int (semiring_1_of_nat int) n) ) 23.83/23.85 ( (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)))), (one_one int) ) 23.83/23.85 ( (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) ) 23.83/23.85 ( (hAPP nat int (semiring_1_of_nat int) (zero_zero nat)), (one_one int) ) 23.83/23.85 ( (hAPP nat int (semiring_1_of_nat int) n), (one_one int) ) 23.83/23.85 ( v, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) r) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.83/23.85 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) v) (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) w) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( w, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) ) 23.83/23.85 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) w) (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) v) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.85 ( (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (let ((_let_2 (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) v))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) w)))))) ) 23.83/23.85 ( (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (times_times int) sa) (hAPP int int (hAPP int _let_0 (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))), w ) 23.83/23.85 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) x) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))), (hAPP 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(hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 r) w))) (hAPP int int _let_2 (hAPP int int (hAPP int _let_0 _let_1 sa) v)))) (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 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 r) v))) (hAPP int int _let_6 (hAPP int int (hAPP int _let_0 _let_3 sa) w)))) (hAPP int int (hAPP int 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pls))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))))) ) 23.83/23.86 ( (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP 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int (hAPP int _let_0 _let_2 sa) v))) _let_1))))))), (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (hAPP int int (hAPP int _let_0 _let_3 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 r) v)) (hAPP int int (hAPP int _let_0 _let_3 sa) w))) m1)) _let_2)))))))) ) 23.83/23.86 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_6) (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_7) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_7) (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_6) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_23) (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_24) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( (hAPP nat int (hAPP int (fun nat int) (power_power int) skv_24) (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_23) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_a $$unsorted) (BOUND_VARIABLE_165408 $$unsorted) (BOUND_VARIABLE_165409 $$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_165409))) (not (hBOOL (hAPP X_a bool (hAPP X_a _let_0 _let_1 BOUND_VARIABLE_165408) _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_165409) BOUND_VARIABLE_165408)) _let_2)))))) ) 23.83/23.86 ( int, m, (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), sa ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), r ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_13 ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), skv_19 ) 23.83/23.86 ( 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))) ) 23.83/23.86 ( int, v, y ) 23.83/23.86 ( int, v, sa ) 23.83/23.86 ( int, v, x ) 23.83/23.86 ( int, v, r ) 23.83/23.86 ( int, v, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.86 ( int, v, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.86 ( int, w, y ) 23.83/23.86 ( int, w, sa ) 23.83/23.86 ( int, w, x ) 23.83/23.86 ( int, w, r ) 23.83/23.86 ( int, w, (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 (times_times int) r) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) v))) ) 23.83/23.86 ( int, w, (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 (times_times int) sa) (hAPP int int (hAPP int _let_0 _let_1 (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)))) w))) ) 23.83/23.86 ( int, (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 v) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 w) _let_0))))), (let ((_let_0 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_1 (fun nat int))) (let ((_let_2 (power_power int))) (hAPP int int (hAPP int (fun int int) (plus_plus int) (hAPP nat int (hAPP int _let_1 _let_2 x) _let_0)) (hAPP nat int (hAPP int _let_1 _let_2 y) _let_0))))) ) 23.83/23.86 ( int, (hAPP int int (abs_abs int) w), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) r) w), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (times_times int) sa) v), (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( int, m1, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) ) 23.83/23.86 ( int, m1, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( 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))) m1))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_2 r) v)) (hAPP int int (hAPP int _let_0 _let_2 sa) w))) m1)) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (times_times int))) (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int (hAPP int _let_0 _let_1 r) w)) (hAPP int int (hAPP int _let_0 _let_1 sa) v))) (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) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (minus_minus int))) (let ((_let_7 (hAPP int _let_0 _let_3 sa))) (let ((_let_8 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_3 (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit0 (hAPP int int bit1 pls))))) m)) (one_one int))) m1)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_8 v)) (hAPP int int _let_7 w))) m1)) _let_2))) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_6 (hAPP int int _let_8 w)) (hAPP int int _let_7 v))) _let_2))))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, (hAPP int int (abs_abs int) v), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( int, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) (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))) ) 23.83/23.86 ( int, (let ((_let_0 (fun int int))) (let ((_let_1 (plus_plus int))) (let ((_let_2 (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls))))) (let ((_let_3 (times_times int))) (let ((_let_4 (fun nat int))) (let ((_let_5 (power_power int))) (let ((_let_6 (hAPP int _let_0 _let_3 sa))) (let ((_let_7 (hAPP int _let_0 _let_3 r))) (hAPP int int (hAPP int _let_0 _let_1 (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int (hAPP int _let_0 _let_1 (hAPP int int _let_7 v)) (hAPP int int _let_6 w))) m1)) _let_2)) (hAPP nat int (hAPP int _let_4 _let_5 (hAPP int int (hAPP int _let_0 (minus_minus int) (hAPP int int _let_7 w)) (hAPP int int _let_6 v))) _let_2)))))))))), (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n))) (hAPP int nat (number_number_of nat) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( int, skv_3, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( int, (hAPP int int (abs_abs int) skv_14), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( int, (hAPP int int (abs_abs int) skv_20), (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( int, skv_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))) ) 23.83/23.86 ( real, pi, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( 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))))) ) 23.83/23.86 ( real, (let ((_let_0 (fun real real))) (let ((_let_1 (fun bool bool))) (let ((_let_2 (zero_zero real))) (let ((_let_3 (fun real bool))) (let ((_let_4 (ord_less_eq real))) (let ((_let_5 (fun real _let_3))) (let ((_let_6 (fun real _let_1))) (let ((_let_7 (fun _let_3 _let_3))) (let ((_let_8 (combs real bool bool))) (let ((_let_9 (hAPP (fun bool _let_1) (fun _let_3 _let_6) (combb bool _let_1 real) fconj))) (let ((_let_10 (combc real real bool))) (hAPP _let_3 real (the real) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 _let_4 _let_2))) (hAPP _let_3 _let_3 (hAPP _let_6 _let_7 _let_8 (hAPP _let_3 _let_6 _let_9 (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 _let_4) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (hAPP real _let_3 (hAPP _let_5 _let_5 _let_10 (hAPP _let_0 _let_5 (hAPP _let_5 (fun _let_0 _let_5) (combb real _let_3 real) (fequal real)) cos)) _let_2))))))))))))))), (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( 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)))) ) 23.83/23.86 ( complex, ii, ii ) 23.83/23.86 ( 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)) ) 23.83/23.86 ( complex, (hAPP real complex (of_real complex) pi), (hAPP int complex (number_number_of complex) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X $$unsorted)) (= (hAPP int int (abs_abs int) X) (hAPP int int (hAPP int (fun int int) (gcd_gcd int) X) X)) ) 23.83/23.86 ( v ) 23.83/23.86 ( w ) 23.83/23.86 ( skv_14 ) 23.83/23.86 ( skv_20 ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_a $$unsorted) (A_2 $$unsorted)) (let ((_let_0 (hAPP nat int (hAPP int (fun nat int) (power_power int) (hAPP int int (number_number_of int) min)) (hAPP (fun X_a bool) nat (finite_card X_a) A_2)))) (or (not (hBOOL (hAPP (fun X_a bool) bool (finite_finite_1 X_a) A_2))) (= (one_one int) (hAPP int int (hAPP int (fun int int) (times_times int) _let_0) _let_0)))) ) 23.83/23.86 ( nat, (let ((_let_0 (fun nat bool))) (hAPP _let_0 _let_0 (collect nat) prime)) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_a $$unsorted) (X_b $$unsorted) (BOUND_VARIABLE_165524 $$unsorted) (BOUND_VARIABLE_165525 $$unsorted) (BOUND_VARIABLE_165526 $$unsorted) (BOUND_VARIABLE_165527 $$unsorted)) (let ((_let_0 (fun X_b bool))) (let ((_let_1 (ord_less X_b))) (or (not (order X_a)) (not (order X_b)) (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) BOUND_VARIABLE_165526) BOUND_VARIABLE_165527))) (not (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_165524 BOUND_VARIABLE_165527)) BOUND_VARIABLE_165525))) (not (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (or (not (hBOOL (hAPP X_a bool (hAPP X_a (fun X_a bool) (ord_less_eq X_a) X_1) Y_1))) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 (ord_less_eq X_b) (hAPP X_a X_b BOUND_VARIABLE_165524 X_1)) (hAPP X_a X_b BOUND_VARIABLE_165524 Y_1)))) )) (hBOOL (hAPP X_b bool (hAPP X_b _let_0 _let_1 (hAPP X_a X_b BOUND_VARIABLE_165524 BOUND_VARIABLE_165526)) BOUND_VARIABLE_165525))))) ) 23.83/23.86 ( int, int, bit1, (zero_zero int), (zero_zero int), min ) 23.83/23.86 ( int, int, (uminus_uminus int), min, (zero_zero int), (one_one int) ) 23.83/23.86 ( int, int, bit0, (one_one int), min, pls ) 23.83/23.86 ( int, int, bit0, (let ((_let_0 (fun int int))) (hAPP int int (hAPP int _let_0 (plus_plus int) (hAPP int int (hAPP int _let_0 (times_times int) (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), pls ) 23.83/23.86 ( int, int, succ, (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)), min, min ) 23.83/23.86 ( real, nat, natfloor, n, (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))), (zero_zero real) ) 23.83/23.86 ( real, real, sin, pi, (zero_zero real), pi ) 23.83/23.86 ( real, real, sin, (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))), pi ) 23.83/23.86 ( 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)))), (zero_zero real), skv_10 ) 23.83/23.86 ( real, real, cos, (zero_zero real), skv_10, (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( real, real, (hAPP 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))) ) 23.83/23.86 ( real, real, (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 int real (number_number_of real) (hAPP int int bit0 (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)))) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) skv_1)))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$unsorted)) (let ((_let_0 (norm_norm complex))) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP complex real _let_0 (hAPP complex complex cnj X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) skv_2)))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (fun int int))) (let ((_let_1 (fun int bool))) (let ((_let_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 bit0 (hAPP int int bit1 pls))))) m)) (one_one int)))) (or (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less_eq int) (zero_zero int)) Y_1))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (hAPP int (fun int _let_1) zcong s1) Y_1) _let_2))) (not (hBOOL (hAPP int bool (hAPP int _let_1 (ord_less int) Y_1) _let_2))) (= (ti int Y_1) (ti int skv_4)))))) ) 23.83/23.86 ( pls ) 23.83/23.86 ( (one_one int) ) 23.83/23.86 ( min ) 23.83/23.86 ( (zero_zero int) ) 23.83/23.86 ( s ) 23.83/23.86 ( s1 ) 23.83/23.86 ( m ) 23.83/23.86 ( (hAPP int int (number_number_of int) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( (hAPP int int (hAPP int (fun int int) (plus_plus int) (one_one int)) (hAPP nat int (semiring_1_of_nat int) n)) ) 23.83/23.86 ( t ) 23.83/23.86 ( v ) 23.83/23.86 ( w ) 23.83/23.86 ( (hAPP int int (number_number_of int) (hAPP int int bit1 (hAPP int int bit1 pls))) ) 23.83/23.86 ( y ) 23.83/23.86 ( sa ) 23.83/23.86 ( x ) 23.83/23.86 ( r ) 23.83/23.86 ( m1 ) 23.83/23.86 ( skv_4 ) 23.83/23.86 ( skv_5 ) 23.83/23.86 ( skv_14 ) 23.83/23.86 ( skv_20 ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_8))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_9))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((Y_1 $$unsorted)) (let ((_let_0 (zero_zero real))) (let ((_let_1 (fun real bool))) (let ((_let_2 (ord_less_eq real))) (or (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 Y_1) (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))))) (not (= _let_0 (hAPP real real cos Y_1))) (not (hBOOL (hAPP real bool (hAPP real _let_1 _let_2 _let_0) Y_1))) (= Y_1 skv_10))))) ) 23.83/23.86 ( pi ) 23.83/23.86 ( (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls))) ) 23.83/23.86 ( (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)))) ) 23.83/23.86 ( (zero_zero real) ) 23.83/23.86 ( (hAPP real real sqrt (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( (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))))) ) 23.83/23.86 ( (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) ) 23.83/23.86 ( (hAPP real real cos (hAPP int real (number_number_of real) (hAPP int int bit0 (hAPP int int bit1 pls)))) ) 23.83/23.86 ( (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))))) ) 23.83/23.86 ( (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)))) ) 23.83/23.86 ( (let ((_let_0 (hAPP int int bit1 pls))) (let ((_let_1 (number_number_of real))) (let ((_let_2 (fun real real))) (hAPP real real (hAPP real _let_2 (times_times real) (hAPP real real (hAPP real _let_2 (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)))) ) 23.83/23.86 ( skv_10 ) 23.83/23.86 ( skv_11 ) 23.83/23.86 ( skv_15 ) 23.83/23.86 ( skv_18 ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real _let_0 X_1)) skv_11)))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real im X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_12))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_15))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$unsorted)) (hBOOL (hAPP real bool (hAPP real (fun real bool) (ord_less_eq real) (hAPP real real (norm_norm real) (hAPP complex real re X_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_17))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 (instantiation (forall ((X_1 $$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_1))) (hAPP real real (hAPP real (fun real real) (times_times real) (hAPP complex real (norm_norm complex) X_1)) skv_18))) ) 23.83/23.86 ( (zero_zero complex) ) 23.83/23.86 ( ii ) 23.83/23.86 ( (one_one complex) ) 23.83/23.86 ) 23.83/23.86 % SZS output end Proof for theBenchmark 23.98/23.89 EOF